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the last decade has seen the first instances of statistical studies with quasars using purely photometric samples . examples of these include the measurement of the integrated sachs wolfe effect @xcite and cosmic magnification bias @xcite , and studies of the clustering of quasars on large @xcite and small @xcite scales . the importance of photometrically classified quasar samples will only increase during the next decade as large new imaging surveys will uncover large samples of quasars at fainter magnitudes , with minimal spectroscopy for the faintest objects . while efficient photometric classification is one requirement to facilitate studies of quasars without extensive spectroscopy , it has also been crucial to develop accurate methods for quasar redshift estimation based on broadband photometry . techniques for photometric redshift estimation have long been successful for galaxies ( e.g. , * ? ? ? * ; * ? ? ? * ) and became feasible for quasars with the advent of precise multi - filter photometry @xcite . closely related to the quasar photometric - redshift problem  traditionally seen as a _ regression _ problem  is the question as to how best to perform photometric _ classification _ of quasars . it has become clear that the best classifiers are probabilistic in nature in that they calculate probabilities for objects to be quasars based on accurately calibrated models for stellar and quasar photometry ( e.g. , * ? ? ? * ; * ? ? ? these probabilities are often calculated for quasars in certain broad redshift ranges , and they therefore also act as low - resolution photometric redshifts for the objects they classify as quasars . the object classification technique of @xcite uses bins of width @xmath1 and , thus , achieves classification with a finer photometric - redshift estimate . however , detailed photometric redshift estimates for photometrically classified quasars utilize heterogeneous techniques , such that the resulting redshift probability distributions are inconsistent with the broad probabilities used for the initial quasar classification . for instance , this is the case for the photometric quasar catalogs of @xcite . for these catalogs , a non - parametric kernel - density - estimation ( kde ) technique that ignores photometric uncertainties was used to classify quasars , while a parametric model that convolves the quasar color locus with the photometric uncertainties  a single gaussian distribution in bins of redshift @xmath2was applied to estimate redshift @xcite .    for many purposes , one would like to target quasars in arbitrary redshift ranges that differ from those predetermined and imposed by a broad classification method . for example , the baryon oscillation spectroscopic survey ( _ boss _ ; @xcite ) of _ the sloan digital sky survey iii _ ( _ sdss - iii _ ) aims to measure the baryon acoustic feature in the ly@xmath3 forest of medium - redshift ( @xmath4 ) quasars ( e.g. , * ? ? ? * ; * ? ? ? the spectral range accessible to the _ boss _  spectrographs is @xmath5   ( barkhouser et al . , 2011 , in preparation ) , thus _ boss _  can only study the ly@xmath3 forest as traced by redshift @xmath6 quasars . therefore , _ boss _  requires quasars to be targeted based on their probability to be at redshift @xmath7 , and the _ boss _  quasar classifiers were trained with this constraint ( e.g. , * ? ? ? * ; * ? ? ? however , other ground - based instruments can observe at shorter wavelengths , e.g. , the multi - object double spectrograph for the large binocular telescope , which can observe the spectral range @xmath8   @xcite . this instrument could study the ly@xmath3 forest starting at redshift @xmath9 . an ly@xmath3 forest experiment designed for the large binocular telescope might therefore target quasars in the redshift range @xmath10 in addition to those at higher redshift . another example of a project that requires accurate photometric characterization of quasars is the search for binary quasars @xcite , where the key metric is the probability that two objects are both quasars _ and _ proximate in redshift , i.e. , the joint ( or `` overlapping '' ) probability that both components of a pair of objects are quasars of a particular redshift . similarly , the search for projected quasar pairs for absorption line studies @xcite requires the joint probability that both objects in a projected pair are quasars . such calculations require a full model of quasar probabilities and redshifts . ideally , therefore , photometric redshift estimation and quasar classification ought to be performed together .    in the specific case of objects observed using the @xmath0  filter system @xcite , quasar photometric redshifts are plagued by a host of degeneracies at redshifts where various quasar emission lines are mistaken for the ly@xmath3 line @xcite ; this results in `` catastrophic '' redshift failures , although consideration of the full redshift posterior distribution function ( pdf ) shows that most of these failures have a significant integrated probability around the correct redshift ( e.g. , @xcite ; see below ) . the addition of non-@xmath0  data , e.g. , ultraviolet ( uv ) and near - infrared ( nir ) measurements , can both alleviate these redshift degeneracies _ and _ improve quasar  star separation . quasar classification and characterization in the infrared has been considered for simulated objects and for quasar samples with a range of depths and areas ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the nir  is also the region to search for the highest redshift quasars ( redshift @xmath11 ; * ? ? ? these studies show the great promise that nir  data hold for quasar selection and redshift estimation . the uv  holds a similar potential ( see , e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the technique we introduce in this article , which we denote _ xdqsoz _ , is the first that deals with the simultaneous classification of quasars and assignation of quasar redshifts . this technique extends the _ xdqso _  quasar classification technique of @xcite to model the density of quasars in color  redshift space with a flexible semi - parametric model consisting of a large set of gaussian component distributions . this model can be integrated analytically over any redshift range to calculate probabilities from flux measurements for individual objects . this , in turn , allows quasar probabilities to be calculated over any redshift range . thus , a probability distribution in redshift space ( a `` pdf '' ) is a natural component of the model . because we use the _ extreme deconvolution _ ( xd ) technique @xcite as our density estimation tool , the method can be trained on and applied to low signal - to - noise ratio data , even with missing values , e.g. , to objects missing measurements in any arbitrary collection of filters . this feature allows us to naturally include uv  and nir  broadband fluxes , where sky coverages differ , as part of our model space and to distinguish sources that are missing data in a particular band from objects that are dropping out of that band . we show that the addition of uv  and nir  broadband fluxes improves quasar  star separation significantly and that it essentially breaks all of the redshift degeneracies inherent to the @xmath0  filter set . this article  is organized as follows . in section  [ sec : general ] , we discuss general aspects of photometric redshift estimation and classification in the context of quasars . we briefly describe the data used to train and test the new method in section  [ sec : data ] . section  [ sec : xdqsoz ] contains a full description of the _ xdqsoz _  quasar model and section  [ sec : targeting ] shows how this model is used to calculate quasar probabilities over arbitrary redshift ranges . section  [ sec : photoz ] assesses the performance of the photometric redshifts obtained using the _ xdqsoz _  model . a discussion of various extensions of the model is given in section  [ sec : discussion ] and we conclude in section  [ sec : conclusion ] . the  describes the photometric classification and redshift estimation _ xdqsoz _ code that is made publicly available .    in what follows , ab magnitudes @xcite are used throughout . where dereddened fluxes and magnitudes are required we have used the reddening maps of @xcite . all magnitudes and fluxes should be considered as dereddened unless mentioned otherwise . a technique for photometric redshift estimation of quasars should have the following properties . * it should provide full probability distributions for the redshift of the quasar based on its observed photometry , because this information has particular utility for quasars ( e.g. , * ? ? ? * ) as near - degeneracies in redshift estimation from broadband photometry are ubiquitous for quasars ( e.g. , * ? ? ? * ; * ? ? ? * ) . * upon the evaluation of the probability of the redshift the photometric uncertainties should be treated properly to allow photometric redshift estimation for faint objects . * if based on an empirical training set , the technique should be able to be trained on low signal - to - noise ratio data with potentially missing data . the training set and the evaluation set should also be allowed to have different noise properties , e.g. , different distributions of signal - to - noise ratio . for example , while the optical fluxes are mostly well measured for a spectroscopic training sample , the addition of uv  and nir  data can help break redshift degeneracies ( see below ) , but these measurements often have low signal - to - noise ratio , even for the training set . * the technique should allow an explicit redshift prior to be specified . the key to photometric classification and redshift estimation for quasars based on broadband fluxes is the joint probability of an object s fluxes , its redshift , and the proposition that it is a quasar @xmath12 . this joint probability can be re - written in several ways that correspond to different ways of approaching the problem @xmath13 photometric redshift estimation corresponds to the probability of an object s redshift conditioned on its fluxes and assuming that it is a quasar : @xmath14 quasar classification is the probability that an object is a quasar based on its fluxes . to classify quasars in a certain redshift range @xmath15 , we integrate the joint probability that the object is a quasar with redshift @xmath16 over redshift : @xmath17 the probability that an object is a quasar of any redshift is obtained by setting the redshift range @xmath18 $ ] . the normalization factor @xmath19 in this equation  is given by @xmath20 the probability of an object not being a quasar can be obtained empirically by modeling the fluxes of non - quasars ( see * ? ? ? * ; * ? ? ? the discussion above suggests that a unified approach to classification and photometric redshift estimation is possible . because the method described in this article  is the first technique in this class , we briefly discuss previous attempts at photometric redshift estimation and how they fit in the framework outlined in this section . the @xmath21-nearest neighbors approach of @xcite is an instance - based machine - learning technique that compares the colors of test objects to the @xmath21 nearest objects in color - space in a training set , and assigns a weighted combination of the redshifts of those nearest neighbors to the test object . its generalization to take observational flux - uncertainties into account involves perturbing both the test and the training data within their gaussian noise ellipsoids @xcite . in its noiseless implementation the method does not return a full probability distribution for the redshift . when taking the photometric uncertainties into account the technique essentially returns samples from @xmath22 as in equation  ( [ eq : jointprob3 ] ) , which can be binned to obtain the full posterior distribution function . while the photometric uncertainties of the test objects are handled correctly , the approach for dealing with the uncertainties of the training data effectively convolves with the uncertainties twice , as it adds scatter to the training data that are already scattered from the intrinsic distribution due to photometric noise . because the technique directly uses the training set , it also implicitly applies a redshift prior that approaches the _ observed _ redshift distribution . this choice of prior does not reflect the _ intrinsic _ redshift distribution , as the _ observed _ distribution is shaped by various selection effects @xcite .    the approach taken by @xcite consists of fitting the relative - flux  redshift distribution and its scatter to produce the likelihood of the quasar redshift as in equation  ( [ eq : jointprob1 ] ) . this fit is conducted without taking the flux uncertainties into account , but upon evaluation of test objects the flux uncertainties are fully handled . closest to the approach taken in this article  is the technique of @xcite . the distribution of colors in a set of narrow bins in redshift is fit as a single multi - variate gaussian distribution . this approach is similar to quasar classification approaches where the color or relative - flux distributions of quasars are fit in much broader redshift ranges using more general density models ( @xcite , @xcite ) . @xcite do not use the photometric uncertainties of the data they use for training . but , as in @xcite , photometric uncertainties for test objects are fully taken into account .    all of the techniques described above could be extended to allow quasar classification by specifying the necessary factors of @xmath23 or @xmath24 in equations  ( [ eq : jointprob1])([eq : jointprob3 ] ) . the latter could be taken from a quasar classification scheme such as nbc - kde @xcite or _ xdqso _ @xcite , although care should be taken that the classification method uses the same redshift prior as the photometric redshift technique for consistency . the _ xdqsoz _  technique introduced in this article  uses equation  ( [ eq : jointprob2 ] ) as the basis of both quasar classification and photometric redshift estimation . specifically , we model the relative - flux redshift distribution using a large number of gaussians by deconvolving this distribution for a training set using the xd  technique @xcite . we use empirical relative fluxes that are re - weighted using an explicit , magnitude - dependent redshift prior ( which can easily be divided out ) . as described in section  [ sec : targeting ] , conditioning on the fluxes to obtain full photometric probability distributions for the redshift , and marginalization over redshift to classify quasars , is simple and fast in this approach . because we deconvolve the relative - flux redshift distribution when training , we can straightforwardly incorporate uv  and nir  data , both of which significantly improve the accuracy and precision of the inferred redshifts . the sloan digital sky survey ( _ sdss _ ; @xcite ) has obtained _ u , g , r , i _ and _ z _ ccd imaging of @xmath25 10@xmath26 deg@xmath27 of the northern and southern galactic sky @xcite . _ sdss - iii _ @xcite has extended this area by approximately 2,500 deg@xmath27 in the southern galactic cap @xcite . all the data processing , including astrometry @xcite , source identification , deblending and photometry @xcite , and calibration @xcite are performed with automated _ sdss _  software . dr7 imaging observations were obtained over the period 2000 march to 2007 july . the _ sdss _  training data used here are essentially the same as the data used to train the _ xdqso _  method ; they are described in detail in @xcite . we use a sample of 103,601 spectroscopically - confirmed redshift @xmath28 quasars from the sdss dr7 quasar catalog @xcite . we use _ all _ of these quasars to essentially model the color  redshift relation for quasars ( but see below for the detailed description of our method ) . we combine the color redshift relation with an apparent - magnitude dependent redshift prior obtained by integrating a model for the quasar luminosity function over the apparent - magnitude range of interest @xcite . this prior for a few bins in apparent magnitude is shown in  [ fig : redshiftprior ] ; also shown is the difference between the @xcite redshift prior and the prior derived from the @xcite luminosity function . as the sample of quasars from the _ sdss _ dr7 quasar catalog spans a wide range in luminosity that we apply to a narrow range in apparent magnitude and that we extrapolate to largely unexplored faint flux levels , we are ignoring correlations between quasar spectral properties and luminosity ( e.g. , * ? ? ? * ; * ? ? ? * ) . these correlations mostly affect emission line shapes , such that they are washed out in broadband colors , especially compared to the intrinsic color - scatter . in addition to @xmath0  optical data , we use uv  data obtained by the _ galaxy evolution explorer _ space mission ( _ galex _ ; * ? ? ? _ galex _ has performed an all - sky imaging survey in two uv  bands ( fuv : 1350 to 1750  ; nuv : 1750 to 2750  ) down to @xmath29 and a medium - deep imaging survey that reaches @xmath30 ( e.g. , * ? ? ? * ) . some of the data used below to test the technique described in this article  comes from the medium - deep survey , while much of the data used to _ train _ our technique comes from the shallower all - sky survey ( because our training sample of quasars is drawn from the full @xmath31 deg@xmath27 _ sdss _  footprint ) , but this difference is largely offset by the fact that our training set is brighter than the faint part of the test set . _ galex _ gr5 observations were obtained between april 2003 and february 2009 .    rather than using _ catalog products @xcite we use measurements of the uv  fluxes obtained by force - photometering _ galex _  images ( from _ galex _  data release 5 ) at the _ sdss _  centroids @xcite , such that we obtain low signal - to - noise psf fluxes of objects not detected by _ galex_. as we show below , these low signal - to - noise ratio observations are essential for better classification of redshift @xmath32 quasars . we expect these measurements to be released as part of _ sdss _  data release 9 , scheduled for 2012 . the top panel of  [ fig : galexukidsssnr ] shows the distribution of signal - to - noise ratio for _ sdss _  quasars in the _ galex _  footprint . a total of 62,661 objects lie in the _ galex _  fuv  footprint , 63,372 lie in the nuv  footprint , and 62,628 are covered by both bandpasses . we also use nir  data to improve quasar classification and photometric redshift estimation . the _ ukirt infrared deep sky survey _ ( _ ukidss _ ) is defined in @xcite and consists of five survey components with different wavebands , depths and footprints . for the study in this paper we use data from the _ ukidss _  _ large area survey _ ( _ las _ ) . technical details about the _ ukidss _  _ las _  observing strategy are described in @xcite . the _ ukidss _  _ las _  aims to cover 4,000 deg@xmath27 of the sdss footprint in the y , j , h and k wavebands . in this paper we use data from _ ukidss _  _ las _  dr7 which includes observations obtained between may 2005 and july 2009 inclusive . the _ ukidss _ _  dr7 overlaps the _ _  imaging footprint over @xmath25 2500 deg@xmath27 and has median point source 5-sigma ab magnitude limits in y , j , h and k of 20.9 , 20.6 , 20.2 , and 20.2 , respectively . the _ ukidss _  data are acquired with the ukirt wide field camera ( wfcam ; @xcite ) . the _ ukidss _ photometric system is described in @xcite , and the calibration is described in @xcite . the pipeline processing and science archive are described in m. j. irwin et al . ( 2012 , in preparation ) and @xcite .    as in the case of the _ galex _  data described in section  [ sec : galexdata ] , we use force - photometered nir  fluxes at _ sdss _  positions rather than _ ukidss _  catalog data . this `` list - driven '' information is derived from aperture photometry on data release 7 of the _ ukidss _  _ las_. we choose an aperture radius of 1 arcsec . of the 103,601 quasars in the _ sdss _ dr7 quasar sample , 29,726 lie within the _ ukidss _ dr7 k - band footprint . approximately 22,000 of these quasars are detected in the k band with also overlapping coverage in all four observed wavebands ( y , j , h and k ) in the _ ukidss _  _ las _ dr7 source catalog . the bottom panel of  [ fig : galexukidsssnr ] shows the distribution of signal - to - noise ratio in the nir  for quasars in our training sample . unlike for _ sdss _  imaging , measurements in all four filters of the _ ukidss _  survey are not obtained during the same observing run h and k observations are performed in the same observing block , while y and j are conducted separately . thus the sky coverage in different _ ukidss _  bands varies , and many objects are missing data in one or more of the four bands . the breakdown of training quasars with observations in the nir  by bandpass is : y : 26,876 ; j : 27,328 ; h : 28,911 ; k:29,726 . a total of 25,510 objects have measurements in all four bandpasses . the differing epochs of the _ ukidss _ , _ galex _ , and _ sdss _  can range up to 9 years in the observed frame . for a quasar with a redshift of 2 this is 3 years in the rest frame . the observed optical variability in radio quiet quasars over the rest frame 2 to 5 year timescale is observed to be in the range 0.1 - 0.2 mag and is a function of absolute magnitude @xcite . @xcite find that the variability amplitude decreases with rest - frame wavelength by a factor of two between 1500  and 6000  with an amplitude of @xmath25 0.15 mag at 6000  ( see also @xcite ) . @xcite have studied the mid-_ir _ variability using multi - epoch spitzer observations of a sample of @xmath25 1000 active galactic nuclei and find that the rest - frame j band variability amplitude in the rest - frame timescale is @xmath25 0.1 mag . in summary the quasars in this study are expected to vary by @xmath25 0.3 and 0.1 magnitudes in the uv  and nir , respectively , over the elapsed period of the observations and this is less than the average photometric errors in the individual wavebands and significantly less than the range in colors . the photometric redshift technique _ xdqsoz _  is an adaptation of the _ xdqso _  technique @xcite to include redshift explicitly in the model for the quasar population . _  achieves this by modeling the @xmath33 factor in equation  ( [ eq : jointprob2 ] ) , where the _ xdqso _  technique modeled @xmath34 in three bins in redshift ( corresponding to low- , medium- , and high - redshift quasars ) . as discussed in section  [ sec : general ] , this approach allows us to obtain full posterior distribution functions for the redshift of a photometrically classified quasar based on its broadband fluxes . integrating this redshift probability distribution over a range of redshifts and properly normalizing this result using equation  ( [ eq : normalization ] ) gives a photometric quasar probability in the chosen redshift range that is , as we show below , competitive with the best available photometric quasar classification techniques , e.g. , _ xdqso_.    to estimate the density of quasars in flux  redshift space we use _ _ extreme deconvolution _ _ @xcite . as described in section  [ sec : data ] , our training set consists of the _ sdss _  dr7 quasar sample , which consists mostly of bright , viz . , dereddened @xmath35 mag ( @xmath36 mag for @xmath37 sources ) , objects with small photometric uncertainties . the _ galex _  and _ ukidss _  data described in sections  [ sec : galexdata ] and [ sec : ukidssdata ] are much shallower than the _ sdss _ data and many objects are not detected at high significance in these surveys , such that photometric uncertainties are not insignificant ( see  [ fig : galexukidsssnr ] ) . additional complications are that these two supplemental surveys have not observed the full _ sdss _  footprint and that the _ ukidss _  _ las _  footprint is different for the different nir  bands , such that we have heterogeneous missing data and heteroscedastic uncertainties . xd  is uniquely suited to deal with these complications in the proper probabilistic manner . xd  assumes that the flux uncertainties are known and that they are close to gaussian , as is the case for psf fluxes for point - sources in _ sdss _  @xcite . we assume that the spectroscopic redshifts have vanishing uncertainties because their typical value of @xmath38 @xcite is orders of magnitude smaller than typical uncertainties in broadband photometric redshifts , which are set by the width of the quasar locus . xd  models the underlying , deconvolved distribution as a sum of @xmath39 @xmath40-dimensional gaussian distributions , where @xmath39 is a free parameter that is set using an external objective ( see section  [ sec : modelconstruction ] ) . xd  consists of a fast and robust algorithm to estimate the best - fit parameters of the gaussian mixture . the full quasar - density model is constructed by fitting the flux redshift density of quasars in a number of bins in the @xmath41-band  magnitude . as we use the same set of quasars in each bin with a different redshift prior  see the discussion in section  [ sec : data]we could instead have fit a single bin , e.g. , the brightest . the other bins could have been constructed by dividing out the redshift prior of the first bin and multiplying in the redshift priors for the fainter bins . however , as we will show below , the advantage of a gaussian representation of the flux redshift density is that it allows integrals of this density over arbitrary redshift ranges to be calculated analytically . this leads to fast quasar - probability estimation . if we were instead to divide out the redshift prior and multiply in a different redshift prior , the resulting function would no longer be gaussian and the numerical integration over redshift would be much more computationally expensive . because our short - term objective is to run this algorithm on essentially all of the @xmath42 _ sdss _  point sources and in the future on the @xmath43 pb of _ lsst _  catalog data @xcite , this computational advantage is important . after fitting the first bin , all other fits are initialized using the previous bin s optimal solution ; these extra fits all converge very quickly as the quasar flux redshift density does not vary strongly with apparent magnitude . the redshift prior is shown for a few bins in apparent magnitude in  [ fig : redshiftprior ] . if a different redshift prior is desired , one can divide out this prior and multiply in a new prior ( these priors are included in the code release described in the ) . for example , if one would prefer to use the @xcite model for the quasar luminosity function , one would multiply the posterior distribution function for the redshift obtained using the fiducial @xcite prior with the factor shown in the bottom panel of  [ fig : redshiftprior ] . this panel shows the ratio of the @xcite redshift prior to the @xcite prior in a number of apparent - magnitude bin . it is clear that there is only a significant difference at relatively large redshift and at faint magnitudes , where constraints on the luminosity function are sparse .    as for the _ xdqso _  technique , we divide the quasar - density model into a factor describing , essentially , the color redshift density of quasars but we again use relative fluxes rather than colors  and another factor describing the apparent - magnitude distribution of quasars . we adopted this approach because the flux density of quasars has a dominant power - law shape corresponding to the number counts as a function of apparent magnitude , while the color distribution is much flatter . we write @xmath44 the apparent - magnitude factor does not depend on redshift . so , this factor is the same as used in the _ xdqso _  method . the factor is calculated by the sum of the apparent - magnitude priors in  1 of @xcite weighted by the quasar densities in  1 of the same article . as quasar redshifts are always positive , we model the logarithm of the redshift . since our training sample consists of point - like objects at redshift @xmath45 , about all at @xmath46 , our model should only be trusted to return reasonable densities within this range .    in each bin we model the @xmath40-dimensional relative - flux redshift density , where @xmath40 is the number of independent colors plus one ( for redshift ) , of quasars using 60 gaussians that are allowed to have arbitrary means , variance matrices , and amplitudes  the amplitudes are constrained to sum to one . we use the full set of 103,601 , @xmath47 quasars to train the final model , but in order to test whether we are under- or overfitting the data we performed a cross - validation test . to cross - validate we extract a random subset containing 10percent of the full sample to use as an independent test data set . by training the model on the remaining 90percent of the sample we can select the number of gaussians that optimally predicts  i.e . , predicts with the highest probability  the redshifts of objects in the test sample . the results from this procedure are shown in  [ fig : testloglike ] . our ability to better predict the test redshifts saturates around @xmath48 ; we chose 60 gaussians to represent the relative - flux density of quasars . compared to the _ xdqso _  method , which used 20 gaussians each in three redshift bins , this revised approach uses the same number of gaussians while representing an extra dimension ( redshift ) . one might be concerned that because the gaussians will preferentially be found in high - density , viz . , low - redshift , regions , the density of medium- and high - redshift quasars is not adequately described in the _ xdqsoz _  model . we will see below that this is not the case and that _ xdqsoz _  performs similarly to _ xdqso _  in selecting medium- and high - redshift quasars . the full model consists of 47  bins of width 0.2  mag between @xmath49 and @xmath50 , spaced 0.1  mag apart ( adjacent bins overlap ) . as described above , the xd  fits for all but the brightest bin are initialized using the best - fit parameters for the previous bin . each bin uses the full set of 103,601 redshift @xmath51 quasars .    in each of 47 bins we fit 60 @xmath52-dimensional gaussians , yielding a total of @xmath53 - 1)$ ] parameters . the @xmath0-only model has 59,173 parameters , the model that also uses the two uv  bands has 101,473 parameters , the model that adds the four nir  bands to the optical fluxes has 155,053 parameters , and the full uv-@xmath0-nir  11-dimensional model has 219,913 parameters . to obtain the total number of parameters for photometrically classifying quasars using _ xdqsoz _ , we need to add the number of parameters describing the stellar relative - flux density in 47 bins  from the _ xdqso _  method  to this number , amounting to 14,053 , 26,273 , 42,253 , and 61,993 parameters for the @xmath0 , @xmath0+uv , @xmath0+nir , and @xmath0+uv+nir  models , respectively . models including uv  or nir  data are trained using any available data , i.e. , any object with a measured flux in any of the bandpasses is included in the training set .      in this section , we assess the performance of the xd  technique for modeling the relative - flux  redshift distribution of quasars , and provide examples which demonstrate that the xd  technique produces excellent fits to the data . we demonstrate that the xd  method does an excellent job of empirically calibrating the color redshift relation ; the ability of the xd  technique to model the relative - flux density of quasars in the current _ xdqsoz _  context is excellent as well , but it is very similar to the performance in the _ xdqso _  context and we refer the reader to @xcite for a discussion of this performance .    [ fig : allzexfit ] shows relative - flux  redshift and color  redshift diagrams of quasars for a single @xmath41-band  magnitude bin . the conditional distribution of relative - flux as a function of redshift is shown here ( although the model contains a full model of the density on this manifold ) ; this emphasizes what is new in _ xdqsoz _  as compared to _ we see that the xd  technique is superb at capturing the complexity of the quasar color locus , even at higher redshifts where the data are sparse and noisy . the locations where prominent emission lines cross the relevant _ sdss _  filters are indicated , and it is clear that this drives much of the structure in the color redshift relation . [ fig : allzexfitgalex ] shows similar relative - flux redshift diagrams for the uv  fluxes in the model containing both optical and uv  data . the agreement between the empirical model and the data is excellent . these diagrams clearly demonstrate that the uv  flux of @xmath54 and @xmath55 quasars , for fuv  and nuv  respectively , is suppressed because of absorption below the lyman limit ( @xmath56  ) by intervening systems @xcite . uv  observations are an excellent tool to distinguish @xmath57 quasars from @xmath58 quasars , which have degenerate @xmath0  colors and plague medium - redshift quasar selection ( e.g. , * ? ? ? * ) , even at low uv  signal - to - noise ratio . [ fig : allzexfitukidss ] presents relative - flux  redshift diagrams for the four nir  fluxes in the _ xdqsoz _  model that contains optical and nir  data . the agreement between the _ xdqsoz _  model and the data is again excellent and the _ xdqsoz _  model captures all of the photometric redshift information contained in the nir . we see that much of the variation in the color redshift relation in the nir  is driven by the h@xmath3 line ( see also * ? ? ? * ; * ? ? ? * ) .    the model  data comparisons given in this section are only a small fraction of the model - assessment diagnostics that we performed . for example , we do not show the optical fits here in models that contain uv  or nir  data , nor do we show the uv  models and nir  models in the full @xmath0-uv+nir  model , as all of these comparisons are very similar to the ones shown here . we can use the _ xdqsoz _  model to photometrically classify and target quasars by calculating the probability that an object is a quasar based on its broadband fluxes . the probability that an object is a quasar in a redshift range @xmath15 is obtained by integrating the probability that an object is a redshift @xmath16 quasar over redshift . we start by using equation  ( [ eq : quasardeltazprob ] ) @xmath59 where @xmath60 is the set of fluxes relative to @xmath61 and @xmath61 is the @xmath41-band  flux of the object . the normalization factor is given by @xmath62 because the apparent magnitude factor @xmath63 does not depend on redshift , the integral over redshift is only over the @xmath64 factor , which is modeled as a simple sum of gaussian distributions .    for any given object we can simplify the mixture of @xmath52-dimensional gaussian distributions to a mixture of one - dimensional gaussian distributions for the redshift of the object . first , we find the bin in the @xmath41-band  magnitude that best matches the object s @xmath41-band  magnitude and use the mixture - of - gaussians representation of the relative - flux  redshift density in this bin . assuming that the @xmath52-dimensional mixture of gaussians has amplitudes @xmath65 , means @xmath66 , and variance matrices @xmath67 , we can condition each of the components on the measured relative flux @xmath68 of the object and its uncertainty variance matrix @xmath69 to find ( e.g. ,  b of @xcite ) @xmath70 while the amplitudes of these one - dimensional gaussian distributions are given by the posterior probability that the object was drawn from component @xmath21 @xmath71 in these expressions @xmath72 and @xmath73 are the relative flux and the redshift parts of @xmath66 , respectively ; @xmath74 ; @xmath75 , @xmath76 , and @xmath77 are the relative - flux  relative - flux , redshift  relative - flux , and redshift  redshift parts of @xmath67 , respectively ; and @xmath78 is the multivariate gaussian distribution . @xmath79 includes the uncertainty variance matrix @xmath69 because the necessary uncertainty convolution simply reduces to adding the observational uncertainty variance matrix to the intrinsic variance matrix for each gaussian component .    integrating this one - dimensional mixture of gaussian distributions over an arbitrary redshift range results in a sum over error functions . remembering that our model lives in @xmath80 redshift space @xmath81-\mathrm{erf}\left[\frac{\log z_{\mathrm{min } } - m_{z , k}}{\sqrt{2}\,\sigma_{z , k}}\right]\right)\ , , \end{split}\ ] ] where the error function erf@xmath82 \equiv 2 \int_0^x e^{-t^2}{\mathrm{d}}t\,/\sqrt{\pi}$ ] . the first factor on the right - hand side of this equation  is the integral over the entire redshift range @xmath83 $ ] , which simplifies to @xmath84 i.e. , the denominator in equation  ( [ eq : alphazk ] ) . we can compare the quasar probabilities obtained by integrating the _ xdqsoz _  model over redshift to those from the _ xdqso _  technique , which models the distribution of quasar fluxes in three wide redshift bins . [ fig : xdqsovsxdqsoz ] shows the probabilities that 490,793 objects are medium - redshift ( @xmath85 ) quasars obtained by the two methods for objects in the _ sdss _  imaging stripe 82 . it is clear that most of the objects cluster tightly around the one - to - one line and that the two models are essentially the same for this redshift range . [ fig : xdqsovsxdqsozefficiency ] shows the efficiency of quasar targeting using both the _ xdqso _  and the _ xdqsoz _  method for targeting medium - redshift ( @xmath85 ) quasars . this test uses a sample of medium - redshift quasars spectroscopically confirmed by _ boss_which also re - targets quasars previously identified in earlier surveys  in stripe 82 . this quasar sample is expected to be highly complete , because it was targeted using the superior imaging in stripe 82 where there is variability information @xcite and where a number of campaigns prior to _ boss _  have also obtained extensive spectroscopy . the sample has on average of 30 @xmath86 quasars deg@xmath87 down to @xmath88 mag , which is close to the number expected from current quasar luminosity functions ( e.g. , * ? ? ? we only use regions of stripe 82 that have more than 15 @xmath86 quasars deg@xmath87 . see @xcite and @xcite for a more detailed description of the _ boss _ quasar target selection in general and this test set in particular . the top panel of  [ fig : xdqsovsxdqsozefficiency ] shows selection based on _ sdss _ @xmath0  fluxes alone . we see that the performance of the _ xdqsoz _  and the _ xdqso _ techniques is essentially identical . the lower panels of this figure show how the selection improves when we add _ galex _  uv  and _ ukidss _  _ las _  nir  observations , both of which are available for essentially all objects in _ sdss _  stripe 82 . the _ xdqso _ models with uv  and nir  data are models trained with these uv  and nir  fluxes in the broad redshift ranges used by _ xdqso_. for all intended purposes the _ xdqsoz _  technique performs identically to the _ xdqso _  technique for targeting medium - redshift quasars . we have also checked the performance of the _ xdqsoz _  technique as compared to the kernel - density - estimation based photometric quasar classification technique of @xcite . we find results that are similar to those for the _ xdqso _  technique as shown in  3 of @xcite : at low and medium redshift the _ xdqsoz _  technique performs slightly better than the _ xdqso _  technique ( and thus better than the kde technique ) , while at high - redshift ( @xmath89 ) _ xdqsoz _  performs slightly worse than _ xdqso_. this behavior is expected because the quasar training data do not include much data at high redshift . we thus do not probe the color redshift relation at high redshift as well as the kde approach , which included additional high - redshift data . because we use the same stellar model as _ xdqso _ , the same problem with sampling regions of low stellar density that we encountered for _ xdqso _  persists for _ xdqsoz_.    in summary , the _ xdqsoz _  technique performs almost identically to the _ xdqso _  method for photometrically classifying objects as quasars  and thus for quasar targeting . _ xdqsoz _  has the advantage over _ xdqso _  and any other photometric quasar classification scheme that it can classify quasars in arbitrary redshift ranges `` on the fly '' ( i.e. , without retraining the model ) . we have computed _ xdqsoz _  quasar probabilities for all 160,904,060 point sources with dereddened @xmath41-band  magnitude between 17.75 and 22.45 mag in the 14,555 deg@xmath27 of imaging from sdss data release 8 @xcite in three redshift ranges ( 0.3 @xmath90 , @xmath91 , and @xmath37 ) . [ fig : xdqsoz_imag ] shows the apparent @xmath41-band magnitude distribution of all of the objects with @xmath92 mag in the expected _ boss _  spectroscopic footprint @xcite with _ probability larger than 0.5 over the specified redshift range . these apparent - magnitude distributions are smooth and well - behaved for low and medium redshifts . they also agree at the bright end with number counts derived from spectroscopic observations @xcite . at the faint end ( @xmath93 ) the @xmath41-band  number counts start to decline due to increasing photometric uncertainties and incompleteness of the _ sdss _  imaging near the faint limit of _ sdss_.    the _ boss _  aims to detect the baryon acoustic feature ( baf ) in the ly@xmath3 forest of background redshift @xmath86 quasars . not all quasars contribute equally to this measurement and , as shown by @xcite and @xcite , both brighter quasars and quasars near redshift @xmath94 are the most valuable . combining ly@xmath3 baf  weights with the quasar probabilities as a function of redshift produced by _ xdqsoz _ , we can calculate the expected value of a quasar for the ly@xmath3 baf  measurement . defining a value function @xmath95 , where @xmath96 is the dereddened @xmath96-band magnitude of the object , the expected value of an object is @xmath97 by targeting objects with the highest expected value for a particular ly@xmath3 baf  survey  which is dependent on the exact observational characteristics of that survey we could optimize the targeting of quasars for that baf  measurement . the top panel of  [ fig : xdqsozvsvalue ] shows the number of medium - redshift quasars found by applying this value - based targeting for _ boss _  using the value function of @xcite . value - based targeting finds about 1 quasar deg@xmath87 less than targeting based on the ranked medium - quasar probability list . the bottom panel shows that value - based targeting finds as much value as the straight probability - based targeting but not more  such that the baf  measurement based on both samples should be equally precise . straight probability - based targeting thus finds the same value while assembling a larger overall quasar sample . in addition , value - based targeting optimizes one experiment in a specific survey , whereas straight probability - based targeting returns information that is broadly applicable to a range of experiments and a range of surveys . thus , in general , there is little to be gained from pursuing value - based targeting for _ boss_.    to investigate whether the _ xdqsoz _  quasar selection technique is limited by contamination from galaxies that appear point - like at the faint flux levels to which we push quasar classification , we look at the fraction of objects that appear point - like in a single _ sdss_imaging - pass but are extended in co - added data on _ sdss _  imaging stripe 82 . we match the point sources in a typical _ sdss _  imaging run to the co - added galaxy catalog on stripe 82 @xcite and assess the fraction of point sources that are extended in the co - added data as a function of the @xmath41-band magnitude . this is shown in the top panel of  [ fig : pointgals ] . we see that the fraction of point sources that are extended in the co - added imaging is only a few percent at relatively bright magnitudes , but almost reaches 50percent at @xmath98 mag . to assess whether these point - like galaxies are a significant contaminant for the _ xdqsoz _  quasar selection , we calculate their quasar probabilities ( over all redshifts ) . the fraction of point - like sources that are extended in the co - added imaging and that have quasar probabilities larger than 0.5 is shown as a function of the @xmath41-band magnitude in the lower panel of  [ fig : pointgals ] . for comparison , the fraction of all point sources with quasar probability larger than 0.5 is shown as the dashed curve . point - like galaxies make up only a small ( @xmath99percent ) fraction of _ xdqsoz_-selected photometric quasars . however , because galaxies unlike stars cluster similarly to quasars , even this small contamination fraction might significantly degrade precision quasar - clustering measurements without improved star galaxy separation or proper modeling . given the rising fraction of point - like galaxies with increasing magnitude in the top panel of  [ fig : pointgals ] , point - like galaxies are likely to be the major contaminant for quasar selection at @xmath100 mag . we can use the _ xdqsoz _  flux  redshift density model to derive full posterior probability distributions for the redshift of photometric quasars taking the photometric uncertainties of the object fully into account . because the main advantages of the _ xdqsoz _  technique for photometric redshift estimation are that it a ) returns full pdfs and b ) allows auxiliary data such as that furnished by uv  and nir  surveys to be included , we focus on those points here . @xmath0-only photometric quasar redshifts suffer from various degeneracies that are inherent to the @xmath0  filter system . while including appropriate apparent - magnitude dependent redshift priors  as we do here  can partially relieve these degeneracies somewhat , no photometric redshift technique can entirely remove these degeneracies and _ xdqsoz _  is no exception ( as we will see below ) . crucially , even low signal - to - noise ratio uv  and nir  data _ can _ cleanly resolve these degeneracies .    for each object the posterior probability distribution for its redshift , based on its measured broadband fluxes , is calculated by finding the apparent - magnitude bin that best matches the object s dereddened @xmath41-band  magnitude . the posterior probability distribution is given by the mixture of 60 one - dimensional gaussian distributions , with means , variances , and amplitudes given in equation  ( [ eq : means ] ) , ( [ eq : vars ] ) , and ( [ eq : alphazk ] ) , respectively . this posterior probability distribution can be calculated based on @xmath0  fluxes , or with additional uv  or nir  information if available . we show four examples of such redshift pdfs in  [ fig : predictdr7qso ] for objects from the _ sdss _  dr7 quasar catalog that have measurements in all of the uv  and nir  filters . these objects are from the sample used to train the flux redshift quasar model , but , as we discuss in more detail below , we nevertheless believe that they provide an adequate representation of the performance of the _ xdqsoz _  technique . these objects are chosen to demonstrate the power and weaknesses of the @xmath0 , uv , and nir  data for photometric redshift estimation , and are therefore not a random subset of the data . we discuss the overall performance below . the top left panel shows an example where the @xmath0  fluxes suffice to accurately and precisely measure the redshift , and how the ( relatively high signal - to - noise ratio ) uv  and nir  measurements tighten the pdf significantly . the top right panel shows an example where the extremely low uv  flux basically vetoes the low - redshift peak that is present in the @xmath0-only redshift pdf . if one were to use a simple non - detection _ galex _ catalog at 5@xmath101 this result would not have been clear , because this object could have had the mean @xmath57 uv  flux and still not be detected by _ galex_. the ability of the _ xdqsoz _  technique to use and interpret low signal - to - noise ratio data is therefore crucial in this example . a weakness of the auxiliary uv  data is apparent in the lower left panel . here we see a @xmath102 quasar that is much brighter than the average quasar at this redshift in the uv , such that the addition of the uv  data mistakenly chooses the low - redshift peak of the degenerate @xmath0  redshift pdf . however , the nir  data are able to overcome this error and the addition of all the data confidently assigns this object a close - to - correct redshift . the lower right panel of  [ fig : predictdr7qso ] shows another amusing example . in addition to testing the _ xdqsoz _  technique using the _ sdss _  dr7 quasar sample , we have also drawn a sample of quasars located in the _ sdss _  imaging in stripe 82 discovered as part of the _ 2slaq _  survey @xcite and _ boss _  @xcite . these quasars are generally fainter than the _ sdss _  quasars and therefore they represent a stringent , independent test of the _ xdqsoz _  technique s ability to return accurate redshift pdfs at faint magnitudes . we have specifically selected all @xmath103 quasars with dereddened @xmath104 mag from the _ 2slaq _  sample and all quasars on the _ sdss _  imaging stripe 82 newly discovered by _ boss _  and use their single - pass _ sdss _  photometry . because most of these objects lie in the _ sdss _  equatorial stripe , many of them have measurements from _ galex _  and _ ukidss _  _ las_.    [ fig : predict2slaqboss ] shows posterior probability distributions for the redshift of two objects from the _ 2slaq _  catalog and two from the _ boss _  sample . the trends that were apparent for the _ sdss _ dr7 quasars in  [ fig : predictdr7qso ] are also evident for these fainter objects . the uv  and nir  fluxes for these objects have , in general , been measured much less precisely than those discussed above , but the auxiliary data still provide valuable extra information about the redshift .    while most of the examples in s  [ fig : predictdr7qso ] and [ fig : predict2slaqboss ] have a considerable posterior probability mass associated with the correct redshift , even when multiple peaks are present in the redshift pdf , this situation is generic  in that inspections of many redshift pdfs show that it is rare to have no posterior probability mass associated with the spectroscopic redshift .    as a simple statistic for the degeneracy in the redshift pdf we examine the number of distinct peaks as a function of redshift . a single peak in the pdf is defined here as the widest contiguous region where the pdf is above the uniform distribution between redshift 0.3 and 5.5 ( i.e. , flat in redshift ) . the top panel of  [ fig : peaks ] shows the average number of such peaks as a function of redshift . this statistic clearly shows the main degeneracies of @xmath0-based photometric quasar redshifts . basically the entire @xmath105 region , a region around @xmath106 , and the @xmath107 redshift range are degenerate . higher redshift quasars are readily identified as such using the @xmath0  colors ( e.g. , * ? ? ? * ) . from the lower panels we see that the addition of uv  and nir  data softens all of these degeneracies . essentially no degeneracies remain using the combination of all the uv , optical , and nir  data ( lower panel of  [ fig : peaks ] ) . additionally , requiring that distinct peaks in the photometric - redshift pdf need to have a minimum integrated probability ( e.g. , defining a peak as a contiguous region above the uniform distribution with @xmath108 integrated redshift probability ) gives similar results for the number of peaks and the improvement when adding uv  and nir  data . [ fig : zspeczphotdr7qso ] shows the traditional spectroscopic - redshift vs. photometric - redshift diagram for quasars in the _ sdss _ dr7 quasar sample , for various combinations of wavelength regimes . the right panels restrict the sample to those objects for which the redshift pdf has only a single peak and as such can be accurately described by a single photometric redshift ( plus uncertainty ) . in the top left panel all of the @xmath0-related degeneracies are clearly present and the right panel shows that by restricting the sample to single - peaked pdfs most of these degeneracies vanish , albeit at the cost of entire redshift ranges  most notably redshift - range @xmath109 quasars . the addition of uv  and especially that of nir  observations a ) greatly reduces the degeneracies as witnessed by the diminishing structure in the spectroscopic vs. photometric redshift plane and the increasing fraction of objects with a single peaked redshift pdf , and b ) significantly reduces the scatter . in the individual panels we report the number of 4@xmath101 outliers rather than the number of @xmath110 objects ; the latter number is somewhat meaningless without comparing it to the scatter , but to guide the eye we have included the @xmath111 lines . the scatter is calculated without outlier - rejection . we note that  here and in the test below the distribution of the @xmath41-band  magnitude is unchanged when restricting the sample to objects with measured _ galex _  or _ ukidss _  fluxes ; restricting to objects with nir  fluxes actually creates a fainter sample , because many faint quasars in the _ sdss _  imaging stripe 82 have been observed by _ ukidss _  _ las _ , while many brighter quasars are located outside of the _ ukidss _  _ las _  footprint .    with the addition of uv  and nir  data most objects have accurate and precise single - peaked photometric redshifts over the entire @xmath112 redshift range : 97percent of all objects with uv  and nir  data and 99percent of the subset with single - peaked redshift pdfs have photometric redshifts within @xmath113 ; for @xmath114 these numbers are 84percent and 86percent respectively . this is a significant improvement over @xmath0-only photometric redshifts , where we find 86percent of objects within @xmath113 . similarly , @xcite found 83percent of objects in this range . photometric and spectroscopic redshifts in  [ fig : zspeczphotdr7qso ] are compared for objects in the sample used to train the _ xdqsoz _  technique . as such , one might object that this is not a fair representation of the performance of the _ xdqsoz _  technique . but , the relationship between the photometrically estimated redshift pdf and the spectroscopic redshift of a training object for _ xdqsoz _  is through the many - parameter flux  redshift density model . this model includes reweighting objects in the training set according to a redshift prior . there is therefore no direct connection between output photometric redshifts and input spectroscopic redshifts as there is , for example , in nearest - neighbor approaches to photometric redshift estimation ( @xcite ) . the fact that  [ fig : zspeczphotdr7qso ] contains all of the expected redshift degeneracies for @xmath0-based photometric redshifts is further proof of this independence : if there were a dependent connection we would not suffer from these degeneracies .    to further test this issue we have divided our sample into a 90percent training sample and a 10percent test sample , as described above in section  [ sec : modelconstruction ] . we redo the spectroscopic - redshift vs.  photometric - redshift comparison for the 10percent sample using the model trained in the 90percent of remaining data the results are in  [ fig : zspeczphottestqso ] . because the 10percent sample is much smaller than the full _ sdss _ dr7 quasar sample the statistics are noisier , but the trends are the same as in  [ fig : zspeczphotdr7qso ] .    to test the _ xdqsoz _ technique at fainter magnitudes , in  [ fig : zspeczphot2slaqboss ] we compare spectroscopic redshifts to photometric redshifts for @xmath115 objects in the _ sdss _ dr7 quasar catalog and for objects in the combined _ 2slaq _  and _ boss _  sample . the trends in this figure are the same as those for the brighter _ sdss _  quasar sample and the scatter is somewhat larger ; however , the photometric redshifts remain clustered around the spectroscopic redshifts with no discernible bias . even for the faint _ 2slaq _  and _ boss _  sample , the addition of low signal - to - noise ratio uv  and nir  data leads to a significant increase in accuracy and precision .    using the technique described in this section we have computed photometric redshifts for all point sources in the expected _ boss_spectroscopic footprint with _ xdqsoz _ quasar probabilities larger than 0.5 and @xmath116 mag . the distribution of peaks of the photometric - redshift distribution for these objects is shown in  [ fig : xdqsoz_redshift ] in a few apparent - magnitude bins ( those bins from  [ fig : redshiftprior ] that lie within the @xmath116 apparent - magnitude range . the overall shape of the redshift distribution in each @xmath41-band bin is similar to the redshift prior calculated from the @xcite luminosity - function model . however , the redshift - dependent efficiency of photometric quasar classification and redshift estimation is apparent in this comparison and the low classification efficiency at @xmath117 depresses the distribution in that range while increasing the significance of the @xmath118 peak . all of the results in this section have assumed the @xcite redshift prior , shown in  [ fig : redshiftprior ] . using the difference between the hopkins , richards , & hernquist ( 2007 ) and @xcite redshift prior , given in the bottom panel of  [ fig : redshiftprior ] , we can assess the difference in photometric redshift distribution when using these two alternatives to the quasar luminosity function . the bottom panel of  [ fig : redshiftprior ] shows that the only significant difference between these two models is at relatively high redshift ( @xmath119 ) and near the _ sdss _  detection limit ( @xmath93 mag ) . strongly single - peaked photometric redshift distribution functions , such as many of those shown in s  [ fig : predictdr7qso ] and [ fig : predict2slaqboss ] , are not affected by even order - of - magnitude changes in the redshift prior , especially when uv  or nir  data are available . it is clear from s  [ fig : zspeczphotdr7qso ] and [ fig : zspeczphot2slaqboss ] that , on average , the influence of a different redshift prior will be limited , as the main differences lie at higher redshift , where the _ sdss _  colors provide relatively unambiguous photometric redshifts ( as shown by the lack of degeneracies at higher redshift in the photometric versus spectroscopic redshift plane ) . as the photometric redshift distributions are only marginally affected by the use of a different prior , classification based on integration over these redshift pdfs also does not depend strongly on the details of the redshift prior . we have previously discussed other photometric redshift estimation techniques for quasars in section  [ sec : general ] . comparing  [ fig : zspeczphotdr7qso ] to similar diagrams in @xcite we see , at least qualitatively , that the _ xdqsoz _  technique performs similarly when applied to the @xmath0  fluxes of bright , high signal - to - noise ratio objects . we did not expect to perform better as the near - degeneracies in the @xmath0  color  redshift plane are real and the quasar locus is broad . the advantage of the _ xdqsoz _  technique over these other techniques is that it can be applied to faint objects and that it can incorporate uv  and nir  observations , even at low signal - to - noise ratio , to improve photometric redshift estimation and quasar classification . no other method exists to calculate photometric quasar probabilities over arbitrary redshift ranges . by comparing with state - of - the - art photometric quasar classification using kernel - density estimation or gaussian mixture density deconvolution @xcite , we have shown that the photometric quasar probabilities obtained by integrating the photometric redshift pdf over redshift are as good as those trained on the redshift range in question . two additional sources of information relevant to photometric quasar classification and redshift estimation stand out as the next steps toward a full quasar model , although neither of these is currently available over the large areas of the sky surveyed by projects such as the _ sdss _ : photometric variability and differential - chromatic - refraction - induced astrometric offsets for quasars . of these , photometric variability is the easiest to include in the quasar classification technique discussed here , as we can ignore the redshift information contained in the variability , because this information seems to be limited @xcite . as such , a photometric variability likelihood for quasars and stars could be multiplied with the flux redshift likelihood employed and modeled here to perform simultaneous color and variability selection . the combination of photometric variability and color information will lead to accurate photometric quasar classification and redshift estimation in the _ lsst _  era . the strong spectral features of quasars induce positional offsets to standard differential - chromatic - refraction corrections @xcite . these positional offsets are redshift dependent much as quasar colors are redshift dependent because of spectral features moving through individual filters ( see , e.g. ,  [ fig : allzexfit ] ) . thus , these offsets could be used to break redshift degeneracies . accomplishing this in the _ xdqsoz _  flux redshift density context necessitates adding the astrometric offsets into the density model . because the astrometric offsets are zenith angle dependent , these models would have to be constructed for a range of airmasses , or airmass could be added as an additional dimension . as astrometric redshifts are a subtle and difficult - to - measure effect , the deconvolution aspect of the xd  density - estimation technique could be useful . the technique described in this article  is a step toward a generalized method for object classification and characterization from broadband photometric data , which will become increasingly relevant in this era of major wide - field imaging surveys . while our quasar model includes redshift in addition to the broadband fluxes of an object , our star model does not because stars do not possess a cosmological redshift . stars are characterized by other properties  e.g . , distance and metallicity  that are often estimated photometrically ( e.g. , * ? ? ? * ; * ? ? ? as we are interested here in quasar classification and characterization , our model implicitly marginalized over stellar properties . however , as part of a general object classification pipeline , these properties should be included  and the technique developed in this paper could be applied . more importantly , the general framework outlined in section  [ sec : general ] and the specific implementation in sections  [ sec : xdqsoz ] and [ sec : targeting ] show that we can perform classification when different models are characterized by different parameters  even different _ numbers _ of parameters . this aspect is especially relevant in the context of quasar selection based on variability . quasar variability is commonly modeled as a stochastic gaussian process @xcite characterized by a small number of parameters . recently it has been shown that this framework allows for a clean selection of quasars because most stars  the main contaminants for quasar targeting currently  in general do not vary over long time baselines . in this type of selection , however , quasars and stars are often modeled ( or fit ) using the same stochastic model , which is inappropriate for the stars ( @xcite ; however , see @xcite ) . the use of a stochastic model for variability - based star quasar separation is particularly problematic for rr lyrae stars  a common contaminant in color - based classification of quasars in some redshift ranges . rr lyraes are known to vary periodically rather than stochastically . in the framework we use in this article  all classes of objects can be described using models appropriate for the class  e.g . , stochastically varying objects with a cosmological redshift for the quasars and non - variable sources for most stars because object classification only uses _ marginalized _ probabilities , that is , probabilities marginalized over the internal properties of each class ( cf .  equation  [ [ eq : quasardeltazprob ] ] ) . describing each class with a model appropriate for that class should lead to better classification and simultaneous object classification of sources into _ all _ classes . as photometric quasar classification moves to ever fainter flux levels , contamination from point - like galaxies becomes increasingly important . as discussed by @xcite , unresolved galaxies are implicitly taken into account in our model because our training set of `` stars '' is actually a set of non - variable point - like objects that therefore includes faint galaxies . this model of galaxies again implicitly marginalizes over galaxy properties , most notably the redshift of the galaxy . photometric redshift estimation for galaxies is closely related to obtaining photometric redshifts for quasars , but the galaxy photometric redshift techniques tend to rely more on templates in their model building , while quasars are modeled in a more empirical manner ( e.g. , * ? ? ? * ) . however , this distinction is not fundamental and the general framework discussed here still applies . template - based models are just another way of obtaining the probability @xmath120 or @xmath121 . the _ xdqsoz _  model of section  [ sec : xdqsoz ] also contains the distribution of broadband fluxes as a function of redshift @xmath122 such as is used to compute mean quasar color tracks . this probability density is obtained from the full _ xdqsoz _  model flux redshift density by conditioning on redshift . for the relative flux this leads to a mixture of gaussians with means , variances , and amplitudes given by expressions similar to those in equations  ( [ eq : means ] ) and ( [ eq : alphazk])essentially , relative flux and redshift need to be interchanged in those equations . properties of this distribution can be calculated from the mixture of gaussians . for example , the mean quasar relative flux ( or color ) as a function of redshift is obtained by weighting the means of the gaussian components using the redshift - dependent amplitudes . code to calculate the mean quasar color track is included in the package described in the . in this article  we have introduced a new approach to photometric quasar classification that can simultaneously classify quasars and characterize their redshifts based on broadband photometry . this technique , _ xdqsoz _ , is an extension of the _ xdqso _  technique of @xcite that adds the unknown redshift as an extra parameter to the quasar model to obtain the likelihood @xmath123 that is central to both quasar classification and photometric redshift estimation . we have shown that this combined approach is both the best current quasar classification technique it has similar performance as the _ xdqso _  method  and a competitive photometric redshift method . compared to other approaches to photometric redshift estimation for quasars it has the advantage that it can incorporate additional uv  and nir  data , even at low signal - to - noise ratio , and can be extended to fainter flux levels where photometric uncertainties are significant . using samples of quasars drawn from the _ sdss _ , _ 2slaq _ , and _ boss _  spectroscopic catalogs we have demonstrated this increased performance down to @xmath124 mag . the addition of uv  and nir  data to the photometric redshift estimation problem essentially breaks all of the redshift degeneracies inherent to the @xmath0  filter set . code to use the _ xdqsoz _  technique for classification and redshift estimation , including the ability to calculate full posterior probability distributions for the redshift , are made publicly available . this code is briefly described in the . it is a pleasure to thank the anonymous referee and paul martini , gordon richards , and david weinberg for helpful comments and discussions . j.b . and d.w.h . were partially supported by nasa ( grant nnx08aj48 g ) and the nsf ( grant ast-0908357 ) . a.d.m . acknowledges support under the nasa adap program ( grant nnx08aj28 g ) . j.f.h acknowledges support provided by the alexander von humboldt foundation in the framework of the sofja kovalevskaja award endowed by the german federal ministry of education and research . d.w.h . and a.d.m . are research fellows of the alexander von humboldt foundation of germany . we gratefully acknowledge nasa s support for construction , operation , and science analysis for the _ galex _  mission , developed in cooperation with the centre national detudes spatiale of france and the korean ministry of science and technology .    this work is based in part on data obtained as part of the ukirt infrared deep sky survey ( _ ukidss _ ) . funding for the sdss and sdss - ii has been provided by the alfred p. sloan foundation , the participating institutions , the national science foundation , the u.s . department of energy , the national aeronautics and space administration , the japanese monbukagakusho , the max planck society , and the higher education funding council for england . the sdss web site is http://www.sdss.org/.    the sdss is managed by the astrophysical research consortium for the participating institutions . the participating institutions are the american museum of natural history , astrophysical institute potsdam , university of basel , university of cambridge , case western reserve university , university of chicago , drexel university , fermilab , the institute for advanced study , the japan participation group , johns hopkins university , the joint institute for nuclear astrophysics , the kavli institute for particle astrophysics and cosmology , the korean scientist group , the chinese academy of sciences ( lamost ) , los alamos national laboratory , the max - planck - institute for astronomy ( mpia ) , the max - planck - institute for astrophysics ( mpa ) , new mexico state university , ohio state university , university of pittsburgh , university of portsmouth , princeton university , the united states naval observatory , and the university of washington . sdss - iii is managed by the astrophysical research consortium for the participating institutions of the sdss - iii collaboration including the university of arizona , the brazilian participation group , brookhaven national laboratory , university of cambridge , university of florida , the french participation group , the german participation group , the instituto de astrofisica de canarias , the michigan state / notre dame / jina participation group , johns hopkins university , lawrence berkeley national laboratory , max planck institute for astrophysics , new mexico state university , new york university , the ohio state university , the penn state university , university of portsmouth , princeton university , university of tokyo , the university of utah , vanderbilt university , university of virginia , university of washington , and yale university . the _ xdqsoz _  code for target selection , classification , and photometric redshift estimation is publicly available at        _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ http://www.sdss3.org/svn/repo/xdqso/tags/v0_6/doc/build/html/index.html  . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _      the _ xdqso_/_xdqsoz _ package contains routines for quasar classification using the _ xdqso _  and _ xdqsoz _  techniques . it also contains code to calculate posterior probability distributions for the quasar redshift of objects based on input ` psfflux ` and ` psfflux_ivar ` ; these can be found in standard _ sdss _ data files such as the ` sweeps ' files    the _ xdqsoz _  models for the quasar color  redshift density are contained in the ` data/ ` directory . they are in the form of fits files containing the xd  models for all of the bins in apparent magnitude , with one file for each combination of _ sdss _  with _ galex _  and _ ukidss_. each fits file contains 47  extensions , where extension @xmath21 contains a structure with the amplitudes ( tag `` ) , means ( tag `` ) , and covariance matrices ( tag `` ) for bin @xmath21 in @xmath41-band  magnitude . the zeroth dimension of the gaussian represents the natural logarithm of the redshift , followed by _ sdss _ , _ galex _ , and _ ukidss _  fluxes ( where relevant ) in this order , and ordered as nuv / fuv for the _ galex _ , and yjhk for the _ ukidss_.    abazajian ,  k.  n. , et al . , 2009 , , 182 , 543 abell ,  p.  a. , et al . , 2009 , the lsst science book , arxiv:0912.0201v1 [ astro - 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sigma detection limit is indicated.,scaledwidth=60.0% ]            ) quasar probabilities computed using _ xdqso _ , that is , based on flux - density models in broad redshift ranges , and _ xdqsoz _ , i.e. , obtained by integrating flux density models over the relevant redshift range , for 490,793 objects in _ sdss _  stripe 82 based on single - imaging - run flux measurements . conditional 25 , 50 , and 75percent quantiles are shown . ]    ) quasar selection efficiency for _ xdqso _  and _ xdqsoz _  as a function of target density for objects in _ sdss _  stripe 82 based on single - imaging - run flux measurements . the top panel bases selection solely on _ sdss _ @xmath0  fluxes , the lower panels add _ galex _  nuv  and fuv  medium - deep measurements as well as _ ukidss _ yjhk  photometry , both of which are available for almost all stripe-82 sources , through force - photometering _ galex _  and _ ukidss _  _ las _  imaging data at _ sdss _  positions . the 50percent selection efficiency is indicated and the @xmath0-only curve for _ xdqsoz _  is repeated in gray in each panel . ] -band magnitude distribution of all point sources in the expected _ sdss - iii _  _ boss _  footprint with _ xdqsoz _ quasar probability larger than 0.5 over the indicated redshift range and dereddened @xmath41 between 17.8 mag and 21.5 mag . diamonds indicate number counts from the _ sdss _  spectroscopic survey @xcite.,scaledwidth=70.0% ]     forest , while probability - based selection ranks on @xmath125 quasar ) . the top panel shows the number of mid - redshift quasars found by each method as a function of the target density ; the bottom panel shows the value of the selected quasars . note that some @xmath126 quasars are valuable for the lyman-@xmath3 forest baf measurement . ] -band magnitude . the bottom panel shows the fraction of such point - like galaxies that have an _ xdqsoz _ quasar probability ( over all redshifts ) larger than 0.5 . the dashed curve in the bottom panel shows the fraction of all point - sources that have an _ xdqsoz _ quasar probability larger than 0.5 . even though point - like galaxies start to dominate the number counts around @xmath41 = 22 mag , they only make up a small fraction of photometrically selected quasars at all magnitudes . ]        . the overall shape of the redshift distribution is similar to the prior distribution , except for the drop in @xmath127 due to the decreased efficiency of photometric quasar classification based on _ sdss _ photometry.,scaledwidth=70.0% ]
we describe a technique for simultaneously classifying and estimating the redshift of quasars . 
 it can separate quasars from stars in arbitrary redshift ranges , estimate full posterior distribution functions for the redshift , and naturally incorporate flux uncertainties , missing data , and multi - wavelength photometry . 
 we build models of quasars in flux  redshift space by applying the _ extreme deconvolution _ technique to estimate the underlying density . by integrating this density over redshift 
 one can obtain quasar flux 
 densities in different redshift ranges . 
 this approach allows for efficient , consistent , and fast classification and photometric redshift estimation . 
 this is achieved by combining the speed obtained by choosing simple analytical forms as the basis of our density model with the flexibility of non - parametric models through the use of many simple components with many parameters . 
 we show that this technique is competitive with the best photometric quasar classification techniques  which are limited to fixed , broad redshift ranges and high signal - to - noise ratio data  and with the best photometric redshift techniques when applied to broadband optical data . 
 we demonstrate that the inclusion of uv  and nir  data significantly improves photometric quasar 
 star separation and essentially resolves all of the redshift degeneracies for quasars inherent to the @xmath0  filter system , even when included data have a low signal - to - noise ratio . for quasars 
 spectroscopically confirmed by the _ 
 sdss _  84 and 97percent of the objects with _ 
 _  uv  and _ ukidss _ 
 nir  data have photometric redshifts within 0.1 and 0.3 , respectively , of the spectroscopic redshift ; this amounts to about a factor of three improvement over @xmath0-only photometric redshifts . 
 our code to calculate quasar probabilities and redshift probability distributions is publicly available .