tokens: impossible by using an encryption algorithm and allowing the specification of side constraints to be met. Section 5.6 computes the shift of parameters to determine whether blinding succeeded. Finally, the physical units are restored, and the output is a purposefully biased covariance matrix which leads to the requested bias in physical parameters, with the origin of the bias being untraceable due to the intermediate encryption and side constraints. 3.3 Finding sensible target parameters for blinding At the outset of the blinding strategy, the blinder has to pick an origin of the posterior shift, and target parameters which are preferred after shifting. Typically, shifting the yet unknown posterior by two to three standard deviations is the sought aim. Having never computed the full posterior, its standard deviations are however not known yet, so we effectively wish to shift by the multiple of a yet unknown quantity. We thus require an abstract prediction of the shift’s magnitude. To this aim, we exploit scaling relations: For a multivariate Gaussian posterior, the best-fit will occur at the minimal chisquared, . The associated 90 per cent credibility contour can then be chosen to run along an isocontour which lies by Δχ 2 above this minimum. The more parameters are estimated, the larger Δχ 2 has to be, since more parameters will widen up the joint posterior. The values of Δχ 2 where the 90 per cent credibility contour lies above the minimum are known (they are integrals of χ 2 -distributions), and we tabulate them as a function of free parameters in Table 1 . Table 1. Δχ 2 -values where the 90 percent credibility contour lies above the minimum χ 2 , as a function of number of parameters. If the blinder chooses target parameters which differ from the initial parameters by more than Δχ 2 shown here, then a posterior shift of more than three posterior standard deviations will ensue. This is not advised. The blinder thus has to know how many parameters are to be inferred, and has to pick initial parameters and target parameters which differ approximately by Δχ 2 -values as given in Table 1 . If the blinder has no physical intuition for which parameter values are likely to be preferred by the data, then the linearized best-fitting estimator of equation ( 7 ) can be evaluated, which will yield parameter values close to the full non-linear best fit . We found that the values do not need to be picked with too much care, as long as they are within about two posterior standard deviation from the true best-fit . We provide a public code 2 for the algorithm, which assists the blinder via equation ( 7 ) and Table 1 in finding sensible parameters for the shift origin, and for the shift destination . 3.4 Data transformation The general astronomical data set will come in ‘natural’ units, which might depend on estimator choice or the adopted (physical) units of measurements, such as parsec or mega-parsec. To gain generality, we thus standardize the data set.
ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O