Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The problem of forecasting conditional probabilities of the next event given the past is considered#R##N#in a general probabilistic setting. Given an arbitrary  (large, uncountable) set C of predictors, #R##N# would like to construct a single predictor that  performs asymptotically as ll as  the #R##N#best predictor in C, on any data.  Here  show that there are sets C for which such predictors exist, #R##N#but none of them is a Bayesian predictor with a prior  concentrated on C.#R##N#In other words, there is a predictor with sublinear regret, but every Bayesian predictor must have a linear regret. This negative finding is in sharp contrast with previous results#R##N#that establish the opposite  for the case when one of the predictors in C achieves asymptotically vanishing error.#R##N#In such a case, if there is a predictor that achieves asymptotically vanishing error for any measure in C, then there is #R##N#a Bayesian predictor that also has this property, and  whose prior is concentrated on (a countable subset of)  C.
['Daniil Ryabko']
I am writing a research paper on a idea Things Bayes Can’t Do
[{"from": "human", "value": "I am writing a research paper on a idea Things Bayes Can\u2019t Do"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The problem of forecasting conditional probabilities of the next event given the past is considered#R##N#in a general probabilistic setting. Given an arbitrary  (large, uncountable) set C of predictors, #R##N# would like to construct a single predictor that  performs asymptotically as ll as  the #R##N#best predictor in C, on any data.  Here  show that there are sets C for which such predictors exist, #R##N#but none of them is a Bayesian predictor with a prior  concentrated on C.#R##N#In other words, there is a predictor with sublinear regret, but every Bayesian predictor must have a linear regret. This negative finding is in sharp contrast with previous results#R##N#that establish the opposite  for the case when one of the predictors in C achieves asymptotically vanishing error.#R##N#In such a case, if there is a predictor that achieves asymptotically vanishing error for any measure in C, then there is #R##N#a Bayesian predictor that also has this property, and  whose prior is concentrated on (a countable subset of)  C."}]