Bayes Window (1)

Bayes Factors 1

In a 1935 paper, and in his book Theory of Probability, Je reys developed a methodology for quantifying the evidence in favor of a scienti c theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null is one-half. Although there has been much discussion of Bayesian hypothesis testing in the context ...

Bayes - Adaptive POMDPs 1

Bayesian Reinforcement Learning has generated substantial interest recently, as it provides an elegant solution to the exploration-exploitation trade-off in reinforcement learning. However most investigations of Bayesian reinforcement learning to date focus on the standard Markov Decision Processes (MDPs). Our goal is to extend these ideas to the more general Partially Observable MDP (POMDP) fr...

Bayes Factor 1 Running head: BAYES FACTOR A Bayes Factor Calculation for Accepting the Null Hypothesis

Progress in science often comes from discovering invariances in the relationship between variables. Invariances correspond to null hypotheses. As is commonly known, it is not possible to accumulate evidence for the null hypothesis in conventional significance testing. We highlight a Bayes factor alternative to the t-test for accumulating evidence for either the null or alternative hypotheses. T...

Bayes Factors 1 Running head: BAYES FACTORS Default Bayes Factors for Model Selection in Regression

In this paper, we present a Bayes factor solution for inference in multiple regression. Bayes factors are principled measures of the relative evidence from data for various models or positions, including models that embed null hypotheses. In this regard, they may be used to state positive evidence for a lack of an effect, which is not possible in conventional significance testing. One obstacle ...

Learning from Data 1 Naive Bayes