Within the Kolmogorov theory of probability, Bayes’ rule allows one to perform statistical inference by relating conditional probabilities to unconditional probabilities. As we show here, however, there is a continuous set of alternative inference rules that yield the same results, and that may have computational or practical advantages for certain problems. We formulate generalized axioms for ...

There have been considerable methodological developments of Bayes factors for hypothesis testing in the social and behavioral sciences, related fields. This development is due to flexibility factor multiple hypotheses simultaneously, ability test complex involving equality as well order constraints on parameters interest, interpretability outcome weight evidence provided by data support competi...

1 Learning Goals 1. Be able to explain the difference between the p-value and a posterior probability to a doctor. 2 Introduction We have now learned about two schools of statistical inference: Bayesian and frequentist. Both approaches allow one to evaluate evidence about competing hypotheses. In these notes we will review and compare the two approaches, starting from Bayes formula. 3 Bayes for...

Abstract We introduce two empirical strategies harnessing the randomness in school assignment mechanisms to measure value-added. The first estimator controls for probability of assignment, treating take-up as ignorable. test this assumption using assignments. second approach uses assignments instrumental variables (IVs) low-dimensional models value-added and forms Bayes posteriors from these IV...

A two-factor experiment with interaction between factors wherein observations follow an Inverse Gaussian model is considered. Analysis of the experiment is approached via an empirical Bayes procedure. The conjugate family of prior distributions is considered. Bayes and empirical Bayes estimators are derived. Application of the procedure is illustrated on a data set, which has previously been an...

We will look at the case of a single-item First Price Auction. Our goal will be to estimate the distribution of valuations of the players, by observing samples of bid vectors of players from multiple first price auctions. In particular, we consider the case where we have a data set of m First Price Auctions, each among n bidders. The value v i of each bidder i in each first price auction t, is ...

In Bayesian model selection or testing problems, Bayes factors under proper priors have been very successful. In practice, however, limited information and time constraints often require us to use noninformative priors which are typically improper and are deened only up to arbitrary constants. The resulting Bayes factors are then not well deened. A recently proposed model selection criterion, t...