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...

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...

In this paper, we describe our system that participated in SemEval-2013, Task 2.B (sentiment analysis in Twitter). Our approach consists of adapting Naive Bayes probabilities in order to take into account prior knowledge (represented in the form of a sentiment lexicon). We propose two different methods to efficiently incorporate prior knowledge. We show that our approach outperforms the classic...

Let T deno te a con t inuous t ime hor izon and {Gt:teT} be a net (general ized sequence) of Bayesian games. We show that: (i) if {xt: te T} is a net of Bayes ian Nash Equi l ib r ium (BNE) strategies for G t, we can ext rac t a subsequence which converges to a l imit full in fo rmat ion B N E s t ra tegy for a one shot l imit full in fo rmat ion Bayes ian game. (ii) If {xt:t~T} is a net of a p...

The accuracy of genomic estimated breeding values (GEBV) was evaluated for sixteen meat quality traits in a Berkshire population (n = 1,191) that was collected from Dasan breeding farm, Namwon, Korea. The animals were genotyped with the Illumina porcine 62 K single nucleotide polymorphism (SNP) bead chips, in which a set of 36,605 SNPs were available after quality control tests. Two methods wer...

Genomic selection can increase genetic gain per generation through early selection. Genomic selection is expected to be particularly valuable for traits that are costly to phenotype, and expressed late in the life-cycle of long-lived species. Alternative approaches to genomic selection prediction models may perform differently for traits with distinct genetic properties. Here the performance of...

Bayes factors provide a symmetricalmeasure of evidence for onemodel versus another (e.g. H1 versusH0) in order to relate theory to data. These properties help solve some (but not all) of the problems underlying the credibility crisis in psychology. The symmetry of the measure of evidence means that there can be evidence for H0 just as much as for H1; or the Bayes factor may indicate insufficien...

The “Fourth axiom of probability theory” quickly yields Bayes Theorem – and hence how to deal with inverse probabilities (e.g., P(h|e) versus P(e|h)) – and shows in odds form the importance of likelihood ratios as opposed to simple likelihoods. This paper discusses a problem more basic than ignoring Bayes Theorem. The problem is making no comparisons at all! Just associating. Thus, if P(A|B) or...