This paper develops multiple-prior Bayesian inference for a set-identi…ed parameter whose identi…ed set is constructed by an intersection of two identi…ed sets. We formulate an econometrician’s practice of "adding an assumption" as "updating ambiguous beliefs." Among several ways to update ambiguous beliefs proposed in the literature, we consider the DempsterShafer updating rule (Dempster (1968...

This paper reviews the past and current interest in using Bayesian thinking to introduce statistical inference. Rationale for using a Bayesian approach is described and particular methods are described that make it easier to understand Bayes' rule. Several older and modern introductory statistics books are reviewed that use a Bayesian perspective. It is argued that a Bayesian perspective is ver...

Uncertainty is omnipresent when we perceive or interact with our environment, and the Bayesian framework provides computational methods for dealing with it. Mathematical models for Bayesian decision making typically require datastructures that are hard to implement in neural networks. This article shows that even the simplest and experimentally best supported type of synaptic plasticity, Hebbia...

This tutorial gives a concise overview of existing PAC-Bayesian theory focusing on three generalization bounds. The first is an Occam bound which handles rules with finite precision parameters and which states that generalization loss is near training loss when the number of bits needed to write the rule is small compared to the sample size. The second is a PAC-Bayesian bound providing a genera...

In this chapter I review Bayesian statistics as used for induction and relate it to logic based abduction Much reasoning under un certainty including induction is based on Bayes rule Bayes rule is interesting precisely because it provides a mechanism for abduc tion I review work of Buntine that argues that much of the work on Bayesian learning can be best viewed in terms of graphical models suc...

In this chapter I review Bayesian statistics as used for induction and relate it to logic-based abduction. Much reasoning under uncertainty , including induction, is based on Bayes' rule. Bayes' rule is interesting precisely because it provides a mechanism for abduction. I review work of Buntine that argues that much of the work on Bayesian learning can be best viewed in terms of graphical mode...

In Bayesian inference tasks, information about base rates as well as hit rate and false-alarm rate needs to be integrated according to Bayes' rule after the result of a diagnostic test became known. Numerous studies have found that presenting information in a Bayesian inference task in terms of natural frequencies leads to better performance compared to variants with information presented in te...