In this paper, we present a Non-Bayesian conditioning rule for belief revision. This rule is truly Non-Bayesian in the sense that it doesn’t satisfy the common adopted principle that when a prior belief is Bayesian, after conditioning by X, Bel(X|X) must be equal to one. Our new conditioning rule for belief revision is based on the proportional conflict redistribution rule of combination develo...

When preferences are such that there is no unique additive prior, the issue of which updating rule to use is of extreme importance. This paper presents an axiomatization of the rule which requires updating of all the priors by Bayes rule. The decision maker has conditional preferences over acts. It is assumed that preferences over acts conditional on eventE happening, do not depend on lotteries...

Suppose that the p-value for an hypothesis test has a Uniform [0,1] distribution when the null hypothesis is true. This paper proposes a ”rough and ready” rule for the interpretation of the evidence corresponding to such p-values. The rule is to use B̄∗(p) = 1/{epln(1/p)} as an upper bound on the Bayes factor against the null hypothesis for p ≤ 1/e = 0.368 . The rule is found to work well for tw...

Drawing on insights from psychology, we propose a way to ease the pain of understanding, and teaching, Bayes' Rule.

In a probability-based reasoning system, Bayes’ theorem and its variations are often used to revise the system’s beliefs. However, if the explicit conditions and the implicit conditions of probability assignments are properly distinguished, it follows that Bayes’ theorem is not a generally applicable revision rule. Upon properly distinguishing belief revision from belief updating, we see that J...

A kernel method for realizing Bayes’ rule is proposed, based on representations of probabilities in reproducing kernel Hilbert spaces. Probabilities are uniquely characterized by the mean of the canonical map to the RKHS. The prior and conditional probabilities are expressed in terms of RKHS functions of an empirical sample: no explicit parametric model is needed for these quantities. The poste...

Biometric verification of subjects as users of computers or other devices has mainly based on fingerprints, face, iris or other images. We developed biometric verification using eye movements to be measured with eye movement videocameras. We measured saccades using the same stimulation for each subject. Our data included signals recorded in two manners: electrooculographically from 30 subjects ...

In a Bayesian approach to online learning a simple paramet-ric approximate posterior over rules is updated in each online learning step. Predictions on new data are derived from averages over this posterior. This should be compared to the Bayes optimal batch (or ooine) approach for which the posterior is calculated from the prior and the likelihood of the whole training set. We suggest that min...

Bayesian models of cognition hypothesize that human brains make sense of data by representing probability distributions and applying Bayes’ rule to find the best explanation for available data. Understanding the neural mechanisms underlying probabilistic models remains important because Bayesian models provide a computational framework, rather than specifying mechanistic processes. Here, we pro...

Recently, significant progress has been made developing kernel mean expressions for Bayesian inference. An important success in this domain is the nonparametric kernel Bayes’ filter (nKB-filter), which can be used for sequential inference in state space models. We expand upon this work by introducing a smoothing algorithm, the nonparametric kernel Bayes’ smoother (nKB-smoother) which relies on ...