A nonparametric kernel-based method for realizing Bayes’ rule is proposed, based on kernel representations of probabilities in reproducing kernel Hilbert spaces. The prior and conditional probabilities are expressed as empirical kernel mean and covariance operators, respectively, and the kernel mean of the posterior distribution is computed in the form of a weighted sample. The kernel Bayes’ ru...

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...

In standard models of Bayesian learning agents reduce their uncertainty about an event’s true probability because their consistent estimator concentrates almost surely around this probability’s true value as the number of observations becomes large. This paper takes the empirically observed violations of Savage’s (1954) sure thing principle seriously and asks whether Bayesian learners with ambi...

Coronavirus disease 2019 (COVID-19) has been termed a “Pandemic Disease” that infected many people and caused deaths on nearly unprecedented level. As more are each day, it continues to pose serious threat humanity worldwide. result, healthcare systems around the world facing shortage of medical space such as wards sickbeds. In most cases, healthy experience tolerable symptoms if they infected....

We develop a dynamic model of opinion formation in social networks when the information required for learning a payoff-relevant parameter may not be at the disposal of any single agent. Individuals engage in communication with their neighbors in order to learn from their experiences. However, instead of incorporating the views of their neighbors in a fully Bayesian manner, agents use a simple u...

A previous paper (2] showed how to generate a linear discriminant network (LDN) that computes likely faults for a noisy fault detection problem by using a modification of the perceptron learning algorithm called the pocket algorithm. Here we compare the performance of this connectionist model with performance of the optimal Bayesian decision rule for the example that was previously described. W...

Before we discuss the details of the Bayesian detection, let us take a quick tour about the overall framework to detect (or classify) an object in practice. In the Bayesian setting, we model observations as random samples drawn from some probability distributions. The classification process usually involves extracting features from the observations, and a decision rule that satisfies certain op...