The ways in which an agent’s actions affect the world can often be modeled compactly using a set of relational probabilistic planning rules. This paper addresses the problem of learning such rule sets for multiple related tasks. We take a hierarchical Bayesian approach, in which the system learns a prior distribution over rule sets. We present a class of prior distributions parameterized by a r...

Group sequential stopping rules are often used as guidelines in the monitoring of clinical trials in order to address the ethical and efficiency issues inherent in human testing of a new treatment or preventive agent for disease. Such stopping rules have been proposed based on a variety of different criteria, both scientific (e.g. estimates of treatment effect) and statistical (e.g. frequentist...

We consider the problem of gambling on a quantum experiment and enforce rational behaviour by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality theorems. In our quantum setting, they yield the Bayesian theory generalised to the space of Hermitian matrices. This very theory is quantum mechanics: in fact, we derive all its four postulates from t...

We formulate and evaluate a Bayesian approach to probabilistic input modeling. Taking into account the parameter and stochastic uncertainties inherent in most simulations, this approach yields valid predictive inferences about the output quantities of interest. We use prior information to construct prior distributions on the input-model parameters. Combining this prior information with the like...

Bayesian models of cognition are typically used to describe human learning and inference at the computational level, identifying which hypotheses people should select to explain observed data given a particular set of inductive biases. However, such an analysis can be consistent with human behavior even if people are not actually carrying out exact Bayesian inference. We analyze a simple algori...

The “Big Data” revolution is spawning systems designed to make decisions from data. In particular, deep learning methods have emerged as the state of the art method in many important breakthroughs [18, 20, 28]. This is due to the statistical flexibility and computational scalability of large and deep neural networks which allows them to harness the information of large and rich datasets. At the...

Most studies of Bayesian updating use experimental data. This paper uses a non-experimental data source– the voter ballots of the Associated Press (AP) college football poll, a weekly subjective ranking of the top 25 teams–to test Bayes’ rule as a descriptive model. I estimate the voters’ Bayesian posterior rankings for the first seven weeks of the 2006-08 seasons (a total of over 31,000 rankin...

We describe a Bayesian Reasoning Framework (BRF) that supports business rule operations for on-line information systems. BRF comprises a three-layer environment with business information systems at the top, a middle-ware Bayesian reasoning server, and a Bayesian reasoning engine at the bottom. The top and middle-ware layers communicate via SOAP/XML protocol, while the middle-ware and bottom lay...