Non-stationary continuous time Bayesian networks are introduced. They allow the parents set of each node to change over continuous time. Three settings are developed for learning non-stationary continuous time Bayesian networks from data: known transition times, known number of epochs and unknown number of epochs. A score function for each setting is derived and the corresponding learning algorithm is developed. A set of numerical experiments on synthetic data is used to compare the effectiveness of non-stationary continuous time Bayesian networks to that of non-stationary dynamic Bayesian networks. Furthermore, the performance achieved by non-stationary continuous time Bayesian networks is compared to that achieved by state-of-the-art algorithms on four real-world datasets, namely drosophila, saccharomyces cerevisiae, songbird and macroeconomics.
Editor's note: The following is an interview with Columbia University Professor Andrew Gelman conducted by Marketing scientist Kevin Gray, in which Gelman spells out the ABCs of Bayesian statistics. Kevin Gray: Most marketing researchers have heard of Bayesian statistics but know little about it. Can you briefly explain in layperson's terms what it is and how it differs from the'ordinary' statistics most of us learned in college? Andrew Gelman: Bayesian statistics uses the mathematical rules of probability to combines data with "prior information" to give inferences which (if the model being used is correct) are more precise than would be obtained by either source of information alone. Classical statistical methods avoid prior distributions.
Bayesian Computational Analyses with R is an introductory course on the use and implementation of Bayesian modeling using R software. The Bayesian approach is an alternative to the "frequentist" approach where one simply takes a sample of data and makes inferences about the likely parameters of the population. In contrast, the Bayesian approach uses both likelihood functions and a sample of observed data (the'prior') to estimate the most likely values and distributions for the estimated population parameters (the'posterior'). The course is useful to anyone who wishes to learn about Bayesian concepts and is suited to both novice and intermediate Bayesian students and Bayesian practitioners. It is both a practical, "hands-on" course with many examples using R scripts and software, and is conceptual, as the course explains the Bayesian concepts. All materials, software, R scripts, slides, exercises and solutions are included with the course materials. It is helpful to have some grounding in basic inferential statistics and probability theory. No experience with R is necessary, although it is also helpful.
A Bayesian network is a compact, expressive representation of uncertain relationships among parameters in a domain. In this article, I introduce basic methods for computing with Bayesian networks, starting with the simple idea of summing the probabilities of events of interest. The article introduces major current methods for exact computation, briefly surveys approximation methods, and closes with a brief discussion of open issues.