Topic
Bayesian probability
About: Bayesian probability is a research topic. Over the lifetime, 26572 publications have been published within this topic receiving 817919 citations.
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TL;DR: To facilitate use of the Bayes factor, an easy-to-use, Web-based program is provided that performs the necessary calculations and has better properties than other methods of inference that have been advocated in the psychological literature.
Abstract: Progress in science often comes from discovering invariances in relationships among variables; these invariances often correspond to null hypotheses. As is commonly known, it is not possible to state evidence for the null hypothesis in conventional significance testing. Here we highlight a Bayes factor alternative to the conventional t test that will allow researchers to express preference for either the null hypothesis or the alternative. The Bayes factor has a natural and straightforward interpretation, is based on reasonable assumptions, and has better properties than other methods of inference that have been advocated in the psychological literature. To facilitate use of the Bayes factor, we provide an easy-to-use, Web-based program that performs the necessary calculations.
3,012 citations
TL;DR: It is found that on a database of more than 100 categories, the Bayesian approach produces informative models when the number of training examples is too small for other methods to operate successfully.
Abstract: Learning visual models of object categories notoriously requires hundreds or thousands of training examples. We show that it is possible to learn much information about a category from just one, or a handful, of images. The key insight is that, rather than learning from scratch, one can take advantage of knowledge coming from previously learned categories, no matter how different these categories might be. We explore a Bayesian implementation of this idea. Object categories are represented by probabilistic models. Prior knowledge is represented as a probability density function on the parameters of these models. The posterior model for an object category is obtained by updating the prior in the light of one or more observations. We test a simple implementation of our algorithm on a database of 101 diverse object categories. We compare category models learned by an implementation of our Bayesian approach to models learned from by maximum likelihood (ML) and maximum a posteriori (MAP) methods. We find that on a database of more than 100 categories, the Bayesian approach produces informative models when the number of training examples is too small for other methods to operate successfully.
2,976 citations
TL;DR: A quantitative and practical Bayesian framework is described for learning of mappings in feedforward networks that automatically embodies "Occam's razor," penalizing overflexible and overcomplex models.
Abstract: A quantitative and practical Bayesian framework is described for learning of mappings in feedforward networks. The framework makes possible (1) objective comparisons between solutions using alternative network architectures, (2) objective stopping rules for network pruning or growing procedures, (3) objective choice of magnitude and type of weight decay terms or additive regularizers (for penalizing large weights, etc.), (4) a measure of the effective number of well-determined parameters in a model, (5) quantified estimates of the error bars on network parameters and on network output, and (6) objective comparisons with alternative learning and interpolation models such as splines and radial basis functions. The Bayesian "evidence" automatically embodies "Occam's razor," penalizing overflexible and overcomplex models. The Bayesian approach helps detect poor underlying assumptions in learning models. For learning models well matched to a problem, a good correlation between generalization ability and the Bayesian evidence is obtained.
2,906 citations
TL;DR: The Bayesian skyline plot is introduced, a new method for estimating past population dynamics through time from a sample of molecular sequences without dependence on a prespecified parametric model of demographic history, and a Markov chain Monte Carlo sampling procedure is described that efficiently samples a variant of the generalized skyline plot, given sequence data.
Abstract: We introduce the Bayesian skyline plot, a new method for estimating past population dynamics through time from a sample of molecular sequences without dependence on a prespecified parametric model of demographic history. We describe a Markov chain Monte Carlo sampling procedure that efficiently samples a variant of the generalized skyline plot, given sequence data, and combines these plots to generate a posterior distribution of effective population size through time. We apply the Bayesian skyline plot to simulated data sets and show that it correctly reconstructs demographic history under canonical scenarios. Finally, we compare the Bayesian skyline plot model to previous coalescent approaches by analyzing two real data sets (hepatitis C virus in Egypt and mitochondrial DNA of Beringian bison) that have been previously investigated using alternative coalescent methods. In the bison analysis, we detect a severe but previously unrecognized bottleneck, estimated to have occurred 10,000 radiocarbon years ago, which coincides with both the earliest undisputed record of large numbers of humans in Alaska and the megafaunal extinctions in North America at the beginning of the Holocene.
2,850 citations
TL;DR: The incremental algorithm is compared experimentally to an earlier batch Bayesian algorithm, as well as to one based on maximum-likelihood, which have comparable classification performance on small training sets, but incremental learning is significantly faster, making real-time learning feasible.
2,597 citations