We describe latent Dirichlet allocation (LDA), a generative probabilistic model for collections of discrete data such as text corpora. LDA is a three-level hierarchical Bayesian model, in which each item of a collection is modeled as a finite mixture over an underlying set of topics. Each topic is, in turn, modeled as an infinite mixture over an underlying set of topic probabilities. In the context of text modeling, the topic probabilities provide an explicit representation of a document. We present efficient approximate inference techniques based on variational methods and an EM algorithm for empirical Bayes parameter estimation. We report results in document modeling, text classification, and collaborative filtering, comparing to a mixture of unigrams model and the probabilistic LSI model. 1.

We propose a novel approach to learn and recognize natural scene categories. Unlike previous work [9, 17], it does not require experts to annotate the training set. We represent the image of a scene by a collection of local regions, denoted as codewords obtained by unsupervised learning. Each region is represented as part of a “theme”. In previous work, such themes were learnt from hand-annotations of experts, while our method learns the theme distributions as well as the codewords distribution over the themes without supervision. We report satisfactory categorization performances on a large set of 13 categories of complex scenes. 1.

Statistical procedures for missing data have vastly improved, yet misconception and unsound practice still abound. The authors frame the missing-data problem, review methods, offer advice, and raise issues that remain unresolved. They clear up common misunderstandings regarding the missing at random (MAR) concept. They summarize the evidence against older procedures and, with few exceptions, dis-courage their use. They present, in both technical and practical language, 2 general approaches that come highly recommended: maximum likelihood (ML) and Bayes-ian multiple imputation (MI). Newer developments are discussed, including some for dealing with missing data that are not MAR. Although not yet in the main-stream, these procedures may eventually extend the ML and MI methods that currently represent the state of the art. Why do missing data create such difficulty in sci-entific research? Because most data analysis proce-dures were not designed for them. Missingness is usu-ally a nuisance, not the main focus of inquiry, but

Social scientists rarely take full advantage of the information available in their statistical results. As a consequence, they miss opportunities to present quantities that are of greatest substantive interest for their research and express the appropriate degree of certainty about these quantities. In this article, we offer an approach, built on the technique of statistical simulation, to extract the currently overlooked information from any statistical method and to interpret and present it in a reader-friendly manner. Using this technique requires some expertise,

WinBUGS is a fully extensible modular framework for constructing and analysing Bayesian full probability models. Models may be specified either textually via the BUGS language or pictorially using a graphical interface called DoodleBUGS. WinBUGS processes the model specification and constructs an object-oriented representation of the model. The software offers a user-interface, based on dialogue boxes and menu commands, through which the model may then be analysed using Markov chain Monte Carlo techniques. In this paper we discuss how and why various modern computing concepts, such as object-orientation and run-time linking, feature in the software’s design. We also discuss how the framework may be extended. It is possible to write specific applications that form an apparently seamless interface with WinBUGS for users with specialized requirements. It is also possible to interface with WinBUGS at a lower level by incorporating new object types that may be used by WinBUGS without knowledge of the modules in which they are implemented. Neither of these types of extension require access to, or even recompilation of, the WinBUGS source-code.

We propose a remedy for the discrepancy between the way political scientists analyze data with missing values and the recommendations of the statistics community. Methodologists and statisticians agree that "multiple imputation" is a superior approach to the problem of missing data scattered through one's explanatory and dependent variables than the methods currently used in applied data analysis. The reason for this discrepancy lies with the fact that the computational algorithms used to apply the best multiple imputation models have been slow, difficult to implement, impossible to run with existing commercial statistical packages, and demanding of considerable expertise. In this paper, we adapt an existing algorithm, and use it to implement a generalpurpose, multiple imputation model for missing data. This algorithm is considerably faster and easier to use than the leading method recommended in the statistics literature. We also quantify the risks of current missing data practices, ...

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.

A new method is presented for robustly estimating multiple view relations from point correspondences. The method comprises two parts. The first is a new robust estimator MLESAC which is a generalization of the RANSAC estimator. It adopts the same sampling strategy as RANSAC to generate putative solutions, but chooses the solution that maximizes the likelihood rather than just the number of inliers. The second part of the algorithm is a general purpose method for automatically parameterizing these relations, using the output of MLESAC. A difficulty with multiview image relations is that there are often nonlinear constraints between the parameters, making optimization a difficult task. The parameterization method overcomes the difficulty of nonlinear constraints and conducts a constrained optimization. The method is general and its use is illustrated for the estimation of fundamental matrices, image–image homographies, and quadratic transformations. Results are given for both synthetic and real images. It is demonstrated that the method gives results equal or superior to those of previous approaches. c ○ 2000 Academic Press 1.

This paper surveys the fundamental principles of subjective Bayesian inference in econometrics and the implementation of those principles using posterior simulation methods. The emphasis is on the combination of models and the development of predictive distributions. Moving beyond conditioning on a fixed number of completely specified models, the paper introduces subjective Bayesian tools for formal comparison of these models with as yet incompletely specified models. The paper then shows how posterior simulators can facilitate communication between investigators (for example, econometricians) on the one hand and remote clients (for example, decision makers) on the other, enabling clients to vary the prior distributions and functions of interest employed by investigators. A theme of the paper is the practicality of subjective Bayesian methods. To this end, the paper describes publicly available software for Bayesian inference, model development, and communication and provides illustrations using two simple econometric models. *This paper was originally prepared for the Australasian meetings of the Econometric Society in Melbourne, Australia,

Abstract: This paper considers Bayesian counterparts of the classical tests for goodness of fit and their use in judging the fit of a single Bayesian model to the observed data. We focus on posterior predictive assessment, in a framework that also includes conditioning on auxiliary statistics. The Bayesian formulation facilitates the construction and calculation of a meaningful reference distribution not only for any (classical) statistic, but also for any parameter-dependent “statistic ” or discrepancy. The latter allows us to propose the realized discrepancy assessment of model fitness, which directly measures the true discrepancy between data and the posited model, for any aspect of the model which we want to explore. The computation required for the realized discrepancy assessment is a straightforward byproduct of the posterior simulation used for the original Bayesian analysis. We illustrate with three applied examples. The first example, which serves mainly to motivate the work, illustrates the difficulty of classical tests in assessing the fitness of a Poisson model to a positron emission tomography image that is constrained to be nonnegative. The second and third examples illustrate the details of the posterior predictive approach in two problems: estimation in a model with inequality constraints on the parameters, and estimation in a mixture model. In all three examples, standard test statistics (either a χ 2 or a likelihood ratio) are not pivotal: the difficulty is not just how to compute the reference distribution for the test, but that in the classical framework no such distribution exists, independent of the unknown model parameters. Key words and phrases: Bayesian p-value, χ 2 test, discrepancy, graphical assessment, mixture model, model criticism, posterior predictive p-value, prior predictive