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Showing papers on "Bayesian probability published in 1998"


Proceedings Article
24 Jul 1998
TL;DR: Several algorithms designed for collaborative filtering or recommender systems are described, including techniques based on correlation coefficients, vector-based similarity calculations, and statistical Bayesian methods, to compare the predictive accuracy of the various methods in a set of representative problem domains.
Abstract: Collaborative filtering or recommender systems use a database about user preferences to predict additional topics or products a new user might like. In this paper we describe several algorithms designed for this task, including techniques based on correlation coefficients, vector-based similarity calculations, and statistical Bayesian methods. We compare the predictive accuracy of the various methods in a set of representative problem domains. We use two basic classes of evaluation metrics. The first characterizes accuracy over a set of individual predictions in terms of average absolute deviation. The second estimates the utility of a ranked list of suggested items. This metric uses an estimate of the probability that a user will see a recommendation in an ordered list. Experiments were run for datasets associated with 3 application areas, 4 experimental protocols, and the 2 evaluation metr rics for the various algorithms. Results indicate that for a wide range of conditions, Bayesian networks with decision trees at each node and correlation methods outperform Bayesian-clustering and vector-similarity methods. Between correlation and Bayesian networks, the preferred method depends on the nature of the dataset, nature of the application (ranked versus one-by-one presentation), and the availability of votes with which to make predictions. Other considerations include the size of database, speed of predictions, and learning time.

4,557 citations


Journal ArticleDOI
TL;DR: The problem of updating a structural model and its associated uncertainties by utilizing dynamic response data is addressed using a Bayesian statistical framework that can handle the inherent ill-conditioning and possible nonuniqueness in model updating applications.
Abstract: The problem of updating a structural model and its associated uncertainties by utilizing dynamic response data is addressed using a Bayesian statistical framework that can handle the inherent ill-conditioning and possible nonuniqueness in model updating applications. The objective is not only to give more accurate response predictions for prescribed dynamic loadings but also to provide a quantitative assessment of this accuracy. In the methodology presented, the updated (optimal) models within a chosen class of structural models are the most probable based on the structural data if all the models are equally plausible a priori. The prediction accuracy of the optimal structural models is given by also updating probability models for the prediction error. The precision of the parameter estimates of the optimal structural models, as well as the precision of the optimal prediction-error parameters, can be examined. A large-sample asymptotic expression is given for the updated predictive probability distribution of the uncertain structural response, which is a weighted average of the prediction probability distributions for each optimal model. This predictive distribution can be used to make model predictions despite possible nonuniqueness in the optimal models.

1,235 citations


Journal ArticleDOI
TL;DR: In this article, the authors develop methods to introduce prior information in both reduced-form and structural VAR models without introducing substantial new computational burdens, which makes it feasible to use a single, large dynamic framework (for example, twenty-variable models) for tasks of policy projections.
Abstract: If dynamic multivariate models are to be used to guide decisionmaking, it is important that probability assessments of forecasts or policy projections be provided. When identified Bayesian vector autoregression (VAR) models are presented with error bands in the existing literature, both conceptual and numerical problems have not been dealt with in an internally consistent way. In this paper, the authors develop methods to introduce prior information in both reduced-form and structural VAR models without introducing substantial new computational burdens. Their approach makes it feasible to use a single, large dynamic framework (for example, twenty-variable models) for tasks of policy projections. Copyright 1998 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

977 citations


Journal ArticleDOI
TL;DR: A Bayesian approach for finding classification and regression tree (CART) models by having the prior induce a posterior distribution that will guide the stochastic search toward more promising CART models.
Abstract: In this article we put forward a Bayesian approach for finding classification and regression tree (CART) models. The two basic components of this approach consist of prior specification and stochastic search. The basic idea is to have the prior induce a posterior distribution that will guide the stochastic search toward more promising CART models. As the search proceeds, such models can then be selected with a variety of criteria, such as posterior probability, marginal likelihood, residual sum of squares or misclassification rates. Examples are used to illustrate the potential superiority of this approach over alternative methods.

749 citations


Proceedings Article
24 Jul 1998
TL;DR: This paper extends Structural EM to deal directly with Bayesian model selection and proves the convergence of the resulting algorithm and shows how to apply it for learning a large class of probabilistic models, including Bayesian networks and some variants thereof.
Abstract: In recent years there has been a flurry of works on learning Bayesian networks from data. One of the hard problems in this area is how to effectively learn the structure of a belief network from incomplete data--that is, in the presence of missing values or hidden variables. In a recent paper, I introduced an algorithm called Structural EM that combines the standard Expectation Maximization (EM) algorithm, which optimizes parameters, with structure search for model selection. That algorithm learns networks based on penalized likelihood scores, which include the BIC/MDL score and various approximations to the Bayesian score. In this paper, I extend Structural EM to deal directly with Bayesian model selection. I prove the convergence of the resulting algorithm and show how to apply it for learning a large class of probabilistic models, including Bayesian networks and some variants thereof.

637 citations


Proceedings ArticleDOI
David McAllester1
24 Jul 1998
TL;DR: The PAC-Bayesian theorems given here apply to an arbitrary prior measure on an arbitrary concept space and provide an alternative to the use of VC dimension in proving PAC bounds for parameterized concepts.
Abstract: This paper gives PAC guarantees for “Bayesian” algorithms—algorithms that optimize risk minimization expressions involving a prior probability and a likelihood for the training data. PAC-Bayesian algorithms are motivated by a desire to provide an informative prior encoding information about the expected experimental setting but still having PAC performance guarantees over all IID settings. The PAC-Bayesian theorems given here apply to an arbitrary prior measure on an arbitrary concept space. These theorems provide an alternative to the use of VC dimension in proving PAC bounds for parameterized concepts.

549 citations


Book ChapterDOI
01 Jan 1998
TL;DR: Model building and data analysis in the biological sciences somewhat presupposes that the person has some advanced education in the quantitative sciences, and statistics in particular, and this requirement also implies that a person has substantial knowledge of statistical hypothesis-testing approaches.
Abstract: Model building and data analysis in the biological sciences somewhat presupposes that the person has some advanced education in the quantitative sciences, and statistics in particular This requirement also implies that a person has substantial knowledge of statistical hypothesis-testing approaches Such people, including ourselves over the past several years, often find it difficult to understand the information-theoretic approach, only because it is conceptually so very different from the testing approach that is so familiar Relatively speaking, the concepts and practical use of the information-theoretic approach are much simpler than those of statistical hypothesis testing, and very much simpler than some of the various Bayesian approaches to data analysis (eg, Laud and Ibrahim 1995 and Carlin and Chib 1995)

446 citations


Proceedings Article
01 Jul 1998
TL;DR: This paper extends Watkins' Q-learning by maintaining and propagating probability distributions over the Q-values and establishes the convergence properties of the algorithm, which can exhibit substantial improvements over other well-known model-free exploration strategies.
Abstract: A central problem in learning in complex environments is balancing exploration of untested actions against exploitation of actions that are known to be good The benefit of exploration can be estimated using the classical notion of Value of Information-the expected improvement in future decision quality that might arise from the information acquired by exploration Estimating this quantity requires an assessment of the agent's uncertainty about its current value estimates for states In this paper, we adopt a Bayesian approach to maintaining this uncertain information We extend Watkins' Q-learning by maintaining and propagating probability distributions over the Q-values These distributions are used to compute a myopic approximation to the value of information for each action and hence to select the action that best balances exploration and exploitation We establish the convergence properties of our algorithm and show experimentally that it can exhibit substantial improvements over other well-known model-free exploration strategies

443 citations


Journal ArticleDOI
TL;DR: A stochastic search form of classification and regression tree (CART) analysis is proposed, motivated by a Bayesian model and an approximation to a probability distribution over the space of possible trees is explored.
Abstract: A stochastic search form of classification and regression tree (CART) analysis (Breiman et al., 1984) is proposed, motivated by a Bayesian model. An approximation to a probability distribution over the space of possible trees is explored using reversible jump Markov chain Monte Carlo methods (Green, 1995).

325 citations


Proceedings Article
Christopher M. Bishop1
01 Dec 1998
TL;DR: This paper uses probabilistic reformulation as the basis for a Bayesian treatment of PCA to show that effective dimensionality of the latent space (equivalent to the number of retained principal components) can be determined automatically as part of the Bayesian inference procedure.
Abstract: The technique of principal component analysis (PCA) has recently been expressed as the maximum likelihood solution for a generative latent variable model. In this paper we use this probabilistic reformulation as the basis for a Bayesian treatment of PCA. Our key result is that effective dimensionality of the latent space (equivalent to the number of retained principal components) can be determined automatically as part of the Bayesian inference procedure. An important application of this framework is to mixtures of probabilistic PCA models, in which each component can determine its own effective complexity.

319 citations


Journal ArticleDOI
TL;DR: A Bayesian-based methodology is presented which automatically penalizes overcomplex models being fitted to unknown data and is able to select an "optimal" number of components in the model and so partition data sets.
Abstract: A Bayesian-based methodology is presented which automatically penalizes overcomplex models being fitted to unknown data. We show that, with a Gaussian mixture model, the approach is able to select an "optimal" number of components in the model and so partition data sets. The performance of the Bayesian method is compared to other methods of optimal model selection and found to give good results. The methods are tested on synthetic and real data sets.

Journal ArticleDOI
TL;DR: The current article develops the theoretical framework of variants of the origin-destination flow problem and introduces Bayesian approaches to analysis and inference.
Abstract: We study Bayesian models and methods for analysing network traffic counts in problems of inference about the traffic intensity between directed pairs of origins and destinations in networks. This is a class of problems very recently discussed by Vardi in a 1996 JASA article and is of interest in both communication and transportation network studies. The current article develops the theoretical framework of variants of the origin-destination flow problem and introduces Bayesian approaches to analysis and inference. In the first, the so-called fixed routing problem, traffic or messages pass between nodes in a network, with each message originating at a specific source node, and ultimately moving through the network to a predetermined destination node. All nodes are candidate origin and destination points. The framework assumes no travel time complications, considering only the number of messages passing between pairs of nodes in a specified time interval. The route count, or route flow, problem is ...

Journal ArticleDOI
TL;DR: An approach to keyhole plan recognition which uses a dynamic belief (Bayesian) network to represent features of the domain that are needed to identify users' plans and goals and shows promise for efficient goal prediction in domains which have similar features to those of this domain.
Abstract: We present an approach to keyhole plan recognition which uses a dynamic belief (Bayesian) network to represent features of the domain that are needed to identify users‘ plans and goals. The application domain is a Multi-User Dungeon adventure game with thousands of possible actions and locations. We propose several network structures which represent the relations in the domain to varying extents, and compare their predictive power for predicting a user‘s current goal, next action and next location. The conditional probability distributions for each network are learned during a training phase, which dynamically builds these probabilities from observations of user behaviour. This approach allows the use of incomplete, sparse and noisy data during both training and testing. We then apply simple abstraction and learning techniques in order to speed up the performance of the most promising dynamic belief networks without a significant change in the accuracy of goal predictions. Our experimental results in the application domain show a high degree of predictive accuracy. This indicates that dynamic belief networks in general show promise for predicting a variety of behaviours in domains which have similar features to those of our domain, while reduced models, obtained by means of learning and abstraction, show promise for efficient goal prediction in such domains.

Journal ArticleDOI
TL;DR: In this article, a Bayesian dynamic latent factor model for a vector of data describing the Iowa economy is proposed, and posterior distributions of parameters and the latent factor are analyzed by Markov Chain Monte Carlo methods, and coincident and leading indicators are given by posterior mean values of current and predictive distributions for the latent factors.
Abstract: This paper designs and implements a Bayesian dynamic latent factor model for a vector of data describing the Iowa economy. Posterior distributions of parameters and the latent factor are analyzed by Markov Chain Monte Carlo methods, and coincident and leading indicators are given by posterior mean values of current and predictive distributions for the latent factor.


Journal ArticleDOI
TL;DR: In this paper, a case study of the application of the Bayesian strategy to inversion of surface seismic field data is presented, where the authors use Bayes theorem to combine this probability with the data misfit function into a final a posteriori probability density reflecting both data fit and model reasonableness.
Abstract: The goal of geophysical inversion is to make quantitative inferences about the Earth from remote observations. Because the observations are finite in number and subject to uncertainty, these inferences are inherently probabilistic. A key step is to define what it means for an Earth model to fit the data. This requires estimation of the uncertainties in the data, both those due to random noise and those due to theoretical errors. But the set of models that fit the data usually contains unrealistic models; i.e., models that violate our a priori prejudices, other data, or theoretical considerations. One strategy for eliminating such unreasonable models is to define an a priori probability density on the space of models, then use Bayes theorem to combine this probability with the data misfit function into a final a posteriori probability density reflecting both data fit and model reasonableness. We show here a case study of the application of the Bayesian strategy to inversion of surface seismic field data. Assuming that all uncertainties can be described by multidimensional Gaussian probability densities, we incorporate into the calculation information about ambient noise, discretization errors, theoretical errors, and a priori information about the set of layered Earth models derived from in situ petrophysical measurements. The result is a probability density on the space of models that takes into account all of this information. Inferences on model parameters can be derived by integration of this function. We begin by estimating the parameters of the Gaussian probability densities assumed to describe the data and model uncertainties. These are combined via Bayes theorem. The a posteriori probability is then optimized via a nonlinear conjugate gradient procedure to find the maximum a posteriori model. Uncertainty analysis is performed by making a Gaussian approximation of the a posteriori distribution about this peak model. We present the results of this analysis in three different forms: the maximum a posteriori model bracketed by one standard deviation error bars, pseudo-random simulations of the a posteriori probability (showing the range of typical subsurface models), and marginals of this probability at selected depths in the subsurface. The models we compute are consistent both with the surface seismic data and the borehole measurements, even though the latter are well below the resolution of the former. We also contrast the Bayesian maximum a posteriori model with the Occam model, which is the smoothest model that fits the surface seismic data alone.

Journal ArticleDOI
TL;DR: In this paper, the authors investigate both proper and improper cases through a series of examples and show that in the case of improper priors, the analysis is problematic, i.e., their marginal prior and posterior distributions are identical.
Abstract: A Bayesian analysis of a nonidentified model is always possible if a proper prior on all the parameters is specified. There is, however, no Bayesian free lunch. The “price” is that there exist quantities about which the data are uninformative, i.e., their marginal prior and posterior distributions are identical. In the case of improper priors the analysis is problematic—resulting posteriors can be improper. This study investigates both proper and improper cases through a series of examples.

Journal ArticleDOI
TL;DR: A tutorial on Bayesian parameter estimation especially relevant to PRA is presented, which summarizes the philosophy behind these methods, approaches for constructing likelihood functions and prior distributions, some simple but realistic examples, and a variety of cautions and lessons regarding practical applications.

Journal ArticleDOI
TL;DR: In this paper, the hierarchical Bayes procedure is implemented via Markov chain Monte Carlo integration techniques for a unified analysis of both discrete and continuous data and a general theorem is provided that ensures the propriety of posteriors under diffuse priors.
Abstract: Bayesian methods have been used quite extensively in recent years for solving small-area estimation problems. Particularly effective in this regard has been the hierarchical or empirical Bayes approach, which is especially suitable for a systematic connection of local areas through models. However, the development to date has mainly concentrated on continuous-valued variates. Often the survey data are discrete or categorical, so that hierarchical or empirical Bayes techniques designed for continuous variates are inappropriate. This article considers hierarchical Bayes generalized linear models for a unified analysis of both discrete and continuous data. A general theorem is provided that ensures the propriety of posteriors under diffuse priors. This result is then extended to the case of spatial generalized linear models. The hierarchical Bayes procedure is implemented via Markov chain Monte Carlo integration techniques. Two examples (one featuring spatial correlation structure) are given to illu...

Journal ArticleDOI
TL;DR: In this paper, a priori information about the parameters may be used in the formulation of likelihood functions and maximum-likelihood objective functions for multifrequency data on a vertical array, and it is suggested that importance sampling based on a directed Monte Carlo method such as genetic algorithms is the preferred method.
Abstract: Inversion methods are applied in ocean acoustics to infer parameters which characterize the environment. The objective of this paper is to provide such estimates, and means of evaluating the inherent uncertainty of the parameter estimates. In a Bayesian approach, the result of inversion is the a posteriori probability density for the estimated parameters, from which all information such as mean, higher moments, and marginal distributions can be extracted. These are multidimensional integrals of the a posteriori probability density, which are complicated to evaluate for many parameters. Various sampling options are examined and it is suggested that “importance sampling” based on a directed Monte Carlo method, such as genetic algorithms, is the preferred method. The formulation of likelihood functions and maximum-likelihood objective functions for multifrequency data on a vertical array is discussed. A priori information about the parameters may be used in the formulation. Shallow-water acoustic data obtained at several frequencies using a vertical array is used to illustrate the applicability of the technique.

Journal ArticleDOI
TL;DR: This paper suggests several item selection criteria for adaptive testing which are all based on the use of the true posterior, and some of the statistical properties of the ability estimator produced by these criteria are discussed and empirically characterized.
Abstract: Owen (1975) proposed an approximate empirical Bayes procedure for item selection in computerized adaptive testing (CAT). The procedure replaces the true posterior by a normal approximation with closed-form expressions for its first two moments. This approximation was necessary to minimize the computational complexity involved in a fully Bayesian approach but is no longer necessary given the computational power currently available for adaptive testing. This paper suggests several item selection criteria for adaptive testing which are all based on the use of the true posterior. Some of the statistical properties of the ability estimator produced by these criteria are discussed and empirically characterized.

Journal ArticleDOI
TL;DR: In this article, the conceptual basis for Bayesian statistical estimation is reviewed and set in the context of fisheries stock assessment, and the use of Bayesian methods is illustrated by fitting a logistic model to relative abundance indices for Namibian hake (Merlucius capensis and M. paradoxus) and presenting a decision analysis of alternative harvest policy options.
Abstract: Bayesian statistical methods have recently been combined with conventional methods for fisheries stock assessment (e.g. catch-age analysis) to provide a conceptually elegant approach for providing fishery management advice under uncertainty. Uncertainties in the advice provided can be conveyed using posterior probability distributions (or “posteriors”) for the potential outcomes of each policy option. Posteriors can be estimated using data (e.g. catch-age data and relative abundance indices) for the fish population of interest and prior probability distributions for population model parameters (e.g. stock-recruit function parameters) based on data from similar fish populations. Despite growing interest, Bayesian methods remain accessible to relatively few. To increase the accessibility of these methods, the conceptual basis for Bayesian statistical estimation is reviewed and set in the context of fisheries stock assessment. The use of Bayesian methods is illustrated by fitting a logistic model to relative abundance indices for Namibian hake (Merlucius capensis and M. paradoxus) and presenting a decision analysis of alternative harvest policy options. Some alternative approaches are outlined for constructing prior and posterior probability distributions and some recent applications in fisheries. Some of the problems that can be encountered while implementing Bayesian methods are also discussed.

Proceedings Article
01 Jan 1998
TL;DR: In this paper, the authors proposed a Bayesian approach to extract structural information from remote-sensing images by selecting from a library of priori models those which best explain the structures within an image.
Abstract: Automatic interpretation of remote-sensing (RS) images and the growing interest for query by image content from large remote-sensing image archives rely on the ability and robustness of information extraction from observed data. In Parts I and II of this article, we turn the attention to the modern Bayesian way of thinking and introduce a pragmatic approach to extract structural information from RS images by selecting from a library of priori models those which best explain the structures within an image. Part I introduces the Bayesian approach and defines the information extraction as a two-level procedure: 1) model fitting, which is the incertitude alleviation over the model parameters, and 2) model selection, which is the incertitude alleviation over the class of models. The superiority of the Bayesian results is commented from an information theoretical perspective. The theoretical assay concludes with the proposal of a new systematic method for scene understanding from RS images: search for the scene that best explains the observed data. The method is demonstrated for high accuracy restoration of synthetic aperture radar (SAR) images with emphasis on new optimization algorithms for simultaneous model selection and parameter estimation. Examples are given for three families of Gibbs random fields (GRF) used as prior model libraries. Part II expands in detail on the information extraction using GRF's at one and at multiple scales. Based on the Bayesian approach, a new method for optimal joint scale and model selection is demonstrated. Examples are given using a nested family of GRF's utilized as prior models for information extraction with applications both to SAR and optical images.

Journal ArticleDOI
TL;DR: The paper studies the construction of confidence values and examines to what extent they approximate frequentist p-values and Bayesian a posteriori probabilities, and derives more accurate confidence levels using both frequentist and objective Bayesian approaches.
Abstract: In the problem of regions, we wish to know which one of a discrete set of possibilities applies to a continuous parameter vector. This problem arises in the following way: we compute a descriptive statistic from a set of data, notice an interesting feature and wish to assign a confidence level to that feature. For example, we compute a density estimate and notice that the estimate is bimodal. What confidence can we assign to bimodality? A natural way to measure confidence is via the bootstrap: we compute our descriptive statistic on a large number of bootstrap data sets and record the proportion of times that the feature appears. This seems like a plausible measure of confidence for the feature. The paper studies the construction of such confidence values and examines to what extent they approximate frequentist $p$-values and Bayesian a posteriori probabilities. We derive more accurate confidence levels using both frequentist and objective Bayesian approaches. The methods are illustrated with a number of examples, including polynomial model selection and estimating the number of modes of a density.

Journal ArticleDOI
TL;DR: An algorithm, the 'Bayes block aligner', which bypasses the requirement of a fixed set of parameter settings, and returns the Bayesian posterior probability for the number of gaps and for the scoring matrices in any series of interest.
Abstract: The selection of a scoring matrix and gap penalty parameters continues to be an important problem in sequence alignment. We describe here an algorithm, the 'Bayes block aligner, which bypasses this requirement. Instead of requiring a fixed set of parameter settings, this algorithm returns the Bayesian posterior probability for the number of gaps and for the scoring matrices in any series of interest. Furthermore, instead of returning the single best alignment for the chosen parameter settings, this algorithm returns the posterior distribution of all alignments considering the full range of gapping and scoring matrices selected, weighing each in proportion to its probability based on the data. We compared the Bayes aligner with the popular Smith-Waterman algorithm with parameter settings from the literature which had been optimized for the identification of structural neighbors, and found that the Bayes aligner correctly identified more structural neighbors. In a detailed examination of the alignment of a pair of kinase and a pair of GTPase sequences, we illustrate the algorithm's potential to identify subsequences that are conserved to different degrees. In addition, this example shows that the Bayes aligner returns an alignment-free assessment of the distance between a pair of sequences.

01 Jan 1998
TL;DR: Reconstructions of phantom data show that the3D Bayesian method can achieve improved FWHM resolution and contrast recovery ratios at matched background noise levels compared to both the 3D reprojection method and an OSEM method based on the shifted-Poisson model.

Journal ArticleDOI
TL;DR: A very efficient Markov chain Monte Carlo scheme is suggested for inference and prediction with fixed-architecture feedforward neural networks and extended to the variable architecture case, providing a data-driven procedure to identify sensible architectures.
Abstract: Stemming from work by Buntine and Weigend (1991) and MacKay (1992), there is a growing interest in Bayesian analysis of neural network models. Although conceptually simple, this problem is computationally involved. We suggest a very efficient Markov chain Monte Carlo scheme for inference and prediction with fixed-architecture feedforward neural networks. The scheme is then extended to the variable architecture case, providing a data-driven procedure to identify sensible architectures.

Journal ArticleDOI
TL;DR: In this paper, a limiting procedure that provides a solid justification for the use of Bayes factor with intrinsic priors for model comparison is presented for nested and non-nested models.
Abstract: Improper priors typically arise in default Bayesian estimation problems. In the Bayesian approach to model selection or hypothesis testing, the main tool is the Bayes factor. When improper priors for the parameters appearing in the models are used, the Bayes factor is not well defined. The intrinsic Bayes factor introduced by Berger and Pericchi is an interesting method for overcoming that difficulty. That method is of particular interest as a means for generating proper prior distributions (intrinsic priors) for model comparison from the improper priors typically used in estimation. The goal of this article is to develop a limiting procedure that provides a solid justification for the use of Bayes factor with intrinsic priors. The procedure is formalized and discussed for nested and nonnested models. Illustrations and comparisons with other approximations to Bayes factors, such as the Bayesian information criterion of Schwarz and the fractional Bayes factor of O'Hagan are provided.

01 Feb 1998
TL;DR: In reviewing a large number of previously published phenomena, it is suggested that the Bayesian estimator predicts a wide range of psychophysical results, and suggests that the seemingly complex set of illusions arise from a single computational strategy that is optimal under reasonable assumptions.
Abstract: In order to estimate the motion of an object, the visual system needs to combine multiple local measurements, each of which carries some degree of ambiguity. We present a model of motion perception whereby measurements from di erent image regions are combined according to a Bayesian estimator | the estimated motion maximizes the posterior probability assuming a prior favoring slow and smooth velocities. In reviewing a large number of previously published phenomena we nd that the Bayesian estimator predicts a wide range of psychophysical results. This suggests that the seemingly complex set of illusions arise from a single computational strategy that is optimal under reasonable assumptions. Copyright c Massachusetts Institute of Technology, 1998 This report describes research done at the Center for Biological and Computational Learning and the Department of Brain and Cognitive Sciences of the Massachusetts Institute of Technology. Support for the Center is provided in part by a grant from the National Science Foundation under contract ASC{9217041. The work was also supported by NEI R01 EY11005 to E. H. Adelson

Journal ArticleDOI
TL;DR: A Bayesian model is presented, and a decision-theoretic procedure for finding the optimal doses for each of a series of cohorts of subjects is derived, which is flexible and can easily be conducted using standard statistical software.
Abstract: Early-phase clinical trials, conducted to determine the appropriate dose of an experimental drug to take forward to later trials, are considered. The objective is to find the dose associated with some low probability of an adverse event. A Bayesian model is presented, and a decision-theoretic procedure for finding the optimal doses for each of a series of cohorts of subjects is derived. The procedure is flexible and can easily be conducted using standard statistical software. The results of simulations investigating the properties of the procedure are presented.