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# Topic: Bayesian inference

###### In the News (Fri 24 May 19)

 Basics of Bayesian Inference Bayesian probability theory is a branch of mathematical probability theory that allows one to model uncertainty about the world and outcomes of interest by combining common-sense knowledge and observational evidence. Inference, or model evaluation, is the process of updating probabilities of outcomes based upon the relationships in the model and the evidence known about the situation at hand. When inference is performed on a model, there are various mathematical schemes for discovering which pieces of evidence would be the most important to discover. research.microsoft.com /adapt/MSBNx/msbnx/Basics_of_Bayesian_Inference.htm   (1245 words)

 Philosophy of Bayesian Inference   (Site not responding. Last check: 2007-11-07) Bayesian inference is an approach to statistics in which all forms of uncertainty are expressed in terms of probability. A Bayesian approach to a problem starts with the formulation of a model that we hope is adequate to describe the situation of interest. When Bayesian methods are too difficult to apply, I think we should use non-Bayesian methods, justified by non-Bayesian criteria, rather than pretend we are being Bayesian when we aren't. www.cs.toronto.edu /~radford/res-bayes-ex.html   (449 words)

 Implement Bayesian inference using PHP, Part 1 Bayesian inference techniques have been widely used in developing various types of Artifical Intelligence (AI) systems (for instance for text retrieval, classification, medical diagnosis, data mining, troubleshooting, and more), so this article series will be of interest to anyone interested in building intelligent Web applications. Bayesian inference is often put forth as a prescriptive framework for hypothesis testing. You will often find Bayesian inference sharing the same bed with a subjective view of probability in which the probability of a proposition is equated with one's subjective degree of belief in the proposition. www-128.ibm.com /developerworks/web/library/wa-bayes1   (5287 words)

 Implement Bayesian inference using PHP, Part 1 Bayesian inference techniques have been widely used in developing various types of Artifical Intelligence (AI) systems (for instance for text retrieval, classification, medical diagnosis, data mining, troubleshooting, and more), so this article series will be of interest to anyone interested in building intelligent Web applications. You will often find Bayesian inference sharing the same bed with a subjective view of probability in which the probability of a proposition is equated with one's subjective degree of belief in the proposition. The likelihood system of inference is preferred by many statisticians because you don't have to resort to the dubious practice of trying to estimate the prior probability of each hypothesis. www.ibm.com /developerworks/web/library/wa-bayes1   (5297 words)

 Bayesian inference In such cases, Bayesian inference still gives valuable insight, as it allows one to estimate the level of prior probability necessary to sustain a belief that the effect is illusory, even in the light of Nelson’s data. Bayesian inference thus strongly suggests that the growing consensus that ETS is a proven and major health risk is misplaced. In the Bayesian approach, however, the M and SD are the so-called "posterior" mean and standard deviation, formed by combining the raw values extracted from the data with "prior" values based on extant knowledge and insight about the effect under study. ourworld.compuserve.com /homepages/rajm/twooesef.htm   (7413 words)

 What is Bayesian Inference?   (Site not responding. Last check: 2007-11-07) Rather we are attempting to provide something for the layman who may know nothing at all about statistical inference in general, and Bayesian inference in particular. The difficulty with such quantifications, and what a Bayesian wants to avoid, is that they do not behave in ways that we feel that a valid quantification of uncertainty should. Others base the inference process on repeated sampling properties of the sampling process and attempt to construct a region that in repeated sampling contains the true values with a high probability or, as it is more appropriately called, confidence. www.bayesian.org /bayesian/whatis.html   (1358 words)

 An Introduction to Bayesian Networks and their Contemporary Applications Bayesian Networks are becoming an increasingly important area for research and application in the entire field of Artificial Intelligence. Bayesian networks are useful for both inferential exploration of previously undetermined relationships among variables as well as descriptions of these relationships upon discovery. Bayesian inference is useful because it allows the inference system to construct its own potential systems of meaning upon the data. www.niedermayer.ca /papers/bayesian/bayes.html   (3803 words)

 Amazon.ca: Learning Bayesian Networks: Books: Richard E. Neapolitan   (Site not responding. Last check: 2007-11-07) Bayesian networks are graphical structures for representing the probabilistic relationships among a large number of variables and for doing probabilistic inference with those variables. Before the advent of Bayesian networks, probabilistic inference depended on the use of Bayes' theorem, which entailed that the problems examined be relatively simple, due to the exponential space and time complexity that can arise in the application of this theorem. Inference in Bayesian networks is the topic of chapter 3, with Pearl's message-passing algorithm starting off the discussion for the case of discrete random variables. www.amazon.ca /Learning-Bayesian-Networks-Richard-Neapolitan/dp/0130125342   (2081 words)

 Implement Bayesian inference using PHP, Part 1 Bayesian inference techniques have been widely used in developing various types of Artifical Intelligence (AI) systems (for instance for text retrieval, classification, medical diagnosis, data mining, troubleshooting, and more), so this article series will be of interest to anyone interested in building intelligent Web applications. You will often find Bayesian inference sharing the same bed with a subjective view of probability in which the probability of a proposition is equated with one's subjective degree of belief in the proposition. The likelihood system of inference is preferred by many statisticians because you don't have to resort to the dubious practice of trying to estimate the prior probability of each hypothesis. www-106.ibm.com /developerworks/web/library/wa-bayes1   (5287 words)

 Bayesian Statistical Inference The following JavaScript performs the Bayesian inference by combining the sample information with prior information to estimate the mean of a normal population. In the Bayesian inference we have also prior information on This is expressed in terms of a probability distribution known as the prior distribution. home.ubalt.edu /ntsbarsh/Business-stat/otherapplets/BayesInfer.htm   (352 words)

 Technology Overview Autonomy's strength lies in advanced pattern-matching techniques (non-linear adaptive digital signal processing), rooted in the theories of Bayesian Inference and Claude Shannon's Principles of Information, that enable identification of the patterns that naturally occur in text, based on the usage and frequency of words or terms that correspond to specific concepts. Bayesian inference is a statistical inference named after Thomas Bayes, an 18th century English cleric whose work on mathematical probability was not published until after his death. An alternative, using the Bayesian approach, is to say that 100 consecutive heads are evidence that the coin is biased, for example, it has heads on both sides. www.autonomy.com /content/Technology   (1276 words)

 ISBA The International Society for Bayesian Analysis (ISBA) was founded in 1992 to promote the development and application of Bayesian analysis useful in the solution of theoretical and applied problems in science, industry and government. Joining ISBA (or renewing your membership) is a good way to learn more about Bayesian Analysis and contribute to its advancement. Bayesian inference provides a logical, quantitative framework for this process. www.bayesian.org   (785 words)

 STAT 295 Home Page Bayesian inference is a powerful and increasingly popular statistical approach, which allows one to deal with complex problems in a conceptually simple and unified way. Bayesian inference in non-Gaussian cases, e.g., Poisson, Cauchy, and arbitrary distributions. Note particularly the first five items in his Bayesian Reprints page, which are very nice tutorials on practical application of Bayesian inference. quasar.as.utexas.edu /stat295.html   (1175 words)

 Statistical Modeling, Causal Inference, and Social Science: Expanding concepts of Bayesian inference It is an important tradition in Bayesian statistics to formalize potentially vague ideas, starting with the axiomatic treatment of prior information and decision making from the 1920s through the 1950s. In the 1960s and 1970s, it was recognized that Bayesian inference for a sequence of parameters could have better statistical properties if data-dependent prior distributions were allowed. For example, randomized data collection is hard to justify under the usual Bayesian framework, but, in the context of defining a data-collection scheme, randomization is in fact the only way to select a sample without reference to covariates. www.stat.columbia.edu /~cook/movabletype/archives/2005/04/expanding_conce.html   (1118 words)

 Tom Loredo's Bayesian Reprints   (Site not responding. Last check: 2007-11-07) The talk begins with a survey/tutorial on Bayesian inference, and continues with a description of two astrophysical applications: the "on/off" problem (Poisson counting process with uncertain background), and analysis of neutrino data from SN 1987A. Five lectures on basic Bayesian inference with applications in astronomy and astrophysics, given by invitation at the Center for Interdisciplinary Plasma Science of the Max Planck Institute for Plasma Physics in Garching, Germany, October 2002. The original analyses used Bayesian methods to find credible regions for the two density parameters (due to mass and to a possible cosmological constant), but used an incorrect summary of the evidence for a nonzero cosmological constant (a tail probability rather than a Bayes factor or odds ratio). astrosun.tn.cornell.edu /staff/loredo/bayes/tjl.html   (1544 words)

 Implement Bayesian inference using PHP: Part 3 Learn how Bayesian and conditional probability concepts are applicable to both building classifier systems and analyzing the accuracy of their output. Bayesian and conditional probability concepts are applicable to both building classifier systems and analyzing the accuracy of their output. Explore the Bayesian approach to statistics at a level suitable for final year undergraduate and masters students in Bayesian Methods (Cambridge University Press; 1999), by Leonard and Hsu. www-106.ibm.com /developerworks/web/library/wa-bayes3   (4034 words)

 Implement Bayesian inference using PHP: Part 2 Bayes inference methods are distinguished from other inference methods (such as least squares, maximum likelihood, maximum entrophy, minimum description length) by the fact that a Bayes inference method can be applied to every type of problem in this list and often represents the optimal method to use. This discussion of maximum likelihood estimation is relevant to Bayesian inference because it demonstrates another technique that can be used to compute the likelihood terms in Bayes equation. Bayesian estimators and MLE estimators differ in their small sample behavior as estimators. www-128.ibm.com /developerworks/web/library/wa-bayes2   (5017 words)

 Bayesian Statistics The research area of inference about unknown functions deals with such problems, where we wish to make inference about a function but do not wish to make restrictive assumptions about its form. Research into Bayesian inference for unknown functions at Sheffield has principally modeled the function in question as a Gaussian process, which can be thought of as an infinite-dimensional multivariate normal distribution. Several current areas of application are described in the research page concerning inference about unknown functions, and there are opportunities to apply these methods to other kinds of unknown function arising in a variety of fields. www.shef.ac.uk /pas/research/clusters/bayesian/unknownfns.html   (1230 words)

 BIPS: Bayesian Inference for the Physical Sciences Genz is a leader in the development of new algorithms for numerical computation of mulitiple integrals; his recent research focuses on integrals that arise in Bayesian inference. BUGS is a program for Bayesian inference using the Gibbs Sampler Markov chain Monte Carlo technique produced by the Biostatistics Unit of the Medical Research Council of the United Kingdom. Bayesian content is virtually nonexistant, but it's a useful reference for its description of current statistical practice in high energy physics. www.astro.cornell.edu /staff/loredo/bayes   (2872 words)

 BIPS: Bayesian Inference for the Physical Sciences   (Site not responding. Last check: 2007-11-07) This is an undergraduate text on Bayesian inference written for physical scientists by Devinder Sivia, and published by Oxford University Press. BUGS is a program for Bayesian inference using the Gibbs Sampler Markov chain Monte Carlo technique produced by the Biostatistics Unit of the Medical Research Council of the United Kingdom. Bayesian content is virtually nonexistant, but it's a useful reference for its description of current statistical practice in high energy physics. astrosun.tn.cornell.edu /staff/loredo/bayes   (2872 words)

 SYST/STAT 664: Bayesian Inference and Decision Theory Bayesian statistics is a scientifically justifiable way to integrate informed expert judgment with empirical data. For a Bayesian, statistical inference cannot be treated entirely independently of the context of the decisions that will be made on the basis of the inferences. Bayesian networks, influence diagrams, and general graphical models are introduced for representing complex probability and decision models by specifying modular components. ite.gmu.edu /~klaskey/SYST664/SYST664.html   (819 words)

 Citations: Expectation Propagation for approximate Bayesian inference - Minka (ResearchIndex) Minka, "Expectation propagation for approximate Bayesian inference," in Proceedings of UAI-2001. Thomas Minks, "Expectation propagation for approximate Bayesian inference," in Proceedings of the 17th Annual Conference on Uncertainty in Artificial Intelligence (UAI 2001. Minka, T. Expectation propagation for approximate Bayesian inference, Proceedings of the 17th Conference on Uncertainty in Artificial Intelligence, 362--369, 2001. citeseer.ist.psu.edu /context/1745717/0   (2043 words)

 Frequently asked questions about Bayesian methods for neural networks You may also be interested in Radford's description of the philosophy of Bayesian inference and the giant comp.ai.neural-nets FAQ for which Radford Neal has written a page on Bayesian neural net learning. In contrast, in Bayesian complexity control methods (1) we use the evidence which is not noisy a functions of the parameters; (2) we can find the GRADIENT of the `evidence' with respect to the parameters, so allowing search in high-dimensional complexity control spaces. Bayesian methods can be used to optimize hyperparameters (by maximizing the evidence implicitly); and other model properties. www.inference.phy.cam.ac.uk /mackay/Bayes_FAQ.html   (13525 words)

 Tom Minka's HomePage I work in the field of Bayesian statistical inference, and I develop efficient algorithms for use in machine learning, computer vision, text retrieval, and data mining. My goal is to make Bayesian inference a standard tool for processing information. What makes Bayesian inference special is that it takes into account all possible states of nature, not just the one that is the most likely. research.microsoft.com /~minka   (254 words)

 CRAN Task View: Bayesian Inference   (Site not responding. Last check: 2007-11-07) Applied researchers interested in Bayesian statistics are increasingly attracted to R because of the ease of which one can code algorithms to sample from posterior distributions as well as the significant number of packages contributed to the Comprehensive R Archive Network (CRAN) that provide tools for Bayesian inference. BACCO is an R bundle for Bayesian analysis of random functions. The tgp package implements Bayesian treed Gaussian process models: a spaptial modeling and regression package providing fully Bayesian MCMC posterior inference for models ranging from the simple linear model, to nonstationary treed Gaussian process, and others in between. cran.r-project.org /src/contrib/Views/Bayesian.html   (1213 words)

 LLNL Engineering Systems and Decision Sciences Technology Bayesian Inference This effort is focused upon the development of a new methodology for combining disparate types of observations and process simulations to produce a consolidated body of knowledge indicating those configurations and system parameter values which are most consistent with the available data and models. Bayesian inferencing and a Metropolis search algorithm form the basis for the approach. The Bayesian inferencing is driven by forward process models that predict data values, such as temperature or electrical voltage, for direct comparison to measured field values. www-eng.llnl.gov /sys_dec/sys_dec_bayesian.html   (291 words)

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