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260
Bayesian conditionalisation and the principle of minimum information.
 The British Journal for the Philosophy of Science,
, 1980
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Continuous latent variable models for dimensionality reduction and sequential data reconstruction
, 2001
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SetBased Bayesianism
, 1992
"... . Problems for strict and convex Bayesianism are discussed. A setbased Bayesianism generalizing convex Bayesianism and intervalism is proposed. This approach abandons not only the strict Bayesian requirement of a unique realvalued probability function in any decisionmaking context but also the re ..."
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Cited by 30 (0 self)
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. Problems for strict and convex Bayesianism are discussed. A setbased Bayesianism generalizing convex Bayesianism and intervalism is proposed. This approach abandons not only the strict Bayesian requirement of a unique realvalued probability function in any decisionmaking context but also the requirement of convexity for a setbased representation of uncertainty. Levi's Eadmissibility decision criterion is retained and is shown to be applicable in the nonconvex case. Keywords: Uncertainty, decisionmaking, maximum entropy, Bayesian methods. 1. Introduction. The reigning philosophy of uncertainty representation is strict Bayesianism. One of its central principles is that an agent must adopt a single, realvalued probability function over the events recognized as relevant to a given problem. Prescriptions for defining such a function for a given agent in a given situation range from the extreme personalism of deFinetti (1964, 1974) and Savage (1972) to the objective Bayesianism of...
Prior Information and Uncertainty in Inverse Problems
, 2001
"... Solving any inverse problem requires understanding the uncertainties in the data to know what it means to fit the data. We also need methods to incorporate dataindependent prior information to eliminate unreasonable models that fit the data. Both of these issues involve subtle choices that may ..."
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Solving any inverse problem requires understanding the uncertainties in the data to know what it means to fit the data. We also need methods to incorporate dataindependent prior information to eliminate unreasonable models that fit the data. Both of these issues involve subtle choices that may significantly influence the results of inverse calculations. The specification of prior information is especially controversial. How does one quantify information? What does it mean to know something about a parameter a priori? In this tutorial we discuss Bayesian and frequentist methodologies that can be used to incorporate information into inverse calculations. In particular we show that apparently conservative Bayesian choices, such as representing interval constraints by uniform probabilities (as is commonly done when using genetic algorithms, for example) may lead to artificially small uncertainties. We also describe tools from statistical decision theory that can be used to...
Application of Bayesian inference to fMRI data analysis
 IEEE Transactions on Medical Imaging
, 1999
"... Abstract—The methods of Bayesian statistics are applied to the analysis of fMRI data. Three specific models are examined. The first is the familiar linear model with white Gaussian noise. In this section, the Jeffreys ’ Rule for noninformative prior distributions is stated and it is shown how the po ..."
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Abstract—The methods of Bayesian statistics are applied to the analysis of fMRI data. Three specific models are examined. The first is the familiar linear model with white Gaussian noise. In this section, the Jeffreys ’ Rule for noninformative prior distributions is stated and it is shown how the posterior distribution may be used to infer activation in individual pixels. Next, linear timeinvariant (LTI) systems are introduced as an example of statistical models with nonlinear parameters. It is shown that the Bayesian approach can lead to quite complex bimodal distributions of the parameters when the specific case of a delta function response with a spatially varying delay is analyzed. Finally, a linear model with autoregressive noise is discussed as an alternative to that with uncorrelated white Gaussian noise. The analysis isolates those pixels that have significant temporal correlation under the model. It is shown that the number of pixels that have a significantly large autoregression parameter is dependent on the terms used to account for confounding effects. Index Terms — Autoregressive modeling, Bayesian statistics, functional MRI data analysis, linear timeinvariant systems.
Decision Making with Belief Functions: Compatibility and Incompatibility with the SureThing Principle
 JOURNAL OF RISK AND UNCERTAINTY, 8:255271 (1994) 9 1994
, 1994
"... This article studies situations in which information is ambiguous and only part of it can be probabilized. It is shown that the information can be modeled through belief functions if and only if the nonprobabilizable information is subject to the principles of complete ignorance. Next the representa ..."
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Cited by 28 (2 self)
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This article studies situations in which information is ambiguous and only part of it can be probabilized. It is shown that the information can be modeled through belief functions if and only if the nonprobabilizable information is subject to the principles of complete ignorance. Next the representability of decisions by belief functions on outcomes is justified by means of a neutrality axiom. The natural weakening of Savage's surething principle to unambiguous events is examined and its implications for decision making are identified.
Comparing Infrared DiracBornInfeld Brane Inflation to Observations
, 2008
"... We compare the Infrared DiracBornInfeld (IR DBI) brane inflation model to observations using a Bayesian analysis. The current data cannot distinguish it from the ΛCDM model, but is able to give interesting constraints on various microscopic parameters including the mass of the brane moduli potenti ..."
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Cited by 26 (4 self)
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We compare the Infrared DiracBornInfeld (IR DBI) brane inflation model to observations using a Bayesian analysis. The current data cannot distinguish it from the ΛCDM model, but is able to give interesting constraints on various microscopic parameters including the mass of the brane moduli potential, the fundamental string scale, the charge or warp factor of throats, and the number of the mobile branes. We quantify some distinctive testable predictions with stringy signatures, such as the large nonGaussianity, and the large, but regional, running of the spectral index. These results illustrate how we may be able to probe aspects of string theory using cosmological observations.
Representation Dependence in Probabilistic Inference
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 2004
"... Nondeductive reasoning systems are often representation dependent: representing the same situation in two different ways may cause such a system to return two different answers. Some have viewed ..."
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Nondeductive reasoning systems are often representation dependent: representing the same situation in two different ways may cause such a system to return two different answers. Some have viewed
The Promise of Bayesian Inference for Astrophysics
, 1992
"... . The `frequentist' approach to statistics, currently dominating statistical practice in astrophysics, is compared to the historically older Bayesian approach, which is now growing in popularity in other scientific disciplines, and which provides unique, optimal solutions to wellposed problems ..."
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. The `frequentist' approach to statistics, currently dominating statistical practice in astrophysics, is compared to the historically older Bayesian approach, which is now growing in popularity in other scientific disciplines, and which provides unique, optimal solutions to wellposed problems. The two approaches address the same questions with very different calculations, but in simple cases often give the same final results, confusing the issue of whether one is superior to the other. Here frequentist and Bayesian methods are applied to problems where such a mathematical coincidence does not occur, allowing assessment of their relative merits based on their performance, rather than on philosophical argument. Emphasis is placed on a key distinction between the two approaches: Bayesian methods, based on comparisons among alternative hypotheses using the single observed data set, consider averages over hypotheses; frequentist methods, in contrast, average over hypothetical alternative...