Results 11  20
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39
Bayesian hypothesis testing: A reference approach
 Internat. Statist. Rev
, 2002
"... For any probability model M ≡{p(x  θ, ω), θ ∈ Θ, ω ∈ Ω} assumed to describe the probabilistic behaviour of data x ∈ X, it is argued that testing whether or not the available data are compatible with the hypothesis H0 ≡{θ = θ0} is best considered as a formal decision problem on whether to use (a0), ..."
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Cited by 17 (5 self)
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For any probability model M ≡{p(x  θ, ω), θ ∈ Θ, ω ∈ Ω} assumed to describe the probabilistic behaviour of data x ∈ X, it is argued that testing whether or not the available data are compatible with the hypothesis H0 ≡{θ = θ0} is best considered as a formal decision problem on whether to use (a0), or not to use (a1), the simpler probability model (or null model) M0 ≡{p(x  θ0, ω), ω ∈ Ω}, where the loss difference L(a0, θ, ω) − L(a1, θ, ω) is proportional to the amount of information δ(θ0, θ, ω) which would be lost if the simplified model M0 were used as a proxy for the assumed model M. For any prior distribution π(θ, ω), the appropriate normative solution is obtained by rejecting the null model M0 whenever the corresponding posterior expectation ∫ ∫ δ(θ0, θ, ω) π(θ, ω  x) dθ dω is sufficiently large. Specification of a subjective prior is always difficult, and often polemical, in scientific communication. Information theory may be used to specify a prior, the reference prior, which only depends on the assumed model M, and mathematically describes a situation where no prior information is available about the quantity of interest. The reference posterior expectation, d(θ0, x) = ∫ δπ(δ  x) dδ, of the amount of information δ(θ0, θ, ω) which could be lost if the null model were used, provides an attractive nonnegative test function, the intrinsic statistic, which is
Sequential sampling models of human text classification
 Cognitive Science
, 2003
"... Text classification involves deciding whether or not a document is about a given topic. It is an important problem in machine learning, because automated text classifiers have enormous potential for application in information retrieval systems. It is also an interesting problem for cognitive science ..."
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Cited by 9 (1 self)
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Text classification involves deciding whether or not a document is about a given topic. It is an important problem in machine learning, because automated text classifiers have enormous potential for application in information retrieval systems. It is also an interesting problem for cognitive science, because it involves real world human decision making with complicated stimuli. This paper develops two models of human text document classification based on random walk and accumulator sequential sampling processes. The models are evaluated using data from an experiment where participants classify text documents presented one word at a time under task instructions that emphasize either speed or accuracy, and rate their confidence in their decisions. Fitting the random walk and accumulator models to these data shows that the accumulator provides a better account of the decisions made, and a “balance of evidence ” measure provides the best account of confidence. Both models are also evaluated in the applied information retrieval context, by comparing their performance to established machine learning techniques on the standard Reuters21578 corpus. It is found that they are almost as accurate as the benchmarks, and make decisions much more quickly because they only need to examine a small proportion of the words in the document. In addition, the ability of the accumulator model to produce useful confidence measures is shown to have application in prioritizing the results of classification decisions.
Bayesian Methods For Simulation
"... This tutorial describes some ways that Bayesian methods address problems that arise during simulation studies. This includes quantifying uncertainty about input distributions and parameters, sensitivity analysis, and the selection of the best of several simulated alternatives. Focus is on illustrati ..."
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Cited by 8 (2 self)
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This tutorial describes some ways that Bayesian methods address problems that arise during simulation studies. This includes quantifying uncertainty about input distributions and parameters, sensitivity analysis, and the selection of the best of several simulated alternatives. Focus is on illustrating the main ideas and their relevance to practical problems. Numerous citations for both introductory and more advanced material provide a launching pad into the Bayesian literature.
Bayesian Analysis of Factorial Experiments By Mixture Modelling
, 2000
"... this paper we try our hands at it. One version of the classical theory of factorial experiments, going back to Fisher and further developed by Kempthorne (1955), completely avoids distributional assumptions, assuming only additivity, and uses randomisation to derive the standard tests of hypotheses ..."
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Cited by 5 (1 self)
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this paper we try our hands at it. One version of the classical theory of factorial experiments, going back to Fisher and further developed by Kempthorne (1955), completely avoids distributional assumptions, assuming only additivity, and uses randomisation to derive the standard tests of hypotheses about treatment effects. Here, we are interested in the more familiar classical approach via linear modelling and normal distribution theory. The corresponding Bayesian analysis has been developed mainly in the pioneering works of Box & Tiao (1973) and Lindley & Smith (1972). Box & Tiao (1973, Chapter 6) discuss Bayesian analysis of cross classified designs, including fixed, random and mixed effects models. They point out that in a Bayesian approach the appropriate inference procedure for fixed and random effects "depends upon the nature of the prior distribution used to represent the behavior of the factors". They also show (Chapter 7) that shrinkage estimates of specific effects may result when a random effects model is assumed. Lindley & Smith (1972) use a hierarchically structured linear model built on multivariate normal components (special cases of the model are considered by Lindley, 1972 and Smith, 1973), with the focus on estimation of treatment effects. These are authoritative and attractive approaches, albeit with modest compromises to the Bayesian paradigm  in respect of the estimation of the variance components  necessitated by the computational limitations of the time. Nevertheless, the inference is almost entirely estimative: questions about the indistinguishability of factor levels, or more general hypotheses about contrasts, are answered indirectly trough their joint posterior distribution, e.g. by checking whether the hypothesis falls in a highest poster...
Pathologies of Orthodox Statistics
, 2000
"... By rejecting the use of a prior distribution over parameters, orthodox statistics is forced to focus on estimators, functions which guess parameter values, and to invent heuristics for choosing among estimators. Two popular heuristics are unbiasedness and maximum likelihood. Since these heuristics a ..."
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Cited by 4 (0 self)
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By rejecting the use of a prior distribution over parameters, orthodox statistics is forced to focus on estimators, functions which guess parameter values, and to invent heuristics for choosing among estimators. Two popular heuristics are unbiasedness and maximum likelihood. Since these heuristics are not consistent with Bayes' rule, they are also not consistent with the axioms of common sense from which Bayes' rule is derived. Hence we expect there to be situations in which they violate common sense and indeed it is not hard to find such situations. This paper reviews a few simple, realistic scenarios where pathologies occur with either the unbiasedness heuristic or the maximum likelihood heuristic. 1 Introduction Many inference problems work like this: we observe some data and want to infer something about the process that generated it. If we have a probability distribution over possible processes, parameterized by `, then there is general agreement that Bayes' rule solves ...
Identification of recurrent neural networks by Bayesian interrogation techniques
 J. of
, 2009
"... We introduce novel online Bayesian methods for the identification of a family of noisy recurrent neural networks (RNNs). We present Bayesian active learning techniques for stimulus selection given past experiences. In particular, we consider the unknown parameters as stochastic variables and use Ao ..."
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Cited by 3 (2 self)
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We introduce novel online Bayesian methods for the identification of a family of noisy recurrent neural networks (RNNs). We present Bayesian active learning techniques for stimulus selection given past experiences. In particular, we consider the unknown parameters as stochastic variables and use Aoptimality and Doptimality principles to choose optimal stimuli. We derive myopic cost functions in order to maximize the information gain concerning network parameters at each time step. We also derive the Aoptimal and Doptimal estimations of the additive noise that perturbs the dynamical system of the RNN. Here we investigate myopic as well as nonmyopic estimations, and study the problem of simultaneous estimation of both the system parameters and the noise. Employing conjugate priors our derivations remain approximationfree and give rise to simple update rules for the online learning of the parameters. The efficiency of our method is demonstrated for a number of selected cases, including the task of controlled independent component analysis.
Optimal Design of Experiments for Modeling Processes with Feedback Control Variables
, 1999
"... Feedback control schemes have been widely used in many engineering applications for a long time. Despite this, there has been very little work done on efficient design of experiments for modeling feedback control processes in order to select the appropriate feedback variables. This paper considers a ..."
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Cited by 1 (0 self)
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Feedback control schemes have been widely used in many engineering applications for a long time. Despite this, there has been very little work done on efficient design of experiments for modeling feedback control processes in order to select the appropriate feedback variables. This paper considers a general statistical formulation of this problem and studies the properties of optimal designs in the firstorder case. Locally optimal designs under A and Doptimality criteria as well as Bayesian optimal designs are developed. These results are used to characterize the properties of these designs and to contrast them with traditional optimal designs without feedback variables. In particular, the relative efficiency of the traditional designs is studied for various situations of practical interest.
INCREMENTAL UTILITY ELICITATION FOR ADAPTIVE PERSONALIZATION
"... Medical devices often contain many tunable parameters. The optimal setting of these parameters depends on the patient’s utility function, which is often unknown. This raises two questions. First, how should we optimize the parameters given partial information about the patient’s utility? And secondl ..."
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Cited by 1 (0 self)
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Medical devices often contain many tunable parameters. The optimal setting of these parameters depends on the patient’s utility function, which is often unknown. This raises two questions. First, how should we optimize the parameters given partial information about the patient’s utility? And secondly, what questions do we ask to efficiently elicit this utility information? In this paper, we present a coherent probabilistic decisiontheoretic framework to answer these questions. We illustrate the potential of this framework on a toy problem and discuss directions for future research. 1
The Roles of the Convex Hull and Number of Intersections Upon Performance on Visually Presented Traveling Salesperson Problems.
"... this paper, wec9W;W2 twoapproac hes to understanding how humans solve visually presented SPs. he first assumes a globaltoloc al proc essing strategy, in whic h a rough globalreferenc frame is first established, into whic h loc al information is then integrated. We foc9 on a welldeveloped spec;C i ..."
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Cited by 1 (0 self)
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this paper, wec9W;W2 twoapproac hes to understanding how humans solve visually presented SPs. he first assumes a globaltoloc al proc essing strategy, in whic h a rough globalreferenc frame is first established, into whic h loc al information is then integrated. We foc9 on a welldeveloped spec;C instantiation of this approac h, known as the cT vex hull hypothesis (Mac Gregor & Ormerod 1996), whic h assumes that solutions are guided by the boundary points in the stimulus array. We review the theoretic; and empiricT evidenc e for and against this hypothesis, before suggesting an alternative loc altoglobal approac h. Under this alternativeapproac h, solutions are assumed to be primarily guided by lo procT9;01 cT9;019T ts, suc h as the avoidanc of intersecTGII incC20R1TGIIC a tour. oc ompare these twoapproac hes empiric ally, we present an experiment that measures the di#erent e#ec; the number of points on thec onvex hull and the number of potential intersec9T ns have on human performanc; GwGwwwG cal Processing Gregor and Ormerod (1996) found that the group performanc e of observers in two experiments surpassed that of a suite ofc omputational heuristic and was soc lose to the best known solutions that there were no individual di#erencG and there was zero c rrelation between performa ac6 ss di#erent problems. On this basis, theyc ncyTCW that thec onsistent ability to arrive at nearoptimal solutions argued for the operation of ac ommon underlying pro coT or set of procoT6I and suggested thatsuc h procoTC0 might c orrespond to natural organizing tendenc ies of the visual system. This lastc onc lusion isc onsistent with an experiment by Pomerantz (1981), who found that observers, asked tocTI6;I up the dots in arrays, to illustrate how they percR9 ed the arrays, frequentl...