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19
Bayes Factors
, 1995
"... In a 1935 paper, and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null ..."
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Cited by 973 (70 self)
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In a 1935 paper, and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null is onehalf. Although there has been much discussion of Bayesian hypothesis testing in the context of criticism of P values, less attention has been given to the Bayes factor as a practical tool of applied statistics. In this paper we review and discuss the uses of Bayes factors in the context of five scientific applications in genetics, sports, ecology, sociology and psychology.
Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
 Biometrika
, 1995
"... Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some xed standard underlying measure. They have therefore not been available for application to Bayesian model determi ..."
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Cited by 820 (19 self)
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Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some xed standard underlying measure. They have therefore not been available for application to Bayesian model determination, where the dimensionality of the parameter vector is typically not xed. This article proposes a new framework for the construction of reversible Markov chain samplers that jump between parameter subspaces of di ering dimensionality, which is exible and entirely constructive. It should therefore have wide applicability in model determination problems. The methodology is illustrated with applications to multiple changepoint analysis in one and two dimensions, and toaBayesian comparison of binomial experiments.
Approximate Bayes Factors and Accounting for Model Uncertainty in Generalized Linear Models
, 1993
"... Ways of obtaining approximate Bayes factors for generalized linear models are described, based on the Laplace method for integrals. I propose a new approximation which uses only the output of standard computer programs such as GUM; this appears to be quite accurate. A reference set of proper priors ..."
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Cited by 96 (28 self)
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Ways of obtaining approximate Bayes factors for generalized linear models are described, based on the Laplace method for integrals. I propose a new approximation which uses only the output of standard computer programs such as GUM; this appears to be quite accurate. A reference set of proper priors is suggested, both to represent the situation where there is not much prior information, and to assess the sensitivity of the results to the prior distribution. The methods can be used when the dispersion parameter is unknown, when there is overdispersion, to compare link functions, and to compare error distributions and variance functions. The methods can be used to implement the Bayesian approach to accounting for model uncertainty. I describe an application to inference about relative risks in the presence of control factors where model uncertainty is large and important. Software to implement the
Reference analysis
 In Handbook of Statistics 25
, 2005
"... This chapter describes reference analysis, a method to produce Bayesian inferential statements which only depend on the assumed model and the available data. Statistical information theory is used to define the reference prior function as a mathematical description of that situation where data would ..."
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Cited by 13 (2 self)
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This chapter describes reference analysis, a method to produce Bayesian inferential statements which only depend on the assumed model and the available data. Statistical information theory is used to define the reference prior function as a mathematical description of that situation where data would best dominate prior knowledge about the quantity of interest. Reference priors are not descriptions of personal beliefs; they are proposed as formal consensus prior functions to be used as standards for scientific communication. Reference posteriors are obtained by formal use of Bayes theorem with a reference prior. Reference prediction is achieved by integration with a reference posterior. Reference decisions are derived by minimizing a reference posterior expected loss. An information theory based loss function, the intrinsic discrepancy, may be used to derive reference procedures for conventional inference problems in scientific investigation, such as point estimation, region estimation and hypothesis testing.
Change Point and Change Curve Modeling in Stochastic Processes and Spatial Statistics
 Journal of Applied Statistical Science
, 1993
"... In simple onedimensional stochastic processes it is feasible to model change points explicitly and to make inference about them. I have found that the Bayesian approach produces results more easily than nonBayesian approaches. It has the advantages of relative technical simplicity, theoretical opt ..."
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Cited by 9 (4 self)
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In simple onedimensional stochastic processes it is feasible to model change points explicitly and to make inference about them. I have found that the Bayesian approach produces results more easily than nonBayesian approaches. It has the advantages of relative technical simplicity, theoretical optimality, and of allowing a formal comparison between abrupt and gradual descriptions of change. When it can be assumed that there is at most one changepoint, this is especially simple. This is illustrated in the context of Poisson point processes. A simple approximation is introduced that is applicable to a wide range of problems in which the change point model can be written as a regression or generalized linear model. When the number of change points is unknown, the Bayesian approach proceeds most naturally by statespace modeling or "hidden Markov chains". The general ideas of this are briefly reviewed, particularly the multiprocess Kalman filter. I then describe the application of these...
Prediction and Decision Making Using Bayesian Hierarchical Models Statistics in Medicine
, 1995
"... This paper uses Bayesian hierarchical models to analyze multicenter clinical trial data where the outcome variable of interest is continuous, but not normally distributed, and where censoring has occurred. The goal of such an analysis is the same as for any subgroup analysis, to provide survival es ..."
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Cited by 5 (0 self)
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This paper uses Bayesian hierarchical models to analyze multicenter clinical trial data where the outcome variable of interest is continuous, but not normally distributed, and where censoring has occurred. The goal of such an analysis is the same as for any subgroup analysis, to provide survival estimates for specific subgroups as well as for the population and to provide estimates of the degree of heterogeneity between subgroups. An analysis of the Collaborative Study of LongTerm Maintenance Drug Therapy in Recurrent Affective Illness, a multicenter clinical trial funded by the National Institute for Mental Health's Pharmacologic Research Branch, serves to illustrate the proposed methodology. A feature of this data set is that one treatment group was withdrawn from medication at the time of randomization. The paper contains comparison of models, one that accounts for the drug washout period through the use of a changepoint model as well as a comparison of results across several choi...
Continuoustime Estimation of a Changepoint in a Poisson Process
, 1994
"... this paper. Suppose data over T unit time periods, X 1 ; : : : ; X T , are observed where the observation X i represents the number of events that occurred in the ith ..."
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Cited by 4 (0 self)
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this paper. Suppose data over T unit time periods, X 1 ; : : : ; X T , are observed where the observation X i represents the number of events that occurred in the ith
Two Statistical Methods for the Detection of Environmental Thresholds
, 2001
"... A nonparametric method and a Bayesian hierarchical modelling method are proposed in this paper for the detection of environmental thresholds. The nonparametric method is based on the reduction of deviance, while the Bayesian method is based on the change in the response variable distribution para ..."
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Cited by 3 (0 self)
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A nonparametric method and a Bayesian hierarchical modelling method are proposed in this paper for the detection of environmental thresholds. The nonparametric method is based on the reduction of deviance, while the Bayesian method is based on the change in the response variable distribution parameters.
Assessing Placebo Response Using Bayesian Hierarchical Survival Models
, 1995
"... The National Institute of Mental Health (NIMH) Collaborative Study of LongTerm Maintenance Drug Therapy in Recurrent Affective Illness was a multicenter randomized controlled clinical trial designed to determine the efficacy of a pharmacotherapy for the prevention of the recurrence of unipolar affe ..."
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Cited by 1 (0 self)
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The National Institute of Mental Health (NIMH) Collaborative Study of LongTerm Maintenance Drug Therapy in Recurrent Affective Illness was a multicenter randomized controlled clinical trial designed to determine the efficacy of a pharmacotherapy for the prevention of the recurrence of unipolar affective disorders. The outcome of interest in this study was the time until the recurrence of a depressive episode. The data show much heterogeneity between centers for the placebo group. The aim of this paper is to use Bayesian hierarchical survival models to investigate the heterogeneity of placebo effects among centers in the NIMH study. This heterogeneity is explored in terms of the marginal posterior distributions of parameters of interest and predictive distributions of future observations. The Gibbs sampling algorithm is used to approximate posterior and predictive distributions. Sensitivity of results to the assumption of a constant hazard survival distribution at the first stage of th...
Simultaneous confidence bands for the rate of a nonhomogeneous Poisson process
"... Introduction Let fX(t); 0 t Tg be a nonhomogeneous Poisson process with rate (t), which we assume is continuous, differentiable and bounded away from 0 and 1 on [0; T ]. Suppose we observe X(T ) = n with event times T 1 ; : : : ; T n . Let K(x) be a kernel function, and K h (x) = K(x=h). A kerne ..."
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Introduction Let fX(t); 0 t Tg be a nonhomogeneous Poisson process with rate (t), which we assume is continuous, differentiable and bounded away from 0 and 1 on [0; T ]. Suppose we observe X(T ) = n with event times T 1 ; : : : ; T n . Let K(x) be a kernel function, and K h (x) = K(x=h). A kernel rate estimate of (t) with bandwidth h is (t) = P K h (T i \Gamma t) R T 0 K h (u \Gamma t)du :