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59
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 981 (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.
Bayes factors and model uncertainty
 DEPARTMENT OF STATISTICS, UNIVERSITY OFWASHINGTON
, 1993
"... 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 ..."
Abstract

Cited by 89 (6 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 Pvalues, 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. The points we emphasize are: from Jeffreys's Bayesian point of view, the purpose of hypothesis testing is to evaluate the evidence in favor of a scientific theory; Bayes factors offer a way of evaluating evidence in favor ofa null hypothesis; Bayes factors provide a way of incorporating external information into the evaluation of evidence about a hypothesis; Bayes factors are very general, and do not require alternative models to be nested; several techniques are available for computing Bayes factors, including asymptotic approximations which are easy to compute using the output from standard packages that maximize likelihoods; in "nonstandard " statistical models that do not satisfy common regularity conditions, it can be technically simpler to calculate Bayes factors than to derive nonBayesian significance
Statistics for near independence in multivariate extreme values
, 1996
"... We propose a multivariate extreme value threshold model for joint tail estimation which overcomes the problems encountered with existing techniques when the variables are near independence. We examine inference under the model and develop tests for independence of extremes of the marginal variables, ..."
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Cited by 64 (2 self)
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We propose a multivariate extreme value threshold model for joint tail estimation which overcomes the problems encountered with existing techniques when the variables are near independence. We examine inference under the model and develop tests for independence of extremes of the marginal variables, both when the thresholds are fixed, and when they increase with the sample size. Motivated by results obtained from this model, we give a new and widely applicable characterisation of dependence in the joint tail which includes existing models as special cases. A new parameter which governs the form of dependence is of fundamental importance to this characterisation. By estimating this parameter, we develop a diagnostic test which assesses the applicability of bivariate extreme value joint tail models. The methods are demonstrated through simulation and by analysing two previously published data sets.
Extreme Value Statistics and Wind Storm Losses: A Case Study
 Scand. Actuarial J
, 1995
"... Statistical extreme value theory provides a flexible and theoretically well motivated approach to the study of large losses in insurance. We give a brief review of the modern version of this theory and a "step by step" example of how to use it in large claims insurance. The discussion is based on a ..."
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Cited by 31 (7 self)
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Statistical extreme value theory provides a flexible and theoretically well motivated approach to the study of large losses in insurance. We give a brief review of the modern version of this theory and a "step by step" example of how to use it in large claims insurance. The discussion is based on a detailed investigation of a wind storm insurance problem. New results include a simulation study of estimators in the peaks over thresholds method with Generalised Pareto excesses, a discussion of Pareto and lognormal modelling and methods to detect trends. Further results concern the use of meteorological information in wind storm insurance and, of course, the results of the study of the wind storm claims.
Estimating the extremal index
, 1991
"... The extremal index is an important parameter measuring the degree of clustering of extremes in a stationary process. If we consider the point process of exceedance times over a high threshold, then this can be shown to converge asymptotically to a clustered Poisson process. The extremal index, a par ..."
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Cited by 27 (5 self)
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The extremal index is an important parameter measuring the degree of clustering of extremes in a stationary process. If we consider the point process of exceedance times over a high threshold, then this can be shown to converge asymptotically to a clustered Poisson process. The extremal index, a parameter between 0 and 1, is the reciprocal of the mean cluster size. Apart from being of interest in its own right, it is a crucial parameter for determining the limiting distribution of extreme values from the process. In this paper we review current work on statistical estimation of the extremal index, and consider an optimality criterion based on a biasvariance tradeoff. Theoretical results are presented for some simple stochastic processes, and the practical implications are examined through simulations and some real data analysis.
LIMIT LAWS FOR RANDOM VECTORS WITH AN EXTREME COMPONENT
, 2007
"... Models based on assumptions of multivariate regular variation and hidden regular variation provide ways to describe a broad range of extremal dependence structures when marginal distributions are heavy tailed. Multivariate regular variation provides a rich description of extremal dependence in the c ..."
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Cited by 15 (1 self)
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Models based on assumptions of multivariate regular variation and hidden regular variation provide ways to describe a broad range of extremal dependence structures when marginal distributions are heavy tailed. Multivariate regular variation provides a rich description of extremal dependence in the case of asymptotic dependence, but fails to distinguish between exact independence and asymptotic independence. Hidden regular variation addresses this problem by requiring components of the random vector to be simultaneously large but on a smaller scale than the scale for the marginal distributions. In doing so, hidden regular variation typically restricts attention to that part of the probability space where all variables are simultaneously large. However, since under asymptotic independence the largest values do not occur in the same observation, the region where variables are simultaneously large may not be of primary interest. A different philosophy was offered in the paper of Heffernan and Tawn [J. R. Stat. Soc. Ser. B Stat. Methodol. 66 (2004) 497–546] which allows examination of distributional tails other than the joint tail. This approach used an asymptotic argument which conditions on one component of the random vector and finds the limiting conditional distribution of the remaining components as the conditioning variable becomes large. In this paper, we provide a thorough mathematical examination of the limiting arguments building on the orientation of Heffernan and
Bayesian mixture modeling for spatial Poisson process intensities, with applications to extreme value analysis
 Dept
, 2005
"... Abstract: We propose a method for the analysis of a spatial point pattern, which is assumed to arise as a set of observations from a spatial nonhomogeneous Poisson process. The spatial point pattern is observed in a bounded region, which, for most applications, is taken to be a rectangle in the spa ..."
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Cited by 13 (3 self)
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Abstract: We propose a method for the analysis of a spatial point pattern, which is assumed to arise as a set of observations from a spatial nonhomogeneous Poisson process. The spatial point pattern is observed in a bounded region, which, for most applications, is taken to be a rectangle in the space where the process is defined. The method is based on modeling a density function, defined on this bounded region, that is directly related with the intensity function of the Poisson process. We develop a flexible nonparametric mixture model for this density using a bivariate Beta distribution for the mixture kernel and a Dirichlet process prior for the mixing distribution. Using posterior simulation methods, we obtain full inference for the intensity function and any other functional of the process that might be of interest. We discuss applications to problems where inference for clustering in the spatial point pattern is of interest. Moreover, we consider applications of the methodology to extreme value analysis problems. We illustrate the modeling approach with three previously published data sets. Two of the data sets are from forestry and consist of locations of trees. The third data set consists of extremes from the Dow Jones index over a period of 1303 days.
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...