Results 1  10
of
93
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 ..."
Abstract

Cited by 1176 (71 self)
 Add to MetaCart
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 95 (6 self)
 Add to MetaCart
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, ..."
Abstract

Cited by 80 (2 self)
 Add to MetaCart
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 b ..."
Abstract

Cited by 42 (7 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 39 (5 self)
 Add to MetaCart
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.
Estimating a tail exponent by modelling departure from a Pareto distribution
 Annals Statist
, 1999
"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
Abstract

Cited by 29 (0 self)
 Add to MetaCart
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
Changes in the extremes of the climate simulated by CCC GCM2 under CO2 doubling
 J. Climate
, 1998
"... Changes due to CO2 doubling in the extremes of the surface climate as simulated by the secondgeneration circulation model of the Canadian Centre for Climate Modelling and Analysis are studied in two 20yr equilibrium simulations. Extreme values of screen temperature, precipitation, and nearsurface ..."
Abstract

Cited by 24 (5 self)
 Add to MetaCart
(Show Context)
Changes due to CO2 doubling in the extremes of the surface climate as simulated by the secondgeneration circulation model of the Canadian Centre for Climate Modelling and Analysis are studied in two 20yr equilibrium simulations. Extreme values of screen temperature, precipitation, and nearsurface wind in the control climate are compared to those estimated from 17 yr of the NCEP–NCAR reanalysis data and from some Canadian station data. The extremes of screen temperature are reasonably well reproduced in the control climate. Their changes under CO2 doubling can be connected with other physical changes such as surface albedo changes due to the reduction of snow and sea ice cover as well as a decrease of soil moisture in the warmer world. The signal in the extremes of daily precipitation and nearsurface wind speed due to CO2 doubling is less obvious. The precipitation extremes increase almost everywhere over the globe. The strongest change, over northwest India, is related to the intensification of the summer monsoon in this region in the warmer world. The modest reduction of wind extremes in the Tropics and middle latitudes is consistent with the reduction of the meridional temperature gradient in the 23CO2 climate. The larger wind extremes occur in the areas where sea ice has retreated. 1.
A fully probabilistic approach to extreme rainfall modelling
 Journal of Hydrology
, 2003
"... It is an embarrassingly frequent experience that statistical practice fails to foresee historical disasters. It is all too easy to blame global trends or some sort of external intervention, but in this article we argue that statistical methods that do not take comprehensive account of the uncertaint ..."
Abstract

Cited by 17 (2 self)
 Add to MetaCart
(Show Context)
It is an embarrassingly frequent experience that statistical practice fails to foresee historical disasters. It is all too easy to blame global trends or some sort of external intervention, but in this article we argue that statistical methods that do not take comprehensive account of the uncertainties involved in both model and predictions, are bound to produce an overoptimistic appraisal of future extremes that is often contradicted by observed hydrological events. Based on the annual and daily rainfall data on the central coast of Venezuela, different modeling strategies and inference approaches show that the 1999 rainfall which caused the worst environmentally related tragedy in Venezuelan history was extreme, but not implausible given the historical evidence. We follow in turn a classical likelihood and Bayesian approach, arguing that the latter is the most natural approach for taking into account all uncertainties. In each case we emphasize the importance of making inference on predicted levels of the process rather than model parameters. Our most detailed model comprises of seasons with unknown starting points and durations for the extremes of daily rainfall whose behavior is described using a standard threshold model. Based on a Bayesian analysis of this model, so that both prediction uncertainty and process heterogeneity are properly modeled, we find that the 1999 event has a sizeable probability which implies that such an occurrence within a reasonably short time horizon could have been anticipated. Finally, since accumulation of extreme rainfall over several days is an additional difficulty – and indeed, the catastrophe of 1999 was exaggerated by heavy rainfall on successive days – we examine the effect of timescale on our broad conclusions, finding results to be broadly similar across different choices.