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Assessment and Propagation of Model Uncertainty
, 1995
"... this paper I discuss a Bayesian approach to solving this problem that has long been available in principle but is only now becoming routinely feasible, by virtue of recent computational advances, and examine its implementation in examples that involve forecasting the price of oil and estimating the ..."
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Cited by 108 (0 self)
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this paper I discuss a Bayesian approach to solving this problem that has long been available in principle but is only now becoming routinely feasible, by virtue of recent computational advances, and examine its implementation in examples that involve forecasting the price of oil and estimating the chance of catastrophic failure of the U.S. Space Shuttle.
Implementing approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations: A manual for the inlaprogram
, 2008
"... Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalised) linear models, (generalised) additive models, smoothingspline models, statespace models, semiparametric regression, spatial and spatiotemp ..."
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Cited by 79 (16 self)
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Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalised) linear models, (generalised) additive models, smoothingspline models, statespace models, semiparametric regression, spatial and spatiotemporal models, logGaussian Coxprocesses, geostatistical and geoadditive models. In this paper we consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with nonGaussian response variables. The posterior marginals are not available in closed form due to the nonGaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, both in terms of convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations
Methods for Approximating Integrals in Statistics with Special Emphasis on Bayesian Integration Problems
 Statistical Science
"... This paper is a survey of the major techniques and approaches available for the numerical approximation of integrals in statistics. We classify these into five broad categories; namely, asymptotic methods, importance sampling, adaptive importance sampling, multiple quadrature and Markov chain method ..."
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Cited by 32 (4 self)
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This paper is a survey of the major techniques and approaches available for the numerical approximation of integrals in statistics. We classify these into five broad categories; namely, asymptotic methods, importance sampling, adaptive importance sampling, multiple quadrature and Markov chain methods. Each method is discussed giving an outline of the basic supporting theory and particular features of the technique. Conclusions are drawn concerning the relative merits of the methods based on the discussion and their application to three examples. The following broad recommendations are made. Asymptotic methods should only be considered in contexts where the integrand has a dominant peak with approximate ellipsoidal symmetry. Importance sampling, and preferably adaptive importance sampling, based on a multivariate Student should be used instead of asymptotics methods in such a context. Multiple quadrature, and in particular subregion adaptive integration, are the algorithms of choice for...
Some Adaptive Monte Carlo Methods for Bayesian Inference
 Statistics in Medicine
"... This paper outlines some of the issues in developing adaptive methods and presents some preliminary results. 1 Introduction ..."
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Cited by 24 (3 self)
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This paper outlines some of the issues in developing adaptive methods and presents some preliminary results. 1 Introduction
An Iterative Monte Carlo Method for Nonconjugate Bayesian Analysis
 Statistics and Computing
, 1991
"... The Gibbs sampler has been proposed as a general method for Bayesian calculation in Gelfand and Smith (1990). However, the predominance of experience to date resides in applications assuming conjugacy where implementation is reasonably straightforward. This paper describes a tailored approximate rej ..."
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Cited by 17 (0 self)
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The Gibbs sampler has been proposed as a general method for Bayesian calculation in Gelfand and Smith (1990). However, the predominance of experience to date resides in applications assuming conjugacy where implementation is reasonably straightforward. This paper describes a tailored approximate rejection method approach for implementation of the Gibbs sampler when nonconjugate structure is present. Several challenging applications are presented for illustration.
Benefits of a Bayesian Approach for Synthesizing Multiple Sources of Evidence and Uncertainty Linked by a Deterministic Model
, 1993
"... A Bayesian synthesis approach has been proposed by Raftery, Givens, and Zeh (1992) for making inferences from a deterministic model with many inputs and outputs. The approach was applied to population dynamics models for bowhead whales. The approach consists of establishing a joint prior, or pre ..."
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Cited by 7 (6 self)
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A Bayesian synthesis approach has been proposed by Raftery, Givens, and Zeh (1992) for making inferences from a deterministic model with many inputs and outputs. The approach was applied to population dynamics models for bowhead whales. The approach consists of establishing a joint prior, or premodel distribution, on the model inputs and outputs for which there exists evidence independent of the model. The restriction of this distribution to a subspace defined by the model mapping then constitutes a postmodel distribution, from which inferences are drawn. We briefly review a methodology for implementing the Bayesian synthesis approach, and then consider in detail the potential uses of the results and the strengths and weaknesses of the approach compared to past methodologies. 1 Introduction Complex deterministic models reflect scientists' simplified conceptions of natural mechanisms about which they have incomplete understanding. Such a model depends on a set of input para...
Comparing Institutional Performance using Markov chain Monte Carlo Methods
, 1999
"... There has been a growing interest over recent years in the use of performance indicators in healthcare, which may measure aspects of the process of care, clinical outcomes or the incidence of disease (NHS Executive, 1995; Scottish Office, 1995; New York State Department of Health, 1996). In respo ..."
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Cited by 2 (0 self)
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There has been a growing interest over recent years in the use of performance indicators in healthcare, which may measure aspects of the process of care, clinical outcomes or the incidence of disease (NHS Executive, 1995; Scottish Office, 1995; New York State Department of Health, 1996). In response a sizeable literature has emerged questioning the very use of such indicators as a measure of 'quality of care', as well as stating more specific criticisms of the statistical methods used to obtain estimates adjusted for patient casemix (DuBois et al., 1987; Jencks et al., 1988; Epstein, 1995; Schneider and Epstein, 1996). We do not attempt to further this general discussion of performance indicators and risk adjustment  see, for example (Goldstein and Spiegelhalter, 1996). Rather, the purpose of this chapter is to highlight how recent developments in computerintensive methods can be used to explore a wide range of plausible statisti
Multivariate Densities with Strong Nonlinear Relationships
, 1993
"... We consider adaptive importance sampling techniques which use kernel density estimates at each iteration as importance sampling functions. These can provide more nearly constant importance weights and more precise estimates of quantities of interest than the SIR algorithm when the initial importance ..."
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We consider adaptive importance sampling techniques which use kernel density estimates at each iteration as importance sampling functions. These can provide more nearly constant importance weights and more precise estimates of quantities of interest than the SIR algorithm when the initial importance sampling function is diffuse relative to the target. We propose a new method which adapts to the varying local structure of the target. When the target has unusual structure, such as strong nonlinear relationships between variables, this