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Bayesian model averaging
 STAT.SCI
, 1999
"... Standard statistical practice ignores model uncertainty. Data analysts typically select a model from some class of models and then proceed as if the selected model had generated the data. This approach ignores the uncertainty in model selection, leading to overcon dent inferences and decisions tha ..."
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Cited by 61 (1 self)
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Standard statistical practice ignores model uncertainty. Data analysts typically select a model from some class of models and then proceed as if the selected model had generated the data. This approach ignores the uncertainty in model selection, leading to overcon dent inferences and decisions that are more risky than one thinks they are. Bayesian model averaging (BMA) provides a coherent mechanism for accounting for this model uncertainty. Several methods for implementing BMA haverecently emerged. We discuss these methods and present anumber of examples. In these examples, BMA provides improved outofsample predictive performance. We also provide a catalogue of
Accounting for Model Uncertainty in Survival Analysis Improves Predictive Performance
 In Bayesian Statistics 5
, 1995
"... Survival analysis is concerned with finding models to predict the survival of patients or to assess the efficacy of a clinical treatment. A key part of the modelbuilding process is the selection of the predictor variables. It is standard to use a stepwise procedure guided by a series of significanc ..."
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Cited by 55 (12 self)
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Survival analysis is concerned with finding models to predict the survival of patients or to assess the efficacy of a clinical treatment. A key part of the modelbuilding process is the selection of the predictor variables. It is standard to use a stepwise procedure guided by a series of significance tests to select a single model, and then to make inference conditionally on the selected model. However, this ignores model uncertainty, which can be substantial. We review the standard Bayesian model averaging solution to this problem and extend it to survival analysis, introducing partial Bayes factors to do so for the Cox proportional hazards model. In two examples, taking account of model uncertainty enhances predictive performance, to an extent that could be clinically useful. 1 Introduction From 1974 to 1984 the Mayo Clinic conducted a doubleblinded randomized clinical trial involving 312 patients to compare the drug DPCA with a placebo in the treatment of primary biliary cirrhosis...
Bayesian Model Averaging in proportional hazard models: Assessing the risk of a stroke
 Applied Statistics
, 1997
"... Evaluating the risk of stroke is important in reducing the incidence of this devastating disease. Here, we apply Bayesian model averaging to variable selection in Cox proportional hazard models in the context of the Cardiovascular Health Study, a comprehensive investigation into the risk factors for ..."
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Cited by 43 (5 self)
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Evaluating the risk of stroke is important in reducing the incidence of this devastating disease. Here, we apply Bayesian model averaging to variable selection in Cox proportional hazard models in the context of the Cardiovascular Health Study, a comprehensive investigation into the risk factors for stroke. We introduce a technique based on the leaps and bounds algorithm which e ciently locates and ts the best models in the very large model space and thereby extends all subsets regression to Cox models. For each independent variable considered, the method provides the posterior probability that it belongs in the model. This is more directly interpretable than the corresponding Pvalues, and also more valid in that it takes account of model uncertainty. Pvalues from models preferred by stepwise methods tend to overstate the evidence for the predictive value of a variable. In our data Bayesian model averaging predictively outperforms standard model selection methods for assessing
Maximum likelihood Bayesian averaging of alternative conceptualmathematical models, Stochastic Environ
 Res. Risk Assess
, 2003
"... [1] Hydrologic analyses typically rely on a single conceptualmathematical model. Yet hydrologic environments are open and complex, rendering them prone to multiple interpretations and mathematical descriptions. Adopting only one of these may lead to statistical bias and underestimation of uncertain ..."
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Cited by 37 (2 self)
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[1] Hydrologic analyses typically rely on a single conceptualmathematical model. Yet hydrologic environments are open and complex, rendering them prone to multiple interpretations and mathematical descriptions. Adopting only one of these may lead to statistical bias and underestimation of uncertainty. Bayesian model averaging (BMA) [Hoeting et al., 1999] provides an optimal way to combine the predictions of several competing models and to assess their joint predictive uncertainty. However, it tends to be computationally demanding and relies heavily on prior information about model parameters. Neuman [2002, 2003] proposed a maximum likelihood version (MLBMA) of BMA to render it computationally feasible and to allow dealing with cases where reliable prior information is lacking. We apply MLBMA to seven alternative variogram models of log air permeability data from singlehole pneumatic injection tests in six boreholes at the Apache Leap Research Site (ALRS) in central Arizona. Unbiased ML estimates of variogram and drift parameters are obtained using adjoint state maximum likelihood cross validation [Samper and Neuman, 1989a] in conjunction with universal kriging and generalized least squares. Standard information criteria provide an ambiguous ranking of
A Flexible Approach to Bayesian Multiple Curve Fitting
"... We model sparse functional data from multiple subjects with a mixedeffects regression spline. In this model, the expected values for any subject (conditioned on the random effects) can be written as the sum of a population curve and a subjectspecific deviate from this population curve. The populat ..."
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We model sparse functional data from multiple subjects with a mixedeffects regression spline. In this model, the expected values for any subject (conditioned on the random effects) can be written as the sum of a population curve and a subjectspecific deviate from this population curve. The population curve and the subjectspecific deviates are both modeled as freeknot bsplines with k and k ′ knots located at tk and tk ′ , respectively. To identify the number and location of the “free ” knots, we sample from the posterior p (k, tk, k′, tk ′ y) using reversible jump MCMC methods. Sampling from this posterior distribution is complicated, however, by the flexibility we allow for the model’s covariance structure. No restrictions (other than positive definiteness) are placed on the covariance parameters ψ and σ2 and, as a result, no analytical form for the likelihood p (yk, tk, k′, tk′) exists. In this paper, we consider two approximations to p(yk, tk, k′, tk′) and then sample from the corresponding approximations to p(k, tk, k′, tk ′ y). We also sample from p(k, tk, k′, tk ′ , ψ, σ2y) which has a likelihood that is available in closed form. While sampling from this larger posterior is less efficient, the resulting marginal distribution of knots is exact and allows us to evaluate the accuracy of each approximation. We then consider a real data set and explore the difference between p(k, tk, k′, tk ′ , ψ, σ2y) and the more accurate approximation to p(k, tk, k′, tk ′ y).
SIMULATION
, 2001
"... The primary objectives of this research are formulation andevaluation of a Bayesian approach for selecting input models in discreteevent stochastic simulation. This approach takes into account the model, parameter, and stochastic uncertainties that are inherent in most simulation experiments in ord ..."
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The primary objectives of this research are formulation andevaluation of a Bayesian approach for selecting input models in discreteevent stochastic simulation. This approach takes into account the model, parameter, and stochastic uncertainties that are inherent in most simulation experiments in order to yieldvalidpredictive inferences about the output quantities of interest. We use prior information to specify the prior plausibility of each candidate input model that adequately fits the data, and to construct prior distributions on the parameters of each model. We combine prior information with the likelihoodfunction of the data to compute the posterior model probabilities and the posterior parameter distributions using Bayes ’ rule. This leads to a Bayesian Simulation Replication Algorithm in which: (a) we estimate the parameter uncertainty by sampling from the posterior distribution of each model’s parameters on selectedsimulation runs; (b) we estimate the stochastic uncertainty by multiple independent replications of those selected runs; and (c) we estimate model uncertainty by weighting the results of (a) and(b) using the corresponding posterior model probabilities. We also construct a confidence interval on the posterior mean response from the output of the algorithm, andwe develop a replication allocation procedure that optimally allocates simulation runs to input models so as to minimize the variance of the mean estimator subject to a budget constraint on computer time. To assess the performance of the algorithm, we propose some evaluation criteria that are reasonable within both the Bayesian andfrequentist paradigms. An experimental performance evaluation demonstrates the advantages of the Bayesian approach versus conventional frequentist techniques.
MULTIMODEL BAYESIAN ANALYSIS OF DATA WORTH AND OPTIMIZATION OF SAMPLING SCHEME DESIGN
, 2011
"... Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the aut ..."
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Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.