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Philosophy and the practice of Bayesian statistics
, 2010
"... A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually ..."
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Cited by 33 (8 self)
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A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypotheticodeductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework.
Diagnostic Measures for Model Criticism
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 1996
"... ... In this article we present the general outlook and discuss general families of elaborations for use in practice; the exponential connection elaboration plays a key role. We then describe model elaborations for use in diagnosing: departures from normality, goodness of fit in generalized linear mo ..."
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Cited by 17 (1 self)
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... In this article we present the general outlook and discuss general families of elaborations for use in practice; the exponential connection elaboration plays a key role. We then describe model elaborations for use in diagnosing: departures from normality, goodness of fit in generalized linear models, and variable selection in regression and outlier detection. We illustrate our approach with two applications.
A MultiParadigm Modeling Definition and Language
, 2013
"... This paper discusses a single form for statistical models that accommodates a broad range of models, from ordinary least squares to agentbased microsimulations. The definition makes it almost trivial to define morphisms to transform and combine existing models to produce new models. It offers a uni ..."
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This paper discusses a single form for statistical models that accommodates a broad range of models, from ordinary least squares to agentbased microsimulations. The definition makes it almost trivial to define morphisms to transform and combine existing models to produce new models. It offers a unified means of expressing and implementing methods that are typically given disparate treatment in the literature, including Jacobian transformations, Bayesian updating, multilevel models, some missing data imputation methods, approaches to dealing with nuisance parameters, and several other common procedures. It especially offers benefit to simulationtype models, because of the value in being able to easily calculate robustness measures for simulation statistics and, where appropriate, test hypotheses. Running examples will be given using Apophenia, a software library based largely on the model form and transformations described here. 1
On Small Area Prediction Interval Problems
"... Empirical best linear unbiased prediction (EBLUP) method uses a linear mixed model in combining information from different sources of information. This method is particularly useful in small area problems. The variability of an EBLUP is measured by the mean squared prediction error (MSPE), and int ..."
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Empirical best linear unbiased prediction (EBLUP) method uses a linear mixed model in combining information from different sources of information. This method is particularly useful in small area problems. The variability of an EBLUP is measured by the mean squared prediction error (MSPE), and interval estimates are generally constructed using estimates of the MSPE. Such methods have shortcomings like undercoverage, excessive length and lack of interpretability. We propose a resampling driven approach, and obtain coverage accuracy of O(d3n−3/2), where d is the number of parameters and n the number of observations. Simulation results demonstrate the superiority of our method over the existing ones.
By MALAY GHOSH
"... SUMMARY. The paper revisits Basu’s Theorem, and documents some of its many applications in statistical inference. There is also some discussion on the relationship between the concepts of sufficiency, completeness and ancillarity. 1. ..."
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SUMMARY. The paper revisits Basu’s Theorem, and documents some of its many applications in statistical inference. There is also some discussion on the relationship between the concepts of sufficiency, completeness and ancillarity. 1.