1,507 research outputs found
Bayes, Jeffreys, Prior Distributions and the Philosophy of Statistics
Discussion of "Harold Jeffreys's Theory of Probability revisited," by
Christian Robert, Nicolas Chopin, and Judith Rousseau, for Statistical Science
[arXiv:0804.3173]Comment: Published in at http://dx.doi.org/10.1214/09-STS284D the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Bayesian Statistical Pragmatism
Discussion of "Statistical Inference: The Big Picture" by R. E. Kass
[arXiv:1106.2895]Comment: Published in at http://dx.doi.org/10.1214/11-STS337C the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Struggles with Survey Weighting and Regression Modeling
The general principles of Bayesian data analysis imply that models for survey
responses should be constructed conditional on all variables that affect the
probability of inclusion and nonresponse, which are also the variables used in
survey weighting and clustering. However, such models can quickly become very
complicated, with potentially thousands of poststratification cells. It is then
a challenge to develop general families of multilevel probability models that
yield reasonable Bayesian inferences. We discuss in the context of several
ongoing public health and social surveys. This work is currently open-ended,
and we conclude with thoughts on how research could proceed to solve these
problems.Comment: This paper commented in: [arXiv:0710.5009], [arXiv:0710.5012],
[arXiv:0710.5013], [arXiv:0710.5015], [arXiv:0710.5016]. Rejoinder in
[arXiv:0710.5019]. Published in at
http://dx.doi.org/10.1214/088342306000000691 the Statistical Science
(http://www.imstat.org/sts/) by the Institute of Mathematical Statistics
(http://www.imstat.org
Comment: Bayesian Checking of the Second Levels of Hierarchical Models
Comment: Bayesian Checking of the Second Levels of Hierarchical Models
[arXiv:0802.0743]Comment: Published in at http://dx.doi.org/10.1214/07-STS235A the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Prior distributions for variance parameters in hierarchical models
Various noninformative prior distributions have been suggested for scale parameters in hierarchical models. We construct a new folded-noncentral- t family of conditionally conjugate priors for hierarchical standard deviation parameters, and then consider noninformative and weakly informative priors in this family. We use an example to illustrate serious problems with the inverse-gamma family of ``noninformative'' prior distributions. We suggest instead to use a uniform prior on the hierarchical standard deviation, using the half-t family when the number of groups is small and in other settings where a weakly informative prior is desired.Bayesian inference conditional conjugacy folded noncentral-t distribution half-t distribution hierarchical model multilevel model noninformative prior distribution weakly informative prior distribution
Prior distributions for variance parameters in hierarchical models
Various noninformative prior distributions have been suggested for scale parameters in hierarchical models. We construct a new folded-noncentral- t family of conditionally conjugate priors for hierarchical standard deviation parameters, and then consider noninformative and weakly informative priors in this family. We use an example to illustrate serious problems with the inverse-gamma family of ``noninformative'' prior distributions. We suggest instead to use a uniform prior on the hierarchical standard deviation, using the half-t family when the number of groups is small and in other settings where a weakly informative prior is desired.Bayesian inference, conditional conjugacy, folded noncentral-t distribution, half-t distribution, hierarchical model, multilevel model, noninformative prior distribution, weakly informative prior distribution
Induction and Deduction in Baysian Data Analysis
The classical or frequentist approach to statistics (in which inference is centered on significance testing), is associated with a philosophy in which science is deductive and follows Popperis doctrine of falsification. In contrast, Bayesian inference is commonly associated with inductive reasoning and the idea that a model can be dethroned by a competing model but can never be directly falsified by a significance test. The purpose of this article is to break these associations, which I think are incorrect and have been detrimental to statistical practice, in that they have steered falsificationists away from the very useful tools of Bayesian inference and have discouraged Bayesians from checking the fit of their models. From my experience using and developing Bayesian methods in social and environmental science, I have found model checking and falsification to be central in the modeling process.philosophy of statistics, decision theory, subjective probability, Bayesianism, falsification, induction, frequentism
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