The Experts below are selected from a list of 38112 Experts worldwide ranked by ideXlab platform
Andrew Gelman - One of the best experts on this subject based on the ideXlab platform.
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Bayesian Statistics and modelling
Nature Reviews Methods Primers, 2021Co-Authors: Rens Van De Schoot, Sarah Depaoli, Ruth King, Bianca Kramer, Kaspar Märtens, Mahlet G. Tadesse, Marina Vannucci, Andrew Gelman, Duco Veen, Joukje WillemsenAbstract:This Primer on Bayesian Statistics summarizes the most important aspects of determining prior distributions, likelihood functions and posterior distributions, in addition to discussing different applications of the method across disciplines. Bayesian Statistics is an approach to data analysis based on Bayes’ theorem, where available knowledge about parameters in a statistical model is updated with the information in observed data. The background knowledge is expressed as a prior distribution and combined with observational data in the form of a likelihood function to determine the posterior distribution. The posterior can also be used for making predictions about future events. This Primer describes the stages involved in Bayesian analysis, from specifying the prior and data models to deriving inference, model checking and refinement. We discuss the importance of prior and posterior predictive checking, selecting a proper technique for sampling from a posterior distribution, variational inference and variable selection. Examples of successful applications of Bayesian analysis across various research fields are provided, including in social sciences, ecology, genetics, medicine and more. We propose strategies for reproducibility and reporting standards, outlining an updated WAMBS (when to Worry and how to Avoid the Misuse of Bayesian Statistics) checklist. Finally, we outline the impact of Bayesian analysis on artificial intelligence, a major goal in the next decade.
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Holes in Bayesian Statistics
Journal of Physics G: Nuclear and Particle Physics, 2020Co-Authors: Andrew Gelman, Yuling YaoAbstract:Every philosophy has holes, and it is the responsibility of proponents of a philosophy to point out these problems. Here are a few holes in Bayesian data analysis: (1) the usual rules of conditional probability fail in the quantum realm, (2) flat or weak priors lead to terrible inferences about things we care about, (3) subjective priors are incoherent, (4) Bayes factors fail in the presence of flat or weak priors, (5) for Cantorian reasons we need to check our models, but this destroys the coherence of Bayesian inference. Some of the problems of Bayesian Statistics arise from people trying to do things they should not be trying to do, but other holes are not so easily patched. In particular, it may be a good idea to avoid flat, weak, or conventional priors, but such advice, if followed, would go against the vast majority of Bayesian practice and requires us to confront the fundamental incoherence of Bayesian inference. This does not mean that we think Bayesian inference is a bad idea, but it does mean that there is a tension between Bayesian logic and Bayesian workflow which we believe can only be resolved by considering Bayesian logic as a tool, a way of revealing inevitable misfits and incoherences in our model assumptions, rather than as an end in itself.
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Decision theory and Bayesian Statistics
Oxford Scholarship Online, 2017Co-Authors: Andrew Gelman, Deborah NolanAbstract:This chapter outlines some of our more effective demonstrations for teaching decision theory and Bayesian Statistics. Our contribution here is in the tricks used to involve students; the ideas behind most of the demonstrations are well known. The activities serve several purposes, including focusing student attention on difficult conceptual issues that are hard to learn in a lecture or by solving homework problems (e.g., the principle of expected gain and determining the value of a life); alerting students to their cognitive illusions (e.g., the incoherent utilities for money and uncalibrated subjective probability intervals); bringing personal issues into the class (e.g., different areas of knowledge in the subjective probability intervals and personal decision problems); dramatizing counterintuitive results which a student might not realize as counterintuitive; and demonstrating the multiple levels of uncertainty in a Bayesian analysis, as well as the coverage property of posterior intervals.
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Philosophy and the practice of Bayesian Statistics
The British journal of mathematical and statistical psychology, 2012Co-Authors: Andrew Gelman, Cosma Rohilla ShaliziAbstract:A substantial school in the philosophy of science identies 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 hypothetico-deductivism. 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
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philosophy and the practice of Bayesian Statistics
arXiv: Statistics Theory, 2010Co-Authors: Andrew Gelman, Cosma Rohilla ShaliziAbstract: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 hypothetico-deductivism. 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.
Jeff Gill - One of the best experts on this subject based on the ideXlab platform.
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Introduction to Applied Bayesian Statistics and Estimation for Social Scientists
Journal of the American Statistical Association, 2008Co-Authors: Jeff GillAbstract:Gill reviews Introduction to Applied Bayesian Statistics and Estimation for Social Scientists by Scott M. Lynch.
Deborah Ashby - One of the best experts on this subject based on the ideXlab platform.
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Bayesian Statistics in medicine: a 25 year review
Statistics in medicine, 2006Co-Authors: Deborah AshbyAbstract:This review examines the state of Bayesian thinking as Statistics in Medicine was launched in 1982, reflecting particularly on its applicability and uses in medical research. It then looks at each subsequent five-year epoch, with a focus on papers appearing in Statistics in Medicine, putting these in the context of major developments in Bayesian thinking and computation with reference to important books, landmark meetings and seminal papers. It charts the growth of Bayesian Statistics as it is applied to medicine and makes predictions for the future. From sparse beginnings, where Bayesian Statistics was barely mentioned, Bayesian Statistics has now permeated all the major areas of medical Statistics, including clinical trials, epidemiology, meta-analyses and evidence synthesis, spatial modelling, longitudinal modelling, survival modelling, molecular genetics and decision-making in respect of new technologies.
Yuling Yao - One of the best experts on this subject based on the ideXlab platform.
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Holes in Bayesian Statistics
Journal of Physics G: Nuclear and Particle Physics, 2020Co-Authors: Andrew Gelman, Yuling YaoAbstract:Every philosophy has holes, and it is the responsibility of proponents of a philosophy to point out these problems. Here are a few holes in Bayesian data analysis: (1) the usual rules of conditional probability fail in the quantum realm, (2) flat or weak priors lead to terrible inferences about things we care about, (3) subjective priors are incoherent, (4) Bayes factors fail in the presence of flat or weak priors, (5) for Cantorian reasons we need to check our models, but this destroys the coherence of Bayesian inference. Some of the problems of Bayesian Statistics arise from people trying to do things they should not be trying to do, but other holes are not so easily patched. In particular, it may be a good idea to avoid flat, weak, or conventional priors, but such advice, if followed, would go against the vast majority of Bayesian practice and requires us to confront the fundamental incoherence of Bayesian inference. This does not mean that we think Bayesian inference is a bad idea, but it does mean that there is a tension between Bayesian logic and Bayesian workflow which we believe can only be resolved by considering Bayesian logic as a tool, a way of revealing inevitable misfits and incoherences in our model assumptions, rather than as an end in itself.
Cosma Rohilla Shalizi - One of the best experts on this subject based on the ideXlab platform.
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Philosophy and the practice of Bayesian Statistics
The British journal of mathematical and statistical psychology, 2012Co-Authors: Andrew Gelman, Cosma Rohilla ShaliziAbstract:A substantial school in the philosophy of science identies 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 hypothetico-deductivism. 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
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philosophy and the practice of Bayesian Statistics
arXiv: Statistics Theory, 2010Co-Authors: Andrew Gelman, Cosma Rohilla ShaliziAbstract: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 hypothetico-deductivism. 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.
