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Bayes Factors
, 1995
"... In a 1935 paper, and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null ..."
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Cited by 1176 (71 self)
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In a 1935 paper, and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null is onehalf. Although there has been much discussion of Bayesian hypothesis testing in the context of criticism of P values, less attention has been given to the Bayes factor as a practical tool of applied statistics. In this paper we review and discuss the uses of Bayes factors in the context of five scientific applications in genetics, sports, ecology, sociology and psychology.
Bayesian Model Selection in Social Research (with Discussion by Andrew Gelman & Donald B. Rubin, and Robert M. Hauser, and a Rejoinder)
 SOCIOLOGICAL METHODOLOGY 1995, EDITED BY PETER V. MARSDEN, CAMBRIDGE,; MASS.: BLACKWELLS.
, 1995
"... It is argued that Pvalues and the tests based upon them give unsatisfactory results, especially in large samples. It is shown that, in regression, when there are many candidate independent variables, standard variable selection procedures can give very misleading results. Also, by selecting a singl ..."
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Cited by 323 (19 self)
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It is argued that Pvalues and the tests based upon them give unsatisfactory results, especially in large samples. It is shown that, in regression, when there are many candidate independent variables, standard variable selection procedures can give very misleading results. Also, by selecting a single model, they ignore model uncertainty and so underestimate the uncertainty about quantities of interest. The Bayesian approach to hypothesis testing, model selection and accounting for model uncertainty is presented. Implementing this is straightforward using the simple and accurate BIC approximation, and can be done using the output from standard software. Specific results are presented for most of the types of model commonly used in sociology. It is shown that this approach overcomes the difficulties with P values and standard model selection procedures based on them. It also allows easy comparison of nonnested models, and permits the quantification of the evidence for a null hypothesis...
Bayes factors and model uncertainty
 DEPARTMENT OF STATISTICS, UNIVERSITY OFWASHINGTON
, 1993
"... In a 1935 paper, and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null ..."
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Cited by 95 (6 self)
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In a 1935 paper, and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null is onehalf. Although there has been much discussion of Bayesian hypothesis testing in the context of criticism of Pvalues, less attention has been given to the Bayes factor as a practical tool of applied statistics. In this paper we review and discuss the uses of Bayes factors in the context of five scientific applications. The points we emphasize are: from Jeffreys's Bayesian point of view, the purpose of hypothesis testing is to evaluate the evidence in favor of a scientific theory; Bayes factors offer a way of evaluating evidence in favor ofa null hypothesis; Bayes factors provide a way of incorporating external information into the evaluation of evidence about a hypothesis; Bayes factors are very general, and do not require alternative models to be nested; several techniques are available for computing Bayes factors, including asymptotic approximations which are easy to compute using the output from standard packages that maximize likelihoods; in "nonstandard " statistical models that do not satisfy common regularity conditions, it can be technically simpler to calculate Bayes factors than to derive nonBayesian significance
What We Have Learned: RC 28’s contributions to Knowledge about
 Social Stratification.” Research in Social Stratification and Mobility 24(1):1–20
, 2006
"... about 40 RC members collectively took stock of the empirical generalizations and conceptual developments that can be traced to the activities of RC28. The session was billed as a discussion of our research agenda for the future, but it quickly became clear that we could not specify a future until we ..."
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Cited by 17 (2 self)
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about 40 RC members collectively took stock of the empirical generalizations and conceptual developments that can be traced to the activities of RC28. The session was billed as a discussion of our research agenda for the future, but it quickly became clear that we could not specify a future until we agreed on our past, that is, what we have learned up till now. The exchange was very engaging. Some generalizations and ideas drew assent quickly, but most spawned discussion. Some were nominated only to be withdrawn after the consensus in the room contradicted the nomination. We moved the “MMI ” hypothesis1 from “empirical generalization ” to “concept ” after several speakers cited exceptions to MMI’s predictions but affirmed the usefulness of those predictions as a guide to research. I was very gratified by the amount and quality of the collective discussion. It was a risk to walk into a room and ask 40 people to assess our collective life with very little prompting. People responded enthusiastically, and all the participants I heard from declared it an interesting and useful exercise. Table 1 (at the back of this document) lists our generalizations and concepts in the order they appeared on the board in
Intergenerational occupational mobility in britain and the us since 1850
 American Economic Review
, 2012
"... The U.S. tolerates more inequality than Europe and believes its economic mobility is greater than Europe’s, though they had roughly equal rates of intergenerational occupational mobility in the late twentieth century. We extend this comparison into the nineteenth century using 23,000 nationallyrepr ..."
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Cited by 4 (1 self)
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The U.S. tolerates more inequality than Europe and believes its economic mobility is greater than Europe’s, though they had roughly equal rates of intergenerational occupational mobility in the late twentieth century. We extend this comparison into the nineteenth century using 23,000 nationallyrepresentative British and U.S. fathers and sons. The U.S. was more mobile than Britain through 1900, so in the experience of those who created the U.S. welfare state in the 1930s, the U.S. had indeed been “exceptional. ” The U.S. mobility lead over Britain was erased by the 1950s, as U.S. mobility fell from its nineteenth century levels. [W]e have really everything in common with America nowadays, except, of course, language. Oscar Wilde, The Canterville Ghost (1887). The economies of Britain and the U.S. have had much in common over the two centuries since the American Revolution: their legal traditions and property rights systems, sources of labor, capital, and technology, political ties and alliances in two world wars, and – Wilde’s quip notwithstanding – language and culture are the most obvious. One significant respect in which
Bayes Factors and BIC: Comment on Weakliem
, 1998
"... Weakliem agrees that Bayes factors are useful for model selection and hypothesis testing. He reminds us that the simple and convenient BIC approximation corresponds most closely to one particular prior on the parameter space, the unit information prior, and points out that researchers may have diffe ..."
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Cited by 4 (0 self)
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Weakliem agrees that Bayes factors are useful for model selection and hypothesis testing. He reminds us that the simple and convenient BIC approximation corresponds most closely to one particular prior on the parameter space, the unit information prior, and points out that researchers may have different prior information or opinions. Clearly a prior that represents the available information should be used, although the unit information prior often seems reasonable in the absence of strong prior information. It seems that, among the Bayes factors likely to be used in practice, BIC is conservative in the sense of tending to provide less evidence for additional parameters or "effects". Thus if a Bayes factor based on additional prior information favors an effect, but BIC does not, the prior information is playing a crucial role and this should be made clear when the research is reported. BIC may well have a role as a baseline reference analysis to be provided in routine reporting of research results, perhaps along with Bayes factors based on other priors. In Weakliem's 2 x 2 table examples, BIC and Bayes factors based on Weakliem's preferred priors lead to similar substantive conclusions, but both differ from those based on P values. When there is additional prior information, the technology now exists to express it as
JEL Classification: J62, N30 Page Proofs to:
, 2006
"... Late nineteenth century intergenerational occupational mobility was higher in the US than in Britain. Differences between them in this type of mobility are absent today. Using data on 10,000 US and British father and son pairs followed over two intervals (the 1860s and 1870s, and the 1880s and 1890s ..."
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Late nineteenth century intergenerational occupational mobility was higher in the US than in Britain. Differences between them in this type of mobility are absent today. Using data on 10,000 US and British father and son pairs followed over two intervals (the 1860s and 1870s, and the 1880s and 1890s), we examine how this convergence occurred. The US remained more mobile then Britain through 1900, but the difference fell over the last two decades of the nineteenth century (as British mobility rose) and was erased by the 1950s (as mobility fell by more in the US than in Britain).
Effects of SelfRated Disability and Subjective Health on Job
"... This paper represents the views of the author and does not necessarily reflect the opinions of Statistics Canada. Data in many forms Statistics Canada disseminates data in a variety of forms. In addition to publications, both standard and special tabulations are offered. Data are available on the In ..."
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This paper represents the views of the author and does not necessarily reflect the opinions of Statistics Canada. Data in many forms Statistics Canada disseminates data in a variety of forms. In addition to publications, both standard and special tabulations are offered. Data are available on the Internet, compact disc, diskette, computer printouts, microfiche and microfilm, and magnetic tape. Maps and other geographic reference materials are available for some types of data. Direct online access to aggregated information is possible through CANSIM, Statistics Canada’s machinereadable database and retrieval system. How to obtain more information Inquiries about this product and related statistics or services should be directed to: Client Services, Income
Statistics in Sociology, 19502000: A Vignette
, 1999
"... Statistical methods have had a successful halfcentury in sociology, contributing to a greatly improved standard of scientic rigor in the discipline. I identify three overlapping postwar generations of statistical methods in sociology, based on the kinds of data they address. The rst generation, whi ..."
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Statistical methods have had a successful halfcentury in sociology, contributing to a greatly improved standard of scientic rigor in the discipline. I identify three overlapping postwar generations of statistical methods in sociology, based on the kinds of data they address. The rst generation, which started in the late 1940s, deals with crosstabulations, and focuses on measures of association and loglinear models, perhaps the area of statistics to which sociology has contributed the most. The second generation, which began in the 1960s, deals with unitlevel survey data, and focuses on LISRELtype causal models and event history analysis. The third generation, starting to emerge in the late 1980s, deals with data that are neither crosstabulations nor data matrices, either because they have a dierent form, such as texts or narratives, or because dependence is a crucial aspect, as with spatial or social network data. There are many new challenges and the area is ripe for statistic...