A General Framework for Model-Based Statistics

Hill, Joe R.

doi:10.2307/2336054

Cited by 10 publications

(20 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This similarity is expected to be the case more generally whenever non-informative priors are used in the Bayesian setting. As Hill (1990) describes "besides varying interpretation of probability, the only essential difference between the schools is in the model itself", that is, compare the model (14) used for the maximum likelihood frequentist procedure to the model (18) used for the Bayesian method which includes the addition of a prior. The fact that the posterior distribution for a parameter in the Bayesian setting is proportion to the likelihood function used in maximum likelihood times the prior should give intuition that there will not be much difference in the results as long as the likelihood (i.e.…”

Section: Resultsmentioning

confidence: 99%

Maximum Likelihood and Bayesian Estimation for Nonlinear Structural Equation Models

Wall

2009

The SAGE Handbook of Quantitative Methods in Psychology

View full text Add to dashboard Cite

Section: Resultsmentioning

confidence: 99%

Maximum Likelihood and Bayesian Estimation for Nonlinear Structural Equation Models

Wall

2009

The SAGE Handbook of Quantitative Methods in Psychology

View full text Add to dashboard Cite

“…Nor do we recommend that anyone become either of them, or anything other than a good rational scientist open to using whatever tools work well for the immediate task. [9][10][11][12][13] Simply put, a statistician claiming that one statistical philosophy (whether Bayesian, frequentist, or another) is preferred for all analyses would be like a carpenter claiming that screws are always better than nails for joining wood. 7,8 Many statisticians who include Bayesian methods prominently in their toolkit emphasize the need for model checks, including frequentist devices such as P values.…”

Section: Bayesians and Frequentists Versus Scientistsmentioning

confidence: 99%

Rejoinder

Greenland

Poole

2013

Epidemiology

View full text Add to dashboard Cite

REJOINDER W e thank Andrew Gelman for his comments 1 on our article. 2 We hope our response will clarify areas of agreement and disagreement. We also take the opportunity to address some larger issues about apparent disconnections: the disconnection between conventional statistical models and the realities of health and social-science research, and the disconnection between what methodologists seem to say one should do and what everyone, including methodologists, do (or, rather, do not do) in reality. BAYESIANS AND FREQUENTISTS VERSUS SCIENTISTSIt seems to us that Bayesian viewpoints and methods have a greater ability to reflect observational research realities than do conventional frequentist methods, 3 although relatively unconventional frequentist methods have been developed to address these concerns. 4 That is largely because conventional methods start from models of ideal experiments and elaborate them, always ending with a model that assumes "no confounding" or "ignorability" or the like, which is operationally equivalent to claiming that our data were produced by some kind of intricately designed randomized experiment. These approaches never confront the fact that (by definition) observational research is about situations in which no experiment has been conducted.In recommending Bayesian perspectives, we emphasize that we are neither Bayesians nor frequentists. Nor do we recommend that anyone become either of them, or anything other than a good rational scientist open to using whatever tools work well for the immediate task. 5,6 Pure Bayesian methodology is clearly insufficient if frequency performance is of concern (as it often is) and has other limits as well. 7,8 Many statisticians who include Bayesian methods prominently in their toolkit emphasize the need for model checks, including frequentist devices such as P values. 9-13 Simply put, a statistician claiming that one statistical philosophy (whether Bayesian, frequentist, or another) is preferred for all analyses would be like a carpenter claiming that screws are always better than nails for joining wood.More generally and relevantly for epidemiology, in the preface to his remarkable 1978 book on statistical modeling, Specification Searches 14 (out of print but available free online at the Anderson Project website), the econometrician Edward Leamer wrote: I am confident that the Bayesian approach helps us understand nonexperimental inference. It helps also to avoid certain errors. But I do not think it can truly solve all the problems. Nor do I foresee developments on the horizon that will make any mathematical theory of inference fully applicable. For better or for worse, real inference will remain a highly complicated, poorly understood phenomenon. 15 A generation earlier, Jerome Cornfield, perhaps the first Bayesian epidemiologic statistician, voiced similar reservations about statistical developments:From the

show abstract

“…Our perspective is not new; in methods and also in philosophy we follow statisticians such as Box (1980Box ( , 1983Box ( , 1990), Good and Crook (1974), Good (1983), Morris (1986), Hill (1990), and Jaynes (2003). All these writers emphasized the value of model checking and frequency evaluation as guidelines for Bayesian inference (or, to look at it another way, the value of Bayesian inference as an approach for obtaining statistical methods with good frequency peroperties; see Rubin 1984).…”

Section: It Then Continues Withmentioning

confidence: 99%

Philosophy and the Practice of Bayesian Statistics in the Social Sciences

Gelman

Shalizi

2012

Oxford Handbooks Online

View full text Add to dashboard Cite

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. The usual story-which we don't likeIn so far as I have a coherent philosophy of statistics, I hope it is "robust" enough to cope in principle with the whole of statistics, and sufficiently undogmatic not to imply that all those who may think rather differently from me are necessarily stupid. If at times I do seem dogmatic, it is because it is convenient to give my own views as unequivocally as possible. (Bartlett, 1967, p. 458) Schools of statistical inference are sometimes linked to approaches to the philosophy of science. "Classical" statistics-as exemplified by Fisher's p-values, Neyman-Pearson hypothesis tests, and Neyman's confidence intervals-is associated with the hypotheticodeductive and falsificationist view of science. Scientists devise hypotheses, deduce implications for observations from them, and test those implications. Scientific hypotheses can be rejected (that is, falsified), but never really established or accepted in the same way. Mayo (1996) presents the leading contemporary statement of this view. 1In contrast, Bayesian statistics or "inverse probability"-starting with a prior distribution, getting data, and moving to the posterior distribution-is associated with an inductive approach of learning about the general from particulars. Rather than testing and attempted falsification, learning proceeds more smoothly: an accretion of evidence is summarized by a posterior distribution, and scientific process is associated with the rise and fall in the posterior probabilities of various models; see Figure 1 for a schematic illustration. In this view, the expression p(θ|y) says it all, and the central goal of Bayesian inference is computing the posterior probabilities of hypotheses. Anything not contained in the posterior distribution p(θ|y) is simply irrelevant, and it would be irrational (or incoherent) to attempt falsification, unless that somehow shows up in the posterior. The goal is to learn about general law...

show abstract

A General Framework for Model-Based Statistics

Cited by 10 publications

References 19 publications

Maximum Likelihood and Bayesian Estimation for Nonlinear Structural Equation Models

Maximum Likelihood and Bayesian Estimation for Nonlinear Structural Equation Models

Rejoinder

Philosophy and the Practice of Bayesian Statistics in the Social Sciences

Contact Info

Product

Resources

About