46,667 research outputs found
Where do statistical models come from? Revisiting the problem of specification
R. A. Fisher founded modern statistical inference in 1922 and identified its
fundamental problems to be: specification, estimation and distribution. Since
then the problem of statistical model specification has received scant
attention in the statistics literature. The paper traces the history of
statistical model specification, focusing primarily on pioneers like Fisher,
Neyman, and more recently Lehmann and Cox, and attempts a synthesis of their
views in the context of the Probabilistic Reduction (PR) approach. As argued by
Lehmann [11], a major stumbling block for a general approach to statistical
model specification has been the delineation of the appropriate role for
substantive subject matter information. The PR approach demarcates the
interrelated but complemenatry roles of substantive and statistical information
summarized ab initio in the form of a structural and a statistical model,
respectively. In an attempt to preserve the integrity of both sources of
information, as well as to ensure the reliability of their fusing, a purely
probabilistic construal of statistical models is advocated. This probabilistic
construal is then used to shed light on a number of issues relating to
specification, including the role of preliminary data analysis, structural vs.
statistical models, model specification vs. model selection, statistical vs.
substantive adequacy and model validation.Comment: Published at http://dx.doi.org/10.1214/074921706000000419 in the IMS
Lecture Notes--Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
Mathematical models of games of chance: Epistemological taxonomy and potential in problem-gambling research
Games of chance are developed in their physical consumer-ready form on the basis of mathematical models, which stand as the premises of their existence and represent their physical processes. There is a prevalence of statistical and probabilistic models in the interest of all parties involved in the study of gambling – researchers, game producers and operators, and players – while functional models are of interest more to math-inclined players than problem-gambling researchers. In this paper I present a structural analysis of the knowledge attached to mathematical models of games of chance and the act of modeling, arguing that such knowledge holds potential in the prevention and cognitive treatment of excessive gambling, and I propose further research in this direction
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