کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6799301 | 542041 | 2016 | 22 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Bayes Factors, relations to Minimum Description Length, and overlapping model classes
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
This article presents a non-technical perspective on two prominent methods for analyzing experimental data in order to select among model classes. Each class consists of model instances; each instance predicts a unique distribution of data outcomes. One method is Bayesian Model Selection (BMS), instantiated with the Bayes factor. The other is based on the Minimum Description Length principle (MDL), instantiated by a variant of Normalized Maximum Likelihood (NML): the variant is termed NML* and takes prior probabilities into account. The methods are closely related. The Bayes factor is a ratio of two values: V1 for model class M1, and V2 for M2. Each Vjis the sum over the instances of Mj,of thejoint probabilities (prior times likelihood) for the observed data, normalized by a sum of such sums for all possible data outcomes. NML* is qualitatively similar: The value it assigns to each class is the maximum over the instances in Miof the joint probability for the observed data normalized by a sum of such maxima for all possible data outcomes. The similarity of BMS to NML* is particularly close when model classes do not have instances that overlap, a way of comparing model classes that we advocate generally. These observations and suggestions are illustrated throughout with use of a simple example borrowed from Heck, Wagenmakers, and Morey (2015) in which the instances predict a binomial distribution of number of successes in N trials. The model classes posit the binomial probability of success to lie in various regions of the interval [0,1]. We illustrate the theory and the example not with equations but with tables coupled with simple arithmetic. Using the binomial example we carry out comparisons of BMS and NML* that do and do not involve model classes that overlap, and do and do not have uniform priors. When the classes do not overlap BMS and NML* produce qualitatively similar results.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Psychology - Volume 72, June 2016, Pages 56-77
Journal: Journal of Mathematical Psychology - Volume 72, June 2016, Pages 56-77
نویسندگان
Richard M. Shiffrin, Suyog H. Chandramouli, Peter D. Grünwald,