Journal of Statistical Theory and Applications

Volume 17, Issue 2, June 2018, Pages 307 - 323

A Tutorial on Levels of Granularity: From Histograms to Clusters to Predictive Distributions

Authors
STANLEY L. SCLOVEslsclove@uic.edu
Department of Information & Decision Sciences, University of Illinois at Chicago, 601 S. Morgan St., Chicago, IL 60607-7124
Received 13 March 2017, Accepted 30 May 2017, Available Online 30 June 2018.
DOI
https://doi.org/10.2991/jsta.2018.17.2.10How to use a DOI?
Keywords
Cluster Analysis; Finite Mixture Model; Bayesian models; Compound models; prior distribution; infinite mixture
Abstract

Consider the problem of modeling datasets such as numbers of accidents in a population of insured persons, or incidences of an illness in a population. Various levels of detail or granularity may be considered in describing the parent population. The levels used in fitting data and hence in describing the population may vary from a single distribution, possibly with extreme values, to a bimodal distribution, to a mixture of two or more distributions via the Finite Mixture Model, to modeling the population at the individual level via a compound model, which may be viewed as an infinite mixture model. Given a dataset, it is shown how to evaluate the fits of the various models by information criteria. Two datasets are considered in detail, one discrete, the other, continuous.

Copyright
Copyright © 2018, the Authors. Published by Atlantis Press.
Open Access
This is an open access article under the CC BY-NC license (http://creativecommons.org/licences/by-nc/4.0/).

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Journal
Journal of Statistical Theory and Applications
Volume-Issue
17 - 2
Pages
307 - 323
Publication Date
2018/06/30
ISSN (Online)
2214-1766
ISSN (Print)
1538-7887
DOI
https://doi.org/10.2991/jsta.2018.17.2.10How to use a DOI?
Copyright
Copyright © 2018, the Authors. Published by Atlantis Press.
Open Access
This is an open access article under the CC BY-NC license (http://creativecommons.org/licences/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - STANLEY L. SCLOVE
PY  - 2018
DA  - 2018/06/30
TI  - A Tutorial on Levels of Granularity: From Histograms to Clusters to Predictive Distributions
JO  - Journal of Statistical Theory and Applications
SP  - 307
EP  - 323
VL  - 17
IS  - 2
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.2018.17.2.10
DO  - https://doi.org/10.2991/jsta.2018.17.2.10
ID  - SCLOVE2018
ER  -