A Tutorial on Levels of Granularity: From Histograms to Clusters to Predictive Distributions
- https://doi.org/10.2991/jsta.2018.17.2.10How to use a DOI?
- Cluster Analysis; Finite Mixture Model; Bayesian models; Compound models; prior distribution; infinite mixture
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 © 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 -