A Tutorial on Levels of Granularity: From Histograms to Clusters to Predictive Distributions
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 describi...
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| Format: | Article |
| Language: | English |
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Springer
2018-06-01
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| Series: | Journal of Statistical Theory and Applications (JSTA) |
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| Online Access: | https://www.atlantis-press.com/article/25898352/view |
| _version_ | 1818007060239876096 |
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| author | STANLEY L. SCLOVE |
| author_facet | STANLEY L. SCLOVE |
| author_sort | STANLEY L. SCLOVE |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-14T05:10:48Z |
| format | Article |
| id | doaj.art-4c5e19b1d58146e79be788233fd9f710 |
| institution | Directory Open Access Journal |
| issn | 1538-7887 |
| language | English |
| last_indexed | 2024-04-14T05:10:48Z |
| publishDate | 2018-06-01 |
| publisher | Springer |
| record_format | Article |
| series | Journal of Statistical Theory and Applications (JSTA) |
| spelling | doaj.art-4c5e19b1d58146e79be788233fd9f7102022-12-22T02:10:35ZengSpringerJournal of Statistical Theory and Applications (JSTA)1538-78872018-06-0117210.2991/jsta.2018.17.2.10A Tutorial on Levels of Granularity: From Histograms to Clusters to Predictive DistributionsSTANLEY L. SCLOVEConsider 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.https://www.atlantis-press.com/article/25898352/viewCluster AnalysisFinite Mixture ModelBayesian modelsCompound modelsprior distributioninfinite mixture |
| spellingShingle | STANLEY L. SCLOVE A Tutorial on Levels of Granularity: From Histograms to Clusters to Predictive Distributions Journal of Statistical Theory and Applications (JSTA) Cluster Analysis Finite Mixture Model Bayesian models Compound models prior distribution infinite mixture |
| title | A Tutorial on Levels of Granularity: From Histograms to Clusters to Predictive Distributions |
| title_full | A Tutorial on Levels of Granularity: From Histograms to Clusters to Predictive Distributions |
| title_fullStr | A Tutorial on Levels of Granularity: From Histograms to Clusters to Predictive Distributions |
| title_full_unstemmed | A Tutorial on Levels of Granularity: From Histograms to Clusters to Predictive Distributions |
| title_short | A Tutorial on Levels of Granularity: From Histograms to Clusters to Predictive Distributions |
| title_sort | tutorial on levels of granularity from histograms to clusters to predictive distributions |
| topic | Cluster Analysis Finite Mixture Model Bayesian models Compound models prior distribution infinite mixture |
| url | https://www.atlantis-press.com/article/25898352/view |
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