Prior-based model checking

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  • Author: Luai Al-Labadi and Michael Evans
  • Date: 29 March 2019
  • Copyright: Image copyright of Patrick Rhodes

Model checking procedures are considered based on the use of the Dirichlet process and relative belief. This combination is seen to lead to some unique advantages for this problem. Of considerable importance is the selection of the hyperparameters for the Dirichlet process. A particular choice is advocated in a paper published in The Canadian Journal of Statistics for the base distribution that avoids prior‐data conflict and double use of the data, while the choice of the concentration parameter is based on elicitation. Several examples are presented in which the proposed approach exhibits excellent performance.

The paper is available here and the authors explain their findings below:

Prior‐based model checking

Luai Al-Labadi and Michael Evans

The Canadian Journal of Statistics, Volume 46, Issue 3, September 2018, pages 380-398

thumbnail image: Prior-based model checking

Statistical analyses always incorporate assumptions. It is never certain whether these assumptions are true or false. If an assumption is indeed false, then any conclusions drawn in the analysis may be seriously in error. As such, it is important that, as part of a statistical analysis, all assumptions made be checked. Part of the development of statistical theory is providing methodology for carrying out such checks and these are generally based on the data.

The statistical model chosen for the analysis is undoubtedly the most important assumption. The model is a set of candidate probability distributions such that the data can be considered as being generated from one of these. Model checking methodology assesses how likely it is that the data could have arisen from the model. Naturally, if the data is very unlikely for every distribution in the model, then the validity of the model is suspect.

This paper supplies a Bayesian methodology for checking the model. This means that the statistician can incorporate into the analysis their prior beliefs about how suitable the model is while allowing for the possibility that it is incorrect. A measure of statistical evidence is used to determine whether there is evidence in favor of or against the model being correct and an assessment of the strength of the evidence is provided. The fact that evidence in favor of the model can be achieved is a unique aspect of the methodology. When strong evidence in favour of a model is realized, this can only increase confidence in the subsequent use of the model. Also quite complicated models can be checked with this approach.

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