On the large-sample limits of some Bayesian model evaluation statistics
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914116954750976 |
|---|---|
| author | Nguyen, Hien Duy Gupta, Mayetri Westerhout, Jacob Nguyen, TrungTin |
| author_facet | Nguyen, Hien Duy Gupta, Mayetri Westerhout, Jacob Nguyen, TrungTin |
| contents | Model selection and order selection problems frequently arise in statistical practice. A popular approach to addressing these problems in the frequentist setting involves information criteria based on penalised maxima of log-likelihoods for competing models. In the Bayesian context, similar criteria are employed, replacing the maximised log-likelihoods with posterior expectations of the log-likelihood. Despite their popularity in applications, the large-sample behaviour of these criteria -- such as the deviance information criterion (DIC), Bayesian predictive information criterion (BPIC), and widely applicable Bayesian information criterion (WBIC) -- has received relatively little attention. In this work, we investigate the almost-sure limits of these criteria and establish novel results on posterior and generalised posterior consistency, which are of independent interest. The utility of our theoretical findings is demonstrated via illustrative technical and numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03846 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the large-sample limits of some Bayesian model evaluation statistics Nguyen, Hien Duy Gupta, Mayetri Westerhout, Jacob Nguyen, TrungTin Statistics Theory Model selection and order selection problems frequently arise in statistical practice. A popular approach to addressing these problems in the frequentist setting involves information criteria based on penalised maxima of log-likelihoods for competing models. In the Bayesian context, similar criteria are employed, replacing the maximised log-likelihoods with posterior expectations of the log-likelihood. Despite their popularity in applications, the large-sample behaviour of these criteria -- such as the deviance information criterion (DIC), Bayesian predictive information criterion (BPIC), and widely applicable Bayesian information criterion (WBIC) -- has received relatively little attention. In this work, we investigate the almost-sure limits of these criteria and establish novel results on posterior and generalised posterior consistency, which are of independent interest. The utility of our theoretical findings is demonstrated via illustrative technical and numerical examples. |
| title | On the large-sample limits of some Bayesian model evaluation statistics |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2502.03846 |