|
| 1 | +- abstract': >- |
| 2 | + In Bayesian statistics, the choice of the prior can have |
| 3 | + an important influence on the posterior and the parameter |
| 4 | + estimation, especially when few data samples are available. To limit |
| 5 | + the added subjectivity from a priori information, one can use the |
| 6 | + framework of objective priors, more particularly, we focus on |
| 7 | + reference priors in this work. However, computing such priors is a |
| 8 | + difficult task in general. Hence, we consider cases where the |
| 9 | + reference prior simplifies to the Jeffreys prior. We develop in this |
| 10 | + paper a flexible algorithm based on variational inference which |
| 11 | + computes approximations of priors from a set of parametric |
| 12 | + distributions using neural networks. We also show that our algorithm |
| 13 | + can retrieve modified Jeffreys priors when constraints are specified |
| 14 | + in the optimization problem to ensure the solution is proper. We |
| 15 | + propose a simple method to recover a relevant approximation of the |
| 16 | + parametric posterior distribution using Markov Chain Monte Carlo |
| 17 | + (MCMC) methods even if the density function of the parametric prior |
| 18 | + is not known in general. Numerical experiments on several |
| 19 | + statistical models of increasing complexity are presented. We show |
| 20 | + the usefulness of this approach by recovering the target |
| 21 | + distribution. The performance of the algorithm is evaluated on both |
| 22 | + prior and posterior distributions, jointly using variational |
| 23 | + inference and MCMC sampling. |
| 24 | + authors: Nils Baillie, Antoine Van Biesbroeck and Clément Gauchy |
| 25 | + bibtex: >+ |
| 26 | + @article{baillie2025, |
| 27 | + author = {Baillie, Nils and Van Biesbroeck, Antoine and Gauchy, |
| 28 | + Clément}, |
| 29 | + publisher = {French Statistical Society}, |
| 30 | + title = {Variational Inference for Approximate Objective Priors Using |
| 31 | + Neural Networks}, |
| 32 | + journal = {Computo}, |
| 33 | + date = {2025-12-01}, |
| 34 | + doi = {10.57750/76fh-t442}, |
| 35 | + issn = {2824-7795}, |
| 36 | + langid = {en}, |
| 37 | + abstract = {In Bayesian statistics, the choice of the prior can have |
| 38 | + an important influence on the posterior and the parameter |
| 39 | + estimation, especially when few data samples are available. To limit |
| 40 | + the added subjectivity from a priori information, one can use the |
| 41 | + framework of objective priors, more particularly, we focus on |
| 42 | + reference priors in this work. However, computing such priors is a |
| 43 | + difficult task in general. Hence, we consider cases where the |
| 44 | + reference prior simplifies to the Jeffreys prior. We develop in this |
| 45 | + paper a flexible algorithm based on variational inference which |
| 46 | + computes approximations of priors from a set of parametric |
| 47 | + distributions using neural networks. We also show that our algorithm |
| 48 | + can retrieve modified Jeffreys priors when constraints are specified |
| 49 | + in the optimization problem to ensure the solution is proper. We |
| 50 | + propose a simple method to recover a relevant approximation of the |
| 51 | + parametric posterior distribution using Markov Chain Monte Carlo |
| 52 | + (MCMC) methods even if the density function of the parametric prior |
| 53 | + is not known in general. Numerical experiments on several |
| 54 | + statistical models of increasing complexity are presented. We show |
| 55 | + the usefulness of this approach by recovering the target |
| 56 | + distribution. The performance of the algorithm is evaluated on both |
| 57 | + prior and posterior distributions, jointly using variational |
| 58 | + inference and MCMC sampling.} |
| 59 | + } |
| 60 | +
|
| 61 | + date: 2025-12-01 |
| 62 | + description: '' |
| 63 | + doi: 10.57750/76fh-t442 |
| 64 | + draft: false |
| 65 | + journal: Computo |
| 66 | + pdf: '' |
| 67 | + repo: published-202512-baillie-varp |
| 68 | + title: Variational inference for approximate objective priors using neural networks |
| 69 | + url: '' |
| 70 | + year: 2025 |
1 | 71 | - abstract': >- |
2 | 72 | The Maximum Mean Discrepancy (MMD) is a kernel-based |
3 | 73 | metric widely used for nonparametric tests and estimation. Recently, |
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