# Laplace's Method Approximations for Probabilistic Inference in Belief Networks with Continuous Variables

arXiv: https://arxiv.org/abs/1302.6782 · HTML: https://mlsanity.com/paper/1302.6782/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2013.

## Built on by (most cited first, 5 of 5)

- [CFARnet: deep learning for target detection with constant false alarm rate](https://mlsanity.com/paper/2208.02474/) (2022)
- [Towards Zero-shot Language Modeling](https://mlsanity.com/paper/2108.03334/) (2021)
- [L2M: Practical posterior Laplace approximation with optimization-driven second moment estimation](https://mlsanity.com/paper/2107.04695/) (2021)
- [Variational Laplace for Bayesian neural networks](https://mlsanity.com/paper/2103.00222/) (2021)
- [Deep Learning Aided Laplace Based Bayesian Inference for Epidemiological Systems](https://mlsanity.com/paper/2210.08865/) (2022)

## Abstract (arXiv)

Laplace's method, a family of asymptotic methods used to approximate integrals, is presented as a potential candidate for the tool box of techniques used for knowledge acquisition and probabilistic inference in belief networks with continuous variables. This technique approximates posterior moments and marginal posterior distributions with reasonable accuracy [errors are O(n^-2) for posterior means] in many interesting cases. The method also seems promising for computing approximations for Bayes factors for use in the context of model selection, model uncertainty and mixtures of pdfs. The limitations, regularity conditions and computational difficulties for the implementation of Laplace's method are comparable to those associated with the methods of maximum likelihood and posterior mode analysis.