# Model Comparison in Approximate Bayesian Computation

arXiv: https://arxiv.org/abs/2203.11276 · HTML: https://mlsanity.com/paper/2203.11276/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 54 references that are in the map.
- First posted on arXiv 15 Mar 2022.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [Fast ε-free Inference of Simulation Models with Bayesian Conditional Density Estimation](https://mlsanity.com/paper/1605.06376/) (2016)
- [Learning Summary Statistic for Approximate Bayesian Computation via Deep Neural Network](https://mlsanity.com/paper/1510.02175/) (2015)
- [Accelerating Approximate Bayesian Computation with Quantile Regression: Application to Cosmological Redshift Distributions](https://mlsanity.com/paper/1707.07498/) (2017)

## Abstract (arXiv)

A common problem in natural sciences is the comparison of competing models in the light of observed data. Bayesian model comparison provides a statistically sound framework for this comparison based on the evidence each model provides for the data. However, this framework relies on the calculation of likelihood functions which are intractable for most models used in practice. Previous approaches in the field of Approximate Bayesian Computation (ABC) circumvent the evaluation of the likelihood and estimate the model evidence based on rejection sampling, but they are typically computationally intense. Here, I propose a new efficient method to perform Bayesian model comparison in ABC. Based on recent advances in posterior density estimation, the method approximates the posterior over models in parametric form. In particular, I train a mixture-density network to map features of the observed data to the posterior probability of the models. The performance is assessed with two examples. On a tractable model comparison problem, the underlying exact posterior probabilities are predicted accurately. In a use-case scenario from computational neuroscience -- the comparison between two ion channel models -- the underlying ground-truth model is reliably assigned a high posterior probability. Overall, the method provides a new efficient way to perform Bayesian model comparison on complex biophysical models independent of the model architecture.