# Does Bayesian Model Averaging improve polynomial extrapolations? Two toy problems as tests

arXiv: https://arxiv.org/abs/2106.05906 · HTML: https://mlsanity.com/paper/2106.05906/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2021.

## Built on by (most cited first, 1 of 1)

- [Machine Learning in Nuclear Physics](https://mlsanity.com/paper/2112.02309/) (2021)

## Abstract (arXiv)

We assess the accuracy of Bayesian polynomial extrapolations from small parameter values, x, to large values of x. We consider a set of polynomials of fixed order, intended as a proxy for a fixed-order effective field theory (EFT) description of data. We employ Bayesian Model Averaging (BMA) to combine results from different order polynomials (EFT orders). Our study considers two "toy problems" where the underlying function used to generate data sets is known. We use Bayesian parameter estimation to extract the polynomial coefficients that describe these data at low x. A "naturalness" prior is imposed on the coefficients, so that they are O(1). We Bayesian-Model-Average different polynomial degrees by weighting each according to its Bayesian evidence and compare the predictive performance of this Bayesian Model Average with that of the individual polynomials. The credibility intervals on the BMA forecast have the stated coverage properties more consistently than does the highest evidence polynomial, though BMA does not necessarily outperform every polynomial.