Does Bayesian model averaging improve polynomial extrapolations? Two toy problems as tests

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