Phenomenological R-Matrix Theory and Bayesian Inference

For many years, $\chi^2$ minimization has been the tool of choice for applying the phenomenological $R$-matrix theory. The need for comprehensive error estimates, more flexible statistical models, and the inclusion of prior information has driven progress in applying Bayesian inference to the $R$-matrix. While those projects have included sophisticated statistical models, they are limited to fairly simple $R$-matrix approximations. I will discuss recent efforts to expand the reach of Bayesian inference to much more complex $R$-matrix calculations. This has been achieved by coupling a Markov Chain Monte Carlo sampler to a high-performance $R$-matrix code, AZURE2. I will present the results of a benchmark calculation of $^{12}\rm{C}(p,\gamma)$ as well as recent developments in the analysis of $^3\rm{He}-^4\rm{He}$ scattering and capture. In particular, I will emphasize the usefulness and scope of the implementation as well as the importance of statistical modeling.