2022/05/16 by Paranjape, Aseem
#Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #Instrumentation and Methods for Astrophysics (astro-ph.IM)
paper · doi:10.48550/arxiv.2205.07906
We present a new approach to parameter inference targeted on generic situations where the evaluation of the likelihood L (i.e., the probability to observe the data given a fixed model configuration) is numerically expensive. Inspired by ideas underlying simulated annealing, the method first evaluates χ2=-2\lnL on a sparse sequence of Latin hypercubes of increasing density in parameter (eigen)space. The semi-stochastic choice of sampling points accounts for anisotropic gradients of χ2 and rapidly zooms in on the minimum of χ2. The sampled χ2 values are then used to train an interpolator which is further used in a standard Markov Chain Monte Carlo (MCMC) algorithm to inexpensively explore the parameter space with high density, similarly to emulator-based approaches now popular in cosmological studies. Comparisons with example linear and non-linear problems show gains in the number of likelihood evaluations of factors of 10 to 100 or more, as compared to standard MCMC algorithms. As a specific implementation, we publicly release the code PICASA: Parameter Inference using Cobaya with Anisotropic Simulated Annealing, which combines the minimizer (of a user-defined χ2) with Gaussian Process Regression for training the interpolator and a subsequent MCMC implementation using the COBAYA framework. Being agnostic to the nature of the observable data and the theoretical model, our implementation is potentially useful for a number of emerging problems in cosmology, astrophysics and beyond.