Papers › A simulated annealing approach to parameter inference with expensive likelihoods
A simulated annealing approach to parameter inference with expensive likelihoods
Aseem Paranjape
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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=-2lnℒ 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.
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