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We present a new approach to parameter inference targeted on genericsituations where the evaluation of the likelihood $\mathcal{L}$ (i.e., theprobability to observe the data given a fixed model configuration) isnumerically expensive. Inspired by ideas underlying simulated annealing, themethod first evaluates $\chi^2=-2\ln\mathcal{L}$ on a sparse sequence of Latinhypercubes of increasing density in parameter (eigen)space. The semi-stochasticchoice of sampling points accounts for anisotropic gradients of $\chi^2$ andrapidly zooms in on the minimum of $\chi^2$. The sampled $\chi^2$ values arethen used to train an interpolator which is further used in a standard MarkovChain Monte Carlo (MCMC) algorithm to inexpensively explore the parameter spacewith high density, similarly to emulator-based approaches now popular incosmological studies. Comparisons with example linear and non-linear problemsshow gains in the number of likelihood evaluations of factors of 10 to 100 ormore, as compared to standard MCMC algorithms. As a specific implementation, wepublicly release the code PICASA: Parameter Inference using Cobaya withAnisotropic Simulated Annealing, which combines the minimizer (of auser-defined $\chi^2$) with Gaussian Process Regression for training theinterpolator 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 incosmology, astrophysics and beyond.

A simulated annealing approach to parameter inference with expensive likelihoods