  We present a new approach to parameter inference targeted on generic
situations where the evaluation of the likelihood $\mathcal{L}$ (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 $\chi^2=-2\ln\mathcal{L}$ 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 $\chi^2$ and
rapidly zooms in on the minimum of $\chi^2$. The sampled $\chi^2$ 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 $\chi^2$) 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.
