{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-simulated-annealing-approach-to-parameter","title":"A simulated annealing approach to parameter inference with expensive likelihoods","arxiv_id":"2205.07906","date":"2022-05-16","proceeding":null,"authors":["Aseem Paranjape"],"abstract":"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.","url_abs":"https://arxiv.org/abs/2205.07906v1","url_pdf":"https://arxiv.org/pdf/2205.07906v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-simulated-annealing-approach-to-parameter","repo_url":"https://bitbucket.org/aparanjape/picasa","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}