Efficient Likelihood Evaluation of State-Space Representations

We develop a numerical procedure that facilitates efficient likelihood evaluation in applications involving non-linear and non-Gaussian state-space models. The procedure employs continuous approximations of filtering densities, and delivers unconditionally optimal global approximations of targeted integrands to achieve likelihood approximation. Optimized approximations of targeted integrands are constructed via efficient importance sampling. Resulting likelihood approximations are continuous functions of model parameters, greatly enhancing parameter estimation. We illustrate our procedure in applications to dynamic stochastic general equilibrium models.Adaption, dynamic stochastic general equilibrium model, efficient importance sampling, kernel density approximation, particle filter.

Bayesian optimisation for likelihood-free cosmological inference

Many cosmological models have only a finite number of parameters of interest, but a very expensive data-generating process and an intractable likelihood function. We address the problem of performing likelihood-free Bayesian inference from such black-box simulation-based models, under the constraint of a very limited simulation budget (typically a few thousand). To do so, we adopt an approach based on the likelihood of an alternative parametric model. Conventional approaches to approximate Bayesian computation such as likelihood-free rejection sampling are impractical for the considered problem, due to the lack of knowledge about how the parameters affect the discrepancy between observed and simulated data. As a response, we make use of a strategy previously developed in the machine learning literature (Bayesian optimisation for likelihood-free inference, BOLFI), which combines Gaussian process regression of the discrepancy to build a surrogate surface with Bayesian optimisation to actively acquire training data. We extend the method by deriving an acquisition function tailored for the purpose of minimising the expected uncertainty in the approximate posterior density, in the parametric approach. The resulting algorithm is applied to the problems of summarising Gaussian signals and inferring cosmological parameters from the Joint Lightcurve Analysis supernovae data. We show that the number of required simulations is reduced by several orders of magnitude, and that the proposed acquisition function produces more accurate posterior approximations, as compared to common strategies.Comment: 16+9 pages, 12 figures. Matches PRD published version after minor modification

Earth System Modeling 2.0: A Blueprint for Models That Learn From Observations and Targeted High-Resolution Simulations

Climate projections continue to be marred by large uncertainties, which originate in processes that need to be parameterized, such as clouds, convection, and ecosystems. But rapid progress is now within reach. New computational tools and methods from data assimilation and machine learning make it possible to integrate global observations and local high-resolution simulations in an Earth system model (ESM) that systematically learns from both. Here we propose a blueprint for such an ESM. We outline how parameterization schemes can learn from global observations and targeted high-resolution simulations, for example, of clouds and convection, through matching low-order statistics between ESMs, observations, and high-resolution simulations. We illustrate learning algorithms for ESMs with a simple dynamical system that shares characteristics of the climate system; and we discuss the opportunities the proposed framework presents and the challenges that remain to realize it.Comment: 32 pages, 3 figure