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Computer models, aiming at simulating a complex real system, are often calibrated in the light of data to improve performance. Standard calibration methods assume that the optimal values of calibration parameters are invariant to the model…

Probabilistic integration provides a criterion for stopping a simulation when a specified error tolerance is satisfied with high confidence. We comment on some of the modeling assumptions and implementation issues involved in designing an…

Model fitting is possibly the most extended problem in science. Classical approaches include the use of least-squares fitting procedures and maximum likelihood methods to estimate the value of the parameters in the model. However, in recent…

Importance Sampling (IS), an effective variance reduction strategy in Monte Carlo (MC) simulation, is frequently utilized for Bayesian inference and other statistical challenges. Quasi-Monte Carlo (QMC) replaces the random samples in MC…

Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator.…

In numerical integration, cubature methods are effective, especially when the integrands can be well-approximated by known test functions, such as polynomials. However, the construction of cubature formulas has not generally been known, and…

Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…

Approximate Bayesian computation (ABC) using a sequential Monte Carlo method provides a comprehensive platform for parameter estimation, model selection and sensitivity analysis in differential equations. However, this method, like other…

Bayesian optimization is a promising methodology for analog circuit synthesis. However, the sequential nature of the Bayesian optimization framework significantly limits its ability to fully utilize real-world computational resources. In…

We advocate for a new paradigm of cosmological likelihood-based inference, leveraging recent developments in machine learning and its underlying technology, to accelerate Bayesian inference in high-dimensional settings. Specifically, we…

Bayesian inference is a widely used technique for real-time characterization of quantum systems. It excels in experimental characterization in the low data regime, and when the measurements have degrees of freedom. A decisive factor for its…

The popularity of Bayesian optimization methods for efficient exploration of parameter spaces has lead to a series of papers applying Gaussian processes as surrogates in the optimization of functions. However, most proposed approaches only…

We develop efficient numerical integration methods for computing an integral whose integrand is a product of a smooth function and the Gaussian function with a small standard deviation. Traditional numerical integration methods applied to…

Approximate Bayesian Computation is widely used in systems biology for inferring parameters in stochastic gene regulatory network models. Its performance hinges critically on the ability to summarize high-dimensional system responses such…

Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…

We compute the integral of a function or the expectation of a random variable with minimal cost and use, for our new algorithm and for upper bounds of the complexity, i.i.d. samples. Under certain assumptions it is possible to select a…

We propose a Bayesian optimization algorithm for objective functions that are sums or integrals of expensive-to-evaluate functions, allowing noisy evaluations. These objective functions arise in multi-task Bayesian optimization for tuning…

The basic idea of importance sampling is to use independent samples from a proposal measure in order to approximate expectations with respect to a target measure. It is key to understand how many samples are required in order to guarantee…

This article presents new methodology for sample-based Bayesian inference when data are partitioned and communication between the parts is expensive, as arises by necessity in the context of "big data" or by choice in order to take…

Bayesian inference is a powerful paradigm for quantum state tomography, treating uncertainty in meaningful and informative ways. Yet the numerical challenges associated with sampling from complex probability distributions hampers Bayesian…