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This paper tackles the challenge presented by small-data to the task of Bayesian inference. A novel methodology, based on manifold learning and manifold sampling, is proposed for solving this computational statistics problem under the…
Calibration of computer models is a key step in making inferences, predictions, and decisions for complex science and engineering systems. We formulate and analyze a nonparametric Bayesian methodology for computer model calibration. This…
This paper proposes a new nonparametric Bayesian bootstrap for a mixture model, by developing the traditional Bayesian bootstrap. We first reinterpret the Bayesian bootstrap, which uses the P\'olya-urn scheme, as a gradient ascent algorithm…
In distributed, or privacy-preserving learning, we are often given a set of probabilistic models estimated from different local repositories, and asked to combine them into a single model that gives efficient statistical estimation. A…
Current approaches in approximate inference for Bayesian neural networks minimise the Kullback-Leibler divergence to approximate the true posterior over the weights. However, this approximation is without knowledge of the final application,…
Bayesian synthetic likelihood (BSL) is now a well established method for performing approximate Bayesian parameter estimation for simulation-based models that do not possess a tractable likelihood function. BSL approximates an intractable…
This paper studies parametric bootstrap methods for network data, with the goal of quantifying the uncertainty of network statistics of interest. While existing network resampling methods primarily focus on count statistics under…
Motivated by parametric models for which the likelihood is analytically unavailable, numerically unstable, or prohibitively expensive to compute or optimize, we develop a prior- and likelihood-free framework for fully probabilistic…
Likelihood-free Bayesian inference algorithms are popular methods for calibrating the parameters of complex, stochastic models, required when the likelihood of the observed data is intractable. These algorithms characteristically rely…
This paper is concerned with Bayesian inference when the likelihood is analytically intractable but can be unbiasedly estimated. We propose an annealed importance sampling procedure for estimating expectations with respect to the posterior.…
This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…
We propose a simple approach that provides accurate uncertainty quantification for Bayesian inference in misspecified or approximate models, and for generalized (Gibbs) posteriors. While existing solutions in this context are based on…
Some machine learning applications require continual learning - where data comes in a sequence of datasets, each is used for training and then permanently discarded. From a Bayesian perspective, continual learning seems straightforward:…
This study presents a novel approach to quantifying uncertainties in Bayesian model updating, which is effective in sparse or single observations. Conventional uncertainty quantification metrics such as the Euclidean and Bhattacharyya…
Approximate Bayesian computation (ABC) or likelihood-free inference algorithms are used to find approximations to posterior distributions without making explicit use of the likelihood function, depending instead on simulation of sample data…
We present a novel technique for amortized posterior estimation using Normalizing Flows trained with likelihood-weighted importance sampling. This approach allows for the efficient inference of theoretical parameters in high-dimensional…
We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…
We develop and apply two calibration procedures for checking the coverage of approximate Bayesian credible sets including intervals estimated using Monte Carlo methods. The user has an ideal prior and likelihood, but generates a credible…
Standard Bayesian inference is known to be sensitive to model misspecification, leading to unreliable uncertainty quantification and poor predictive performance. However, finding generally applicable and computationally feasible methods for…
We present a new fitting technique based on the parametric bootstrap method, which relies on the idea to produce artificial measurements using the estimated probability distribution of the experimental data. In order to investigate the main…