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Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…
Approximating complex probability densities is a core problem in modern statistics. In this paper, we introduce the concept of Variational Inference (VI), a popular method in machine learning that uses optimization techniques to estimate…
Importance sampling (IS) is commonly used for cross validation (CV) in Bayesian models, because it only involves reweighting existing posterior draws without needing to re-estimate the model by re-running Markov chain Monte Carlo (MCMC).…
Practitioners of Bayesian statistics have long depended on Markov chain Monte Carlo (MCMC) to obtain samples from intractable posterior distributions. Unfortunately, MCMC algorithms are typically serial, and do not scale to the large…
Bayesian optimization provides sample-efficient global optimization for a broad range of applications, including automatic machine learning, engineering, physics, and experimental design. We introduce BoTorch, a modern programming framework…
A key design constraint when implementing Monte Carlo and variational inference algorithms is that it must be possible to cheaply and exactly evaluate the marginal densities of proposal distributions and variational families. This takes…
Recently, Stochastic Variational Inference (SVI) has been increasingly attractive thanks to its ability to find good posterior approximations of probabilistic models. It optimizes the variational objective with stochastic optimization,…
Importance Sampling (IS) is a widely used variance reduction technique for enhancing the efficiency of Monte Carlo methods, particularly in rare-event simulation and related applications. Despite its effectiveness, the performance of IS is…
Computer models play a crucial role in numerous scientific and engineering domains. To ensure the accuracy of simulations, it is essential to properly calibrate the input parameters of these models through statistical inference. While…
We propose a new sampling algorithm combining two quite powerful ideas in the Markov chain Monte Carlo literature -- adaptive Metropolis sampler and two-stage Metropolis-Hastings sampler. The proposed sampling method will be particularly…
Factors models are routinely used to analyze high-dimensional data in both single-study and multi-study settings. Bayesian inference for such models relies on Markov Chain Monte Carlo (MCMC) methods which scale poorly as the number of…
We consider the problem of fitting variational posterior approximations using stochastic optimization methods. The performance of these approximations depends on (1) how well the variational family matches the true posterior…
One of the core problems of modern statistics is to approximate difficult-to-compute probability densities. This problem is especially important in Bayesian statistics, which frames all inference about unknown quantities as a calculation…
Adaptive importance sampling is a class of techniques for finding good proposal distributions for importance sampling. Often the proposal distributions are standard probability distributions whose parameters are adapted based on the…
Computing the exact likelihood of data in large Bayesian networks consisting of thousands of vertices is often a difficult task. When these models contain many deterministic conditional probability tables and when the observed values are…
Understanding how stochastic gene expression is regulated in biological systems using snapshots of single-cell transcripts requires state-of-the-art methods of computational analysis and statistical inference. A Bayesian approach to…
Bayesian parameter inference for complex stochastic simulators is challenging due to intractable likelihood functions. Existing simulation-based inference methods often require large number of simulations and become costly to use in…
The challenge of noisy multi-objective optimization lies in the constant trade-off between exploring new decision points and improving the precision of known points through resampling. This decision should take into account both the…
We develop a Coordinate Ascent Variational Inference (CAVI) algorithm for Bayesian Mixed Data Sampling (MIDAS) regression with linear weight parameterizations. The model separates impact coeffcients from weighting function parameters…
Bayesian optimization (BO) methods choose sample points by optimizing an acquisition function derived from a statistical model of the objective. These acquisition functions are chosen to balance sampling regions with predicted good…