Related papers: BIMC: The Bayesian Inverse Monte Carlo method for …
A vital stage in the mathematical modelling of real-world systems is to calibrate a model's parameters to observed data. Likelihood-free parameter inference methods, such as Approximate Bayesian Computation, build Monte Carlo samples of the…
The formulation of Bayesian inverse problems involves choosing prior distributions; choices that seem equally reasonable may lead to significantly different conclusions. We develop a computational approach to better understand the impact of…
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…
Approximate Bayesian computation (ABC) methods permit approximate inference for intractable likelihoods when it is possible to simulate from the model. However they perform poorly for high dimensional data, and in practice must usually be…
We introduce an approximate search algorithm for fast maximum a posteriori probability estimation in probabilistic programs, which we call Bayesian ascent Monte Carlo (BaMC). Probabilistic programs represent probabilistic models with…
Population Monte Carlo (PMC) sampling methods are powerful tools for approximating distributions of static unknowns given a set of observations. These methods are iterative in nature: at each step they generate samples from a proposal…
We consider the problem of optimizing a real-valued continuous function $f$ using a Bayesian approach, where the evaluations of $f$ are chosen sequentially by combining prior information about $f$, which is described by a random process…
Models with intractable normalizing functions arise frequently in statistics. Common examples of such models include exponential random graph models for social networks and Markov point processes for ecology and disease modeling. Inference…
Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement,…
Through the Bayesian lens of data assimilation, uncertainty on model parameters is traditionally quantified through the posterior covariance matrix. However, in modern settings involving high-dimensional and computationally expensive…
We present Bayesian techniques for solving inverse problems which involve mean-square convergent random approximations of the forward map. Noisy approximations of the forward map arise in several fields, such as multiscale problems and…
In this paper we consider Bayesian estimation for the parameters of inverse Gaussian distribution. Our emphasis is on Markov Chain Monte Carlo methods. We provide complete implementation of the Gibbs sampler algorithm. Assuming an…
Approximate Bayesian computation (ABC) is a well-established family of Monte Carlo methods for performing approximate Bayesian inference in the case where an ``implicit'' model is used for the data: when the data model can be simulated, but…
Bayesian inversions followed by estimations of rare event probabilities are often needed to analyse groundwater hazards. Instead of focusing on the posterior distribution of model parameters, the main interest lies then in the distribution…
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…
Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…
This paper surveys some well-established approaches on the approximation of Bayes factors used in Bayesian model choice, mostly as covered in Chen et al. (2000). Our focus here is on methods that are based on importance sampling strategies…
A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling…
A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as…
In calculating expected information gain in optimal Bayesian experimental design, the computation of the inner loop in the classical double-loop Monte Carlo requires a large number of samples and suffers from underflow if the number of…