Related papers: The reproducing Stein kernel approach for post-hoc…
This work develops a powerful and versatile framework for determining acceptance ratios in Metropolis-Hastings type Markov kernels widely used in statistical sampling problems. Our approach allows us to derive new classes of kernels which…
In Bayesian inference, we seek to compute information about random variables such as moments or quantiles on the basis of {available data} and prior information. When the distribution of random variables is {intractable}, Monte Carlo (MC)…
This paper addresses the problem of Monte Carlo approximation of posterior probability distributions. In particular, we have considered a recently proposed technique known as population Monte Carlo (PMC), which is based on an iterative…
Markov chain Monte Carlo (MCMC) methods are widely used in machine learning. One of the major problems with MCMC is the question of how to design chains that mix fast over the whole state space; in particular, how to select the parameters…
We consider importance sampling as well as other properly weighted samples with respect to a target distribution $\pi$ from a different point of view. By considering the associated weights as sojourn times until the next jump, we define…
Importance sampling is a variance reduction technique for efficient estimation of rare-event probabilities by Monte Carlo. In standard importance sampling schemes, the system is simulated using an a priori fixed change of measure suggested…
We propose a novel distributed inference algorithm for continuous graphical models, by extending Stein variational gradient descent (SVGD) to leverage the Markov dependency structure of the distribution of interest. Our approach combines…
The Marchenko method retrieves the responses to virtual sources in the Earth's subsurface from reflection data at the surface, accounting for all orders of multiple reflections. The method is based on two integral representations for…
Using Markov chain Monte Carlo to sample from posterior distributions was the key innovation which made Bayesian data analysis practical. Notoriously, however, MCMC is hard to tune, hard to diagnose, and hard to parallelize. This…
Kernel discrepancies are a powerful tool for analyzing worst-case errors in quasi-Monte Carlo (QMC) methods. Building on recent advances in optimizing such discrepancy measures, we extend the subset selection problem to the setting of…
Bias in datasets can be very detrimental for appropriate statistical estimation. In response to this problem, importance weighting methods have been developed to match any biased distribution to its corresponding target unbiased…
Stein discrepancies have emerged as a powerful statistical tool, being applied to fundamental statistical problems including parameter inference, goodness-of-fit testing, and sampling. The canonical Stein discrepancies require the…
Markov Chain Monte Carlo (MCMC) methods are employed to sample from a given distribution of interest, whenever either the distribution does not exist in closed form, or, if it does, no efficient method to simulate an independent sample from…
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…
Importance Sampling methods are broadly used to approximate posterior distributions or some of their moments. In its standard approach, samples are drawn from a single proposal distribution and weighted properly. However, since the…
Slice sampling is a well-established Markov chain Monte Carlo method for (approximate) sampling of target distributions which are only known up to a normalizing constant. The method is based on choosing a new state on a slice, i.e., a…
For many probability distributions of interest, it is quite difficult to obtain samples efficiently. Often, Markov chains are employed to obtain approximately random samples from these distributions. The primary drawback to traditional…
The performance of adaptive estimators that employ embedding in reproducing kernel Hilbert spaces (RKHS) depends on the choice of the location of basis kernel centers. Parameter convergence and error approximation rates depend on where and…
In the design and analysis of political redistricting maps, it is often useful to be able to sample from the space of all partitions of the graph of census blocks into connected subgraphs of equal population. There are influential Markov…
Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…