Related papers: Approximating multivariate posterior distribution …
Approximate Bayesian Computation has been successfully used in population genetics to bypass the calculation of the likelihood. These methods provide accurate estimates of the posterior distribution by comparing the observed dataset to a…
We propose nested sequential Monte Carlo (NSMC), a methodology to sample from sequences of probability distributions, even where the random variables are high-dimensional. NSMC generalises the SMC framework by requiring only approximate,…
Tempering is a popular tool in Bayesian computation, being used to transform a posterior distribution $p_1$ into a reference distribution $p_0$ that is more easily approximated. Several algorithms exist that start by approximating $p_0$ and…
Sparsity has become a key concept for solving of high-dimensional inverse problems using variational regularization techniques. Recently, using similar sparsity-constraints in the Bayesian framework for inverse problems by encoding them in…
Monte Carlo inference has asymptotic guarantees, but can be slow when using generic proposals. Handcrafted proposals that rely on user knowledge about the posterior distribution can be efficient, but are difficult to derive and implement.…
To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the…
Hierarchical Bayesian inference is often conducted with estimates of the target distribution derived from Monte Carlo sums over samples from separate analyses of parts of the hierarchy or from mock observations used to estimate sensitivity…
Bayesian aggregation lets election forecasters combine diverse sources of information, such as state polls and economic and political indicators: as in our collaboration with The Economist magazine. However, the demands of real-time…
Many real-world problems require one to estimate parameters of interest, in a Bayesian framework, from data that are collected sequentially in time. Conventional methods for sampling from posterior distributions, such as {Markov Chain Monte…
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…
Nested sampling is a promising tool for Bayesian statistical analysis because it simultaneously performs parameter estimation and facilitates model comparison. MultiNest is one of the most popular nested sampling implementations, and has…
The generality and robustness of inference algorithms is critical to the success of widely used probabilistic programming languages such as Stan, PyMC, Pyro, and Turing.jl. When designing a new general-purpose inference algorithm, whether…
Doubly intractable problems occur when both the likelihood and the posterior are available only in unnormalised form, with computationally intractable normalisation constants. Bayesian inference then typically requires direct approximation…
Bayesian inference provides principled uncertainty quantification, but accurate posterior sampling with MCMC can be computationally prohibitive for modern applications. Variational inference (VI) offers a scalable alternative and often…
We propose a new method, called MonteCarlo Posterior Fit, to boost the MonteCarlo sampling of likelihood (posterior) functions. The idea is to approximate the posterior function by an analytical multidimensional non-Gaussian fit. The many…
In this paper, we analyse a method for approximating the distribution function and density of a random variable that depends in a non-trivial way on a possibly high number of independent random variables, each with support on the whole real…
Combining data has become an indispensable tool for managing the current diversity and abundance of data. But, as data complexity and data volume swell, the computational demands of previously proposed models for combining data escalate…
Hierarchical models are versatile tools for joint modeling of data sets arising from different, but related, sources. Fully Bayesian inference may, however, become computationally prohibitive if the source-specific data models are complex,…
Many approximate Bayesian inference methods assume a particular parametric form for approximating the posterior distribution. A multivariate Gaussian distribution provides a convenient density for such approaches; examples include the…
Markov chain Monte Carlo methods are often deemed too computationally intensive to be of any practical use for big data applications, and in particular for inference on datasets containing a large number $n$ of individual data points, also…