Related papers: Likelihood Level Adapted Estimation of Marginal Li…
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required…
The marginal likelihood is a well established model selection criterion in Bayesian statistics. It also allows to efficiently calculate the marginal posterior model probabilities that can be used for Bayesian model averaging of quantities…
Statistical inference of the fundamental parameters of supersymmetric theories is a challenging and active endeavor. Several sophisticated algorithms have been employed to this end. While Markov-Chain Monte Carlo (MCMC) and nested sampling…
Many inference problems involve inferring the number $N$ of components in some region, along with their properties $\{\mathbf{x}_i\}_{i=1}^N$, from a dataset $\mathcal{D}$. A common statistical example is finite mixture modelling. In the…
Bayesian change-point detection, together with latent variable models, allows to perform segmentation over high-dimensional time-series. We assume that change-points lie on a lower-dimensional manifold where we aim to infer subsets of…
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…
Stochastic approximation methods play a central role in maximum likelihood estimation problems involving intractable likelihood functions, such as marginal likelihoods arising in problems with missing or incomplete data, and in parametric…
The marginal likelihood plays an important role in many areas of Bayesian statistics such as parameter estimation, model comparison, and model averaging. In most applications, however, the marginal likelihood is not analytically tractable…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
It has been argued that in supervised classification tasks, in practice it may be more sensible to perform model selection with respect to some more focused model selection score, like the supervised (conditional) marginal likelihood, than…
The Linear Ballistic Accumulator (Brown & Heathcote, 2008) model is used as a measurement tool to answer questions about applied psychology. The analyses based on this model depend upon the model selected and its estimated parameters.…
Particle Marginal Metropolis-Hastings (PMMH) is a general approach to Bayesian inference when the likelihood is intractable, but can be estimated unbiasedly. Our article develops an efficient PMMH method that scales up better to higher…
Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…
Recently-proposed particle MCMC methods provide a flexible way of performing Bayesian inference for parameters governing stochastic kinetic models defined as Markov (jump) processes (MJPs). Each iteration of the scheme requires an estimate…
Likelihood-free methods, such as approximate Bayesian computation, are powerful tools for practical inference problems with intractable likelihood functions. Markov chain Monte Carlo and sequential Monte Carlo variants of approximate…
We propose a multilevel Markov chain Monte Carlo (MCMC) method for the Bayesian inference of random field parameters in PDEs using high-resolution data. Compared to existing multilevel MCMC methods, we additionally consider level-dependent…
We investigate the problem of computing a nested expectation of the form $\mathbb{P}[\mathbb{E}[X|Y] \!\geq\!0]\!=\!\mathbb{E}[\textrm{H}(\mathbb{E}[X|Y])]$ where $\textrm{H}$ is the Heaviside function. This nested expectation appears, for…
Our article deals with Bayesian inference for a general state space model with the simulated likelihood computed by the particle filter. We show empirically that the partially or fully adapted particle filters can be much more efficient…
By providing a framework of accounting for the shared ancestry inherent to all life, phylogenetics is becoming the statistical foundation of biology. The importance of model choice continues to grow as phylogenetic models continue to…
Bayesian inference with Markov Chain Monte Carlo (MCMC) is challenging when the likelihood function is irregular and expensive to compute. We explore several sampling algorithms that make use of subset evaluations to reduce computational…