Related papers: Efficient SMC$^2$ schemes for stochastic kinetic m…
In recent times empirical likelihood has been widely applied under Bayesian framework. Markov chain Monte Carlo (MCMC) methods are frequently employed to sample from the posterior distribution of the parameters of interest. However,…
Nonlinear non-Gaussian state-space models are ubiquitous in statistics, econometrics, information engineering and signal processing. Particle methods, also known as Sequential Monte Carlo (SMC) methods, provide reliable numerical…
Probabilistic programming languages can simplify the development of machine learning techniques, but only if inference is sufficiently scalable. Unfortunately, Bayesian parameter estimation for highly coupled models such as regressions and…
Probabilistic modeling provides the capability to represent and manipulate uncertainty in data, models, predictions and decisions. We are concerned with the problem of learning probabilistic models of dynamical systems from measured data.…
Parameter estimation for discretely observed Markov processes is a challenging problem. However, simulation of Markov processes is straightforward using the Gillespie algorithm. We exploit this ease of simulation to develop an effective…
In dynamic Monte Carlo simulations, using for example the Metropolis dynamic, it is often required to simulate for long times and to simulate large systems. We present an overview of advanced algorithms to simulate for larger times and to…
Most solved dynamic structural macrofinance models are non-linear and/or non-Gaussian state-space models with high-dimensional and complex structures. We propose an annealed controlled sequential Monte Carlo method that delivers numerically…
We present a simulation methodology for Bayesian estimation of rate parameters in Markov jump processes arising for example in stochastic kinetic models. To handle the problem of missing components and measurement errors in observed data,…
This paper introduces the R package sgmcmc; which can be used for Bayesian inference on problems with large datasets using stochastic gradient Markov chain Monte Carlo (SGMCMC). Traditional Markov chain Monte Carlo (MCMC) methods, such as…
Sequential Monte Carlo (SMC) samplers are powerful tools for Bayesian inference but suffer from high computational costs due to their reliance on large particle ensembles for accurate estimates. We introduce persistent sampling (PS), an…
Sequential Monte Carlo algorithms, or Particle Filters, are Bayesian filtering algorithms which propagate in time a discrete and random approximation of the a posteriori distribution of interest. Such algorithms are based on Importance…
In this work, we present, analyze, and implement a class of Multi-Level Markov chain Monte Carlo (ML-MCMC) algorithms based on independent Metropolis-Hastings proposals for Bayesian inverse problems. In this context, the likelihood function…
Stochastic gradient Markov chain Monte Carlo (SGMCMC) is a popular class of algorithms for scalable Bayesian inference. However, these algorithms include hyperparameters such as step size or batch size that influence the accuracy of…
Markov chain Monte Carlo (MCMC) methods are a powerful but computationally expensive way of performing non-parametric Bayesian inference. MCMC proposals which utilise gradients, such as Hamiltonian Monte Carlo (HMC), can better explore the…
Statistical signal processing applications usually require the estimation of some parameters of interest given a set of observed data. These estimates are typically obtained either by solving a multi-variate optimization problem, as in the…
SMC$^2$ is an efficient algorithm for sequential estimation and state inference of state-space models. It generates $N_{\theta}$ parameter particles $\theta^{m}$, and, for each $\theta^{m}$, it runs a particle filter of size $N_{x}$ (i.e.…
Many applications in signal processing require the estimation of some parameters of interest given a set of observed data. More specifically, Bayesian inference needs the computation of {\it a-posteriori} estimators which are often…
We propose a hierarchy of multi-level kinetic Monte Carlo methods for sampling high-dimensional, stochastic lattice particle dynamics with complex interactions. The method is based on the efficient coupling of different spatial resolution…
Sequential Monte Carlo (SMC) is a methodology for sampling approximately from a sequence of probability distributions of increasing dimension and estimating their normalizing constants. We propose here an alternative methodology named…
Markov chain Monte Carlo is an inherently serial algorithm. Although likelihood calculations for individual steps can sometimes be parallelized, the serial evolution of the process is widely viewed as incompatible with parallelization,…