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In the last few decades, Markov chain Monte Carlo (MCMC) methods have been widely applied to Bayesian updating of structural dynamic models in the field of structural health monitoring. Recently, several MCMC algorithms have been developed…
Stochastic reaction network models are often used to explain and predict the dynamics of gene regulation in single cells. These models usually involve several parameters, such as the kinetic rates of chemical reactions, that are not…
We propose sequential Monte Carlo based algorithms for maximum likelihood estimation of the static parameters in hidden Markov models with an intractable likelihood using ideas from approximate Bayesian computation. The static parameter…
Estimating model parameters of a general family of cure models is always a challenging task mainly due to flatness and multimodality of the likelihood function. In this work, we propose a fully Bayesian approach in order to overcome these…
This paper proposes a new approach for Bayesian and maximum likelihood parameter estimation for stationary Gaussian processes observed on a large lattice with missing values. We propose an MCMC approach for Bayesian inference, and a Monte…
Posterior sampling is a task of central importance in Bayesian inference. For many applications in Bayesian meta-analysis and Bayesian transfer learning, the prior distribution is unknown and needs to be estimated from samples. In practice,…
Inference for continuous-time Markov chains (CTMCs) becomes challenging when the process is only observed at discrete time points. The exact likelihood is intractable, and existing methods often struggle even in medium-dimensional…
A large number of statistical models are "doubly-intractable": the likelihood normalising term, which is a function of the model parameters, is intractable, as well as the marginal likelihood (model evidence). This means that standard…
Markov Chain Monte Carlo (MCMC) methods have become a cornerstone of many modern scientific analyses by providing a straightforward approach to numerically estimate uncertainties in the parameters of a model using a sequence of random…
Bayesian nonparametric inferential procedures based on Markov chain Monte Carlo marginal methods typically yield point estimates in the form of posterior expectations. Though very useful and easy to implement in a variety of statistical…
In many situations we are interested in modeling real data where the response distribution, even conditionally on the covariates, presents asymmetry and/or heavy/light tails. In these situations, it is more suitable to consider models based…
In applications of Gaussian processes where quantification of uncertainty is a strict requirement, it is necessary to accurately characterize the posterior distribution over Gaussian process covariance parameters. Normally, this is done by…
Approximate Bayesian Computation (ABC) methods are increasingly used for inference in situations in which the likelihood function is either computationally costly or intractable to evaluate. Extensions of the basic ABC rejection algorithm…
Approximate Bayesian computation (ABC) methods perform inference on model-specific parameters of mechanistically motivated parametric statistical models when evaluating likelihoods is difficult. Central to the success of ABC methods is…
Models implicitly defined through a random simulator of a process have become widely used in scientific and industrial applications in recent years. However, simulation-based inference methods for such implicit models, like approximate…
Adaptive importance sampling (AIS) methods provide a useful alternative to Markov Chain Monte Carlo (MCMC) algorithms for performing inference of intractable distributions. Population Monte Carlo (PMC) algorithms constitute a family of AIS…
Inferring the infinitesimal rates of continuous-time Markov chains (CTMCs) is a central challenge in many scientific domains. This task is hindered by three factors: quadratic growth in the number of rates as the CTMC state space expands,…
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…
This chapter will appear in the forthcoming Handbook of Approximate Bayesian Computation (2018). The conceptual and methodological framework that underpins approximate Bayesian computation (ABC) is targetted primarily towards problems in…
In Bayesian statistics, many problems can be expressed as the evaluation of the expectation of a quantity of interest with respect to the posterior distribution. Standard Monte Carlo method is often not applicable because the encountered…