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The advantages of sequential Monte Carlo (SMC) are exploited to develop parameter estimation and model selection methods for GARCH (Generalized AutoRegressive Conditional Heteroskedasticity) style models. It provides an alternative method…
Bayesian filtering aims at tracking sequentially a hidden process from an observed one. In particular, sequential Monte Carlo (SMC) techniques propagate in time weighted trajectories which represent the posterior probability density…
Monte Carlo methods, such as Markov chain Monte Carlo (MCMC), remain the most regularly-used approach for implementing Bayesian inference. However, the computational cost of these approaches usually scales worse than linearly with the…
Bayesian spectral deconvolution provides a data-driven framework for mathematical model selection and parameter estimation from spectral data. Although highly versatile, it becomes computationally expensive as the number of model…
Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a new SMC algorithm to compute the expectation of additive functionals recursively.…
Markov chain Monte Carlo (MCMC) algorithms are ubiquitous in Bayesian computations. However, they need to access the full data set in order to evaluate the posterior density at every step of the algorithm. This results in a great…
We introduce Preconditioned Monte Carlo (PMC), a novel Monte Carlo method for Bayesian inference that facilitates efficient sampling of probability distributions with non-trivial geometry. PMC utilises a Normalising Flow (NF) in order to…
An efficient simulation-based methodology is proposed for the rolling window estimation of state space models, called particle rolling Markov chain Monte Carlo (MCMC) with double block sampling. In our method, which is based on Sequential…
Markov chain Monte Carlo (MCMC) methods are foundational algorithms for Bayesian inference and probabilistic modeling. However, most MCMC algorithms are inherently sequential and their time complexity scales linearly with the sequence…
We introduce an efficient MCMC sampling scheme to perform Bayesian inference in the M/G/1 queueing model given only observations of interdeparture times. Our MCMC scheme uses a combination of Gibbs sampling and simple Metropolis updates…
Bayesian inference for models that have an intractable partition function is known as a doubly intractable problem, where standard Monte Carlo methods are not applicable. The past decade has seen the development of auxiliary variable Monte…
Nonlinear non-Gaussian state-space models arise in numerous applications in statistics and signal processing. In this context, one of the most successful and popular approximation techniques is the Sequential Monte Carlo (SMC) algorithm,…
Sequential Monte Carlo (SMC) methods are a class of techniques to sample approximately from any sequence of probability distributions using a combination of importance sampling and resampling steps. This paper is concerned with the…
Bayesian methods are critical for quantifying the behaviors of systems. They capture our uncertainty about a system's behavior using probability distributions and update this understanding as new information becomes available. Probabilistic…
Bayesian model selection enables comparison and ranking of conceptual subsurface models described by spatial prior models, according to the support provided by available geophysical data. Deep generative neural networks can efficiently…
Estimating latent epidemic states and model parameters from partially observed, noisy data remains a major challenge in infectious disease modeling. State-space formulations provide a coherent probabilistic framework for such inference, yet…
In this article we develop a new sequential Monte Carlo (SMC) method for multilevel (ML) Monte Carlo estimation. In particular, the method can be used to estimate expectations with respect to a target probability distribution over an…
Importance sampling (IS) is commonly used for cross validation (CV) in Bayesian models, because it only involves reweighting existing posterior draws without needing to re-estimate the model by re-running Markov chain Monte Carlo (MCMC).…
Decision tree learning is a popular approach for classification and regression in machine learning and statistics, and Bayesian formulations---which introduce a prior distribution over decision trees, and formulate learning as posterior…
We consider the generic problem of performing sequential Bayesian inference in a state-space model with observation process y, state process x and fixed parameter theta. An idealized approach would be to apply the iterated batch importance…