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Recent work incorporating geometric ideas in Markov chain Monte Carlo is reviewed in order to highlight these advances and their possible application in a range of domains beyond Statistics. A full exposition of Markov chains and their use…
We consider the situation where a temporal process is composed of contiguous segments with differing slopes and replicated noise-corrupted time series measurements are observed. The unknown mean of the data generating process is modelled as…
The computational complexity of MCMC methods for the exploration of complex probability measures is a challenging and important problem. A challenge of particular importance arises in Bayesian inverse problems where the target distribution…
An efficient conditioning technique, the so-called Brownian Bridge simulation, has previously been applied to eliminate pricing bias that arises in applications of the standard discrete-time Monte Carlo method to evaluate options written on…
Recent developments in big data and analytics research have produced an abundance of large data sets that are too big to be analyzed in their entirety, due to limits on computer memory or storage capacity. To address these issues,…
In this article we consider likelihood-based estimation of static parameters for a class of partially observed McKean-Vlasov (POMV) diffusion process with discrete-time observations over a fixed time interval. In particular, using the…
A key quantity of interest in Bayesian inference are expectations of functions with respect to a posterior distribution. Markov Chain Monte Carlo is a fundamental tool to consistently compute these expectations via averaging samples drawn…
There is a lack of simple and scalable algorithms for uncertainty quantification. Bayesian methods quantify uncertainty through posterior and predictive distributions, but it is difficult to rapidly estimate summaries of these…
We propose an algorithm for the efficient and robust sampling of the posterior probability distribution in Bayesian inference problems. The algorithm combines the local search capabilities of the Manifold Metropolis Adjusted Langevin…
Markov chain Monte Carlo methods have become standard tools in statistics to sample from complex probability measures. Many available techniques rely on discrete-time reversible Markov chains whose transition kernels build up over the…
We introduce a framework that enables efficient sampling from learned probability distributions for MRI reconstruction. Different from conventional deep learning-based MRI reconstruction techniques, samples are drawn from the posterior…
Markov Chain Monte Carlo (MCMC) algorithms are commonly used for their versatility in sampling from complicated probability distributions. However, as the dimension of the distribution gets larger, the computational costs for a satisfactory…
Stochastic processes of bridge types having pinned initial and terminal conditions have been widely used in applied research areas, but they all have a common drawback in that the model at hand is possibly misspecified owing to its…
Langevin Dynamics is a Stochastic Differential Equation (SDE) central to sampling and generative modeling and is implemented via time discretization. Langevin Monte Carlo (LMC), based on the Euler-Maruyama discretization, is the simplest…
Gradients have been exploited in proposal distributions to accelerate the convergence of Markov chain Monte Carlo algorithms on discrete distributions. However, these methods require a natural differentiable extension of the target discrete…
Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…
We introduce an inferential framework for a wide class of semi-linear stochastic differential equations (SDEs). Recent work has shown that numerical splitting schemes can preserve critical properties of such types of SDEs, give rise to…
Preliminary mission design of low-thrust spacecraft trajectories in the Circular Restricted Three-Body Problem is a global search characterized by a complex objective landscape and numerous local minima. Formulating the problem as sampling…
The need to calibrate increasingly complex statistical models requires a persistent effort for further advances on available, computationally intensive Monte Carlo methods. We study here an advanced version of familiar Markov Chain Monte…
Diffusion models (DMs) have recently shown outstanding capabilities in modeling complex image distributions, making them expressive image priors for solving Bayesian inverse problems. However, most existing DM-based methods rely on…