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A novel discretization is presented for forward-backward stochastic differential equations (FBSDE) with differentiable coefficients, simultaneously solving the BSDE and its Malliavin sensitivity problem. The control process is estimated by…

We generalize the approach of Liu and Lawrence (1999) for multiple changepoint problems where the number of changepoints is unknown. The approach is based on dynamic programming recursion for efficient calculation of the marginal…

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…

Models defined by stochastic differential equations (SDEs) allow for the representation of random variability in dynamical systems. The relevance of this class of models is growing in many applied research areas and is already a standard…

This paper considers the analysis of partial differential equations (PDE) containing multiple random variables. Recently developed collocation methods enable the construction of high-order stochastic solutions by converting a stochastic PDE…

Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement,…

A novel algorithmic discussion of the methodological and numerical differences of competing parametric model reduction techniques for nonlinear problems are presented. First, the Galerkin reduced basis (RB) formulation is presented which…

When performing Bayesian computations in practice, one is often faced with the challenge that the constituent model components and/or the data are only available in a distributed fashion, e.g. due to privacy concerns or sheer volume. While…

The Alternating Direction Method of Multipliers (ADMM) provides a natural way of solving inverse problems with multiple partial differential equations (PDE) forward models and nonsmooth regularization. ADMM allows splitting these…

Bayesian inference provides a systematic framework for integration of data with mathematical models to quantify the uncertainty in the solution of the inverse problem. However, the solution of Bayesian inverse problems governed by complex…

We propose a novel Bayesian inference framework for distributed differentially private linear regression. We consider a distributed setting where multiple parties hold parts of the data and share certain summary statistics of their portions…

Uncertainty Quantification through Markov Chain Monte Carlo (MCMC) can be prohibitively expensive for target probability densities with expensive likelihood functions, for instance when the evaluation it involves solving a Partial…

The Bayesian approach to Inverse Problems relies predominantly on Markov Chain Monte Carlo methods for posterior inference. The typical nonlinear concentration of posterior measure observed in many such Inverse Problems presents severe…

This paper contributes to the study of optimal experimental design for Bayesian inverse problems governed by partial differential equations (PDEs). We derive estimates for the parametric regularity of multivariate double integration…

Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…

Diffusion models have recently been shown to excel in many image reconstruction tasks that involve inverse problems based on a forward measurement operator. A common framework uses task-agnostic unconditional models that are later…

We introduce a new class of Monte Carlo based approximations of expectations of random variables such that their laws are only available via certain discretizations. Sampling from the discretized versions of these laws can typically…

Advances in digital sensors, digital data storage and communications have resulted in systems being capable of accumulating large collections of data. In the light of dealing with the challenges that massive data present, this work proposes…

We propose some numerical schemes for forward-backward stochastic differential equations (FBSDEs) based on a new fundamental concept of transposition solutions. These schemes exploit time-splitting methods for the variation of constants…

Proximal Markov Chain Monte Carlo is a novel construct that lies at the intersection of Bayesian computation and convex optimization, which helped popularize the use of nondifferentiable priors in Bayesian statistics. Existing formulations…