Related papers: A regression Monte-Carlo method for Backward Doubl…
In this article we offer some modification of Monte-Carlo method for multiple parametric integral computation and solving of a linear integral Fredholm equation of a second kind (well posed problem). We prove that the rate of convergence of…
We present a twofold contribution to the numerical simulation of Lindblad equations. First, an adaptive numerical approach to approximate Lindblad equations using low-rank dynamics is described: a deterministic low-rank approximation of the…
We propose an adaptive importance sampling scheme for Gaussian approximations of intractable posteriors. Optimization-based approximations like variational inference can be too inaccurate while existing Monte Carlo methods can be too slow.…
Stochastic gradient Markov chain Monte Carlo (MCMC) algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed…
A rigorous Bayesian formulation of the inverse doping profile problem in infinite dimensions for a stationary linearized unipolar drift-diffusion model for semiconductor devices is given. The goal is to estimate the posterior probability…
Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…
In this paper we study the homeomorphic properties of the solutions to one dimensional backward doubly stochastic differential equations under suitable assumptions, where the terminal values depend on a real parameter. Then, we apply them…
While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…
A new notion of stochastic ordering is introduced to compare multivariate stochastic risk models with respect to extreme portfolio losses. In the framework of multivariate regular variation comparison criteria are derived in terms of…
Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of…
New classes of stochastic differential equations can now be studied using rough path theory (e.g. Lyons et al. [LCL07] or Friz--Hairer [FH14]). In this paper we investigate, from a numerical analysis point of view, stochastic differential…
In this paper, we investigate a continuous time version of the Stochastic Langevin Monte Carlo method, introduced in [WT11], that incorporates a stochastic sampling step inside the traditional over-damped Langevin diffusion. This method is…
In this paper, we deal with a class of one-dimensional reflected backward doubly stochastic differential equations with one continuous lower barrier. We derive the existence and uniqueness of solutions for these equations with Lipschitz…
This paper introduces methodology for performing Bayesian inference sequentially on a sequence of posteriors on spaces of different dimensions. We show how this may be achieved through the use of sequential Monte Carlo (SMC) samplers (Del…
This paper concerns the numerical approximation for the invariant distribution of Markovian switching L\'evy-driven stochastic differential equations. By combining the tamed-adaptive Euler-Maruyama scheme with the Multi-level Monte Carlo…
In this article we consider the approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs); this scenario appears routinely in Bayesian inverse problems. In practice,…
The multistage stochastic variational inequality is reformulated into a variational inequality with separable structure through introducing a new variable. The prediction-correction ADMM which was originally proposed in [B.-S. He, L.-Z.…
The montecarlo method, which is quite commonly used to solve maximum entropy problems in statistical physics, can actually be used to solve inverse problems in a much wider context. The probability distribution which maximizes entropy can…
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…
In this paper we consider multi-dimensional partial differential equations of parabolic type involving divergence form operators that possess a discontinuous coefficient matrix along some smooth interface. The solution of the equation is…