Related papers: Guided proposals for simulating multi-dimensional …
The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the…
In this paper, we develop a Monte Carlo based algorithm for estimating the FPT density of a time-homogeneous SDE through a time-dependent frontier. We consider Brownian bridges as well as localized Daniels curve approximations to obtain…
Simulation of conditioned diffusion processes is an essential tool in inference for stochastic processes, data imputation, generative modelling, and geometric statistics. Whilst simulating diffusion bridge processes is already difficult on…
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…
We introduce a new residual-bridge proposal for approximately simulating conditioned diffusions. This proposal is formed by applying the modified diffusion bridge approximation of Durham and Gallant (2002) to the difference between the true…
We discuss suitable classes of diffusion processes, for which functionals relevant to finance can be computed via Monte Carlo methods. In particular, we construct exact simulation schemes for processes from this class. However, should the…
Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…
In this paper we outline methodology to efficiently simulate (jump) diffusion bridge sample paths without discretisation error. We achieve this by considering the simulation of conditioned (jump) diffusion bridge sample paths in light of…
We describe a Monte Carlo procedure which allows sampling of the disjoint configuration spaces associated with crystalline and fluid phases, within a single simulation. The method utilises biased sampling techniques to enhance the…
Recently Whitaker et al. (2017) considered Bayesian estimation of diffusion driven mixed effects models using data-augmentation. The missing data, diffusion bridges connecting discrete time observations, are drawn using a "residual bridge…
Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…
The model consists of a signal process $X$ which is a general Brownian diffusion process and an observation process $Y$, also a diffusion process, which is supposed to be correlated to the signal process. We suppose that the process $Y$ is…
We propose a hybrid generative model for efficient sampling of high-dimensional, multimodal probability distributions for Bayesian inference. Traditional Monte Carlo methods, such as the Metropolis-Hastings and Langevin Monte Carlo sampling…
An improved real-time quantum Monte Carlo procedure is presented and applied to describe the electronic transfer dynamics along molecular chains. The model consists of discrete electronic sites coupled to a thermal environment which is…
Discrete diffusion models are a class of generative models that produce samples from an approximated data distribution within a discrete state space. Often, there is a need to target specific regions of the data distribution. Current…
This paper introduces a Monte Carlo method for maximum likelihood inference in the context of discretely observed diffusion processes. The method gives unbiased and a.s.\@ continuous estimators of the likelihood function for a family of…
Policy-guided Monte Carlo is an adaptive method to simulate classical interacting systems. It adjusts the proposal distribution of the Metropolis-Hastings algorithm to maximize the sampling efficiency, using a formalism inspired by…
We consider the task of generating draws from a Markov jump process (MJP) between two time-points at which the process is known. Resulting draws are typically termed bridges and the generation of such bridges plays a key role in…
As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable…
Modelling random dynamical systems in continuous time, diffusion processes are a powerful tool in many areas of science. Model parameters can be estimated from time-discretely observed processes using Markov chain Monte Carlo (MCMC) methods…