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Many biochemical systems appearing in applications have a multiscale structure so that they converge to piecewise deterministic Markov processes in a thermodynamic limit. The statistics of the piecewise deterministic process can be obtained…
In this work, we establish $\mathrm{L}^2$-exponential convergence for a broad class of Piecewise Deterministic Markov Processes recently proposed in the context of Markov Process Monte Carlo methods and covering in particular the Randomized…
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…
A common strategy for inference in complex models is the relaxation of a simple model into the more complex target model, for example the prior into the posterior in Bayesian inference. Existing approaches that attempt to generate such…
Survival models are a popular tool for the analysis of time to event data with applications in medicine, engineering, economics, and many more. Advances like the Cox proportional hazard model have enabled researchers to better describe…
This article aims to introduced a new lifetime distribution named as exponentiated xgamma distribution (EXGD). The new generalization obtained from xgamma distribution, a special finite mixture of exponential and gamma distributions. The…
Extrapolation remains a grand challenge in deep neural networks across all application domains. We propose an operator learning method to solve time-dependent partial differential equations (PDEs) continuously and with extrapolation in time…
Inference-time scaling has achieved remarkable success in language models, yet its adaptation to diffusion models remains underexplored. We observe that the efficacy of recent Sequential Monte Carlo (SMC)-based methods largely stems from…
Epidemic models are used to analyze the progression or outcome of an epidemic under different control policies like vaccinations, quarantines, lockdowns, use of face-masks, pharmaceutical interventions, etc. When these models accurately…
Process monitoring and control requires detection of structural changes in a data stream in real time. This article introduces an efficient sequential Monte Carlo algorithm designed for learning unknown changepoints in continuous time. The…
We review recent studies demonstrating a nonuniversal (continuously variable) survival exponent for history-dependent random walks, and analyze a new example, the hard movable partial reflector. These processes serve as a simplified models…
Hamiltonian Monte Carlo (HMC) is an efficient and effective means of sampling posterior distributions on Euclidean space, which has been extended to manifolds with boundary. However, some applications require an extension to more general…
To sample from a general target distribution $p_*\propto e^{-f_*}$ beyond the isoperimetric condition, Huang et al. (2023) proposed to perform sampling through reverse diffusion, giving rise to Diffusion-based Monte Carlo (DMC).…
We introduce MCCE: Monte Carlo sampling of valid and realistic Counterfactual Explanations for tabular data, a novel counterfactual explanation method that generates on-manifold, actionable and valid counterfactuals by modeling the joint…
Health policy decisions are often informed by estimates of long-term survival based primarily on short-term data. A range of methods are available to include longer-term information, but there has previously been no comprehensive and…
This paper proposes a robust Bayesian accelerated failure time model for censored survival data. We develop a new family of life-time distributions using a scale mixture of the generalized gamma distributions, where we propose a novel super…
A piecewise-deterministic Markov process, specified by random jumps and switching semi-flows, as well as the associated Markov chain given by its post-jump locations, are investigated in this paper. The existence of an exponentially…
Multimodal distributions of some physics based model parameters are often encountered in engineering due to different situations such as a change in some environmental conditions, and the presence of some types of damage and nonlinearity.…
The computational cost of a Monte Carlo algorithm can only be meaningfully discussed when taking into account the magnitude of the resulting statistical error. Aiming for a fixed error per particle, we study the scaling behavior of the…
Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with…