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Discrete flow models offer a powerful framework for learning distributions over discrete state spaces and have demonstrated superior performance compared to the discrete diffusion models. However, their convergence properties and error…

Cure rate models address survival data in which a proportion of individuals will never experience the event of interest. Existing parametric approaches are predominantly based on finite mixtures, which impose restrictive assumptions on both…

Accurate estimates of long-term risk probabilities and their gradients are critical for many stochastic safe control methods. However, computing such risk probabilities in real-time and in unseen or changing environments is challenging.…

Data collected from wearable devices and smartphones can shed light on an individual's pattern of behavioral and circadian routine. Phone use can be modeled as alternating event process, between the state of active use and the state of…

In recent years research on credit risk modelling has mainly focused on default probabilities. Recovery rates are usually modelled independently, quite often they are even assumed constant. Then, however, the structural connection between…

We consider the task of filtering a dynamic parameter evolving as a diffusion process, given data collected at discrete times from a likelihood which is conjugate to the marginal law of the diffusion, when a generic dual process on a…

Introducing common shocks is a popular dependence modelling approach, with some recent applications in loss reserving. The main advantage of this approach is the ability to capture structural dependence coming from known relationships. In…

Diffusion-based generative models have recently emerged as powerful solutions for high-quality synthesis in multiple domains. Leveraging the bidirectional Markov chains, diffusion probabilistic models generate samples by inferring the…

This paper presents a focused review of Markov random fields (MRFs)--commonly used probabilistic representations of spatial dependence in discrete spatial domains--for categorical data, with an emphasis on models for binary-valued…

Bayesian nonparametric inferential procedures based on Markov chain Monte Carlo marginal methods typically yield point estimates in the form of posterior expectations. Though very useful and easy to implement in a variety of statistical…

Validating safety-critical autonomous systems in high-dimensional domains such as robotics presents a significant challenge. Existing black-box approaches based on Markov chain Monte Carlo may require an enormous number of samples, while…

A novel class of non-reversible Markov chain Monte Carlo schemes relying on continuous-time piecewise-deterministic Markov Processes has recently emerged. In these algorithms, the state of the Markov process evolves according to a…

Markov chain Monte Carlo (MCMC) algorithms provide a very general recipe for estimating properties of complicated distributions. While their use has become commonplace and there is a large literature on MCMC theory and practice, MCMC users…

Joint modelling of longitudinal and time-to-event data is usually described by a joint model which uses shared or correlated latent effects to capture associations between the two processes. Under this framework, the joint distribution of…

In modern industries, fault diagnosis has been widely applied with the goal of realizing predictive maintenance. The key issue for the fault diagnosis system is to extract representative characteristics of the fault signal and then…

In this paper, we analyse piecewise deterministic Markov processes, as introduced in Davis (1984). Many models in insurance mathematics can be formulated in terms of the general concept of piecewise deterministic Markov processes. In this…

Markov chain Monte Carlo (MCMC) algorithms are based on the construction of a Markov chain with transition probabilities leaving invariant a probability distribution of interest. In this work, we look at these transition probabilities as…

We introduce a generalization of the Adaptive Multilevel Splitting algorithm in the discrete time dynamic setting, namely when it is applied to sample rare events associated with paths of Markov chains. By interpreting the algorithm as a…

We study a multidimensional renewal risk model, with common counting process and cadlag returns. Considering that the claim vectors have common distribution from some multivariate distribution class with heavy tail, are mutually weakly…

Conditional particle filters (CPFs) are powerful smoothing algorithms for general nonlinear/non-Gaussian hidden Markov models. However, CPFs can be inefficient or difficult to apply with diffuse initial distributions, which are common in…