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Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…
Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state…
Markov models are often used to capture the temporal patterns of sequential data for statistical learning applications. While the Hidden Markov modeling-based learning mechanisms are well studied in literature, we analyze a…
Generative modeling via stochastic processes has led to remarkable empirical results as well as to recent advances in their theoretical understanding. In principle, both space and time of the processes can be discrete or continuous. In this…
Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic…
In many applications, data are observed as matrices with temporal dependence. Matrix-variate time series modeling is a new branch of econometrics. Although stylized facts in several fields, the existing models do not account for regime…
Piecewise-deterministic Markov processes form a general class of non-diffusion stochastic models that involve both deterministic trajectories and random jumps at random times. In this paper, we state a new characterization of the jump rate…
Many statistical problems include model parameters that are defined as the solutions to optimization sub-problems. These include classical approaches such as profile likelihood as well as modern applications involving flow networks or…
We describe how graphical Markov models started to emerge in the last 40 years, based on three essential concepts that had been developed independently more than a century ago. Sequences of joint or single regressions and their regression…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…
Motivated by the study of reversal behaviour of myxobacteria, in this article we are interested in a kinetic model for reversal dynamics, in which particles with directions close to be opposite undergo binary collision resulting in…
We investigate the utility to computational Bayesian analyses of a particular family of recursive marginal likelihood estimators characterized by the (equivalent) algorithms known as "biased sampling" or "reverse logistic regression" in the…
In the field of Markov models for image generation, the main idea is to learn how non-trivial images are gradually destroyed by a trivial forward Markov dynamics over the large time window $[0,t]$ converging towards pure noise for $t \to +…
We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of strong Granger causality and can be applied to time series…
We investigate a generalized stochastic model with the property known as mean reversion, that is, the tendency to relax towards a historical reference level. Besides this property, the dynamics is driven by multiplicative and additive…
Spreading processes are often modelled as a stochastic dynamics occurring on top of a given network with edge weights corresponding to the transmission probabilities. Knowledge of veracious transmission probabilities is essential for…
We introduce a general framework for undirected graphical models. It generalizes Gaussian graphical models to a wide range of continuous, discrete, and combinations of different types of data. The models in the framework, called exponential…
We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive…
This paper focuses on recursive estimation of time varying autoregressive processes in a nonparametric setting. The stability of the model is revisited and uniform results are provided when the time-varying autoregressive parameters belong…
The analysis of samples of random objects that do not lie in a vector space is gaining increasing attention in statistics. An important class of such object data is univariate probability measures defined on the real line. Adopting the…