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In this paper we investigate the use of staged tree models for discrete longitudinal data. Staged trees are a type of probabilistic graphical model for finite sample space processes. They are a natural fit for longitudinal data because a…
We develop a Bayesian graphical modeling framework for functional data for correlated multivariate random variables observed over a continuous domain. Our method leads to graphical Markov models for functional data which allows the graphs…
Structured additive distributional regression models offer a versatile framework for estimating complete conditional distributions by relating all parameters of a parametric distribution to covariates. Although these models efficiently…
A two-class mixture model, where the density of one of the components is known, is considered. We address the issue of the nonparametric adaptive estimation of the unknown probability density of the second component. We propose a randomly…
Markov decision processes are a ubiquitous formalism for modelling systems with non-deterministic and probabilistic behavior. Verification of these models is subject to the famous state space explosion problem. We alleviate this problem by…
Aiming to generate realistic synthetic times series of the bivariate process of daily mean temperature and precipitations, we introduce a non-homogeneous hidden Markov model. The non-homogeneity lies in periodic transition probabilities…
Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past…
Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling…
Hidden Markov models (HMMs) are flexible time series models in which the distributions of the observations depend on unobserved serially correlated states. The state-dependent distributions in HMMs are usually taken from some class of…
Density estimation is essential for generative modeling, particularly with the rise of modern neural networks. While existing methods capture complex data distributions, they often lack interpretability and uncertainty quantification.…
Discrete-time hidden Markov models are a broadly useful class of latent-variable models with applications in areas such as speech recognition, bioinformatics, and climate data analysis. It is common in practice to introduce temporal…
Markov chains provide a foundational framework for modeling sequential stochastic processes, with the transition probability matrix characterizing the dynamics of state evolution. While classical estimation methods such as maximum…
Sequential and quantum Monte Carlo methods, as well as genetic type search algorithms can be interpreted as a mean field and interacting particle approximations of Feynman-Kac models in distribution spaces. The performance of these…
A novel approach for non-intrusive uncertainty propagation is proposed. Our approach overcomes the limitation of many traditional methods, such as generalised polynomial chaos methods, which may lack sufficient accuracy when the quantity of…
Time-homogeneous Markov chains are often used as disease progression models in studies of cost-effectiveness and optimal decision-making. Maximum likelihood estimation of these models can be challenging when data are collected at a time…
Conformal inference is a statistical method used to construct prediction sets for point predictors, providing reliable uncertainty quantification with probability guarantees. This method utilizes historical labeled data to estimate the…
Hierarchical clustering has been shown to be valuable in many scenarios. Despite its usefulness to many situations, there is no agreed methodology on how to properly evaluate the hierarchies produced from different techniques, particularly…
We study the performance of a stochastic algorithm based on the power method that adaptively learns the large deviation functions characterizing the fluctuations of additive functionals of Markov processes, used in physics to model…
This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linear-Gaussian models,…
In many insurance contexts, dependence between risks of a portfolio may arise from their frequencies. We investigate a dependent risk model in which we assume the vector of count variables to be a tree-structured Markov random field with…