Related papers: On a risk model with tree-structured Poisson Marko…
Many forest management planning decisions are based on information about the number of trees by species and diameter per unit area. This information is commonly summarized in a stand table, where a stand is defined as a group of forest…
The goal of these lectures is to survey some of the recent progress on the description of large-scale structure of random trees. We use the framework of Markov-Branching sequences of trees and discuss several applications.
We consider the problem of the estimation of a high-dimensional probability distribution from i.i.d. samples of the distribution using model classes of functions in tree-based tensor formats, a particular case of tensor networks associated…
The spread of infectious disease in a human community or the proliferation of fake news on social media can be modeled as a randomly growing tree-shaped graph. The history of the random growth process is often unobserved but contains…
In this paper we assume a multivariate risk model has been developed for a portfolio and its capital derived as a homogeneous risk measure. The Euler (or gradient) principle, then, states that the capital to be allocated to each component…
This paper studies theory and inference of an observation-driven model for time series of counts. It is assumed that the observations follow a Poisson distribution conditioned on an accompanying intensity process, which is equipped with a…
The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…
We study portfolio selection in a complete continuous-time market where the preference is dictated by the rank-dependent utility. As such a model is inherently time inconsistent due to the underlying probability weighting, we study the…
We present a simple yet rigorous approach to the determination of the spectral dimension of random trees, based on the study of the massless limit of the Gaussian model on such trees. As a byproduct, we obtain evidence in favor of a new…
Extremal graphical models are sparse statistical models for multivariate extreme events. The underlying graph encodes conditional independencies and enables a visual interpretation of the complex extremal dependence structure. For the…
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…
Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees. Substitutions in sequences are modelled through a continuous-time Markov process, characterised by an instantaneous rate matrix, which standard…
Environmental phenomena are influenced by complex interactions among various factors. For instance, the amount of rainfall measured at different stations within a given area is shaped by atmospheric conditions, orography, and physics of…
We propose a method for the classification of objects that are structured as random trees. Our aim is to model a distribution over the node label assignments in settings where the tree data structure is associated with node attributes…
A compositional tree refers to a tree structure on a set of random variables where each random variable is a node and composition occurs at each non-leaf node of the tree. As a generalization of compositional data, compositional trees…
Weather parametric insurance relies on weather indices rather than actual loss assessments, enhancing claims efficiency, reducing moral hazard, and improving fairness. In the context of increasing climate change risks, despite growing…
A general random effects model is proposed that allows for continuous as well as discrete distributions of the responses. Responses can be unrestricted continuous, bounded continuous, binary, ordered categorical or given in the form of…
Tree-structured models are a powerful alternative to parametric regression models if non-linear effects and interactions are present in the data. Yet, classical tree-structured models might not be appropriate if data comes in clusters of…
In multivariate data analysis, it is often important to estimate a graph characterizing dependence among (p) variables. A popular strategy uses the non-zero entries in a (p\times p) covariance or precision matrix, typically requiring…
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,…