arXiv subjects

Alan Riva Palacio

Publications and source records attributed to Alan Riva Palacio.

4 recordsLinked to original sources

arXiv2025

Parameter Estimation for Partially Observed Stable Continuous-State Branching Processes

In this article, we present a novel inference framework for estimating the parameters of Continuous-State Branching Processes (CSBPs). We do so by leveraging their subordinator representation. Our method reformulates the estimation problem by shifting the stochastic dynamics to the associated subordinator, enabling a parametric estimation procedure without requiring additional assumptions. This reformulation allows for efficient numerical recovery of the likelihood function via Laplace transform inversion, even in models where closed-form transition densities are unavailable. In addition to offering a flexible approach to parameter estimation, we propose a dynamic simulation framework that generates discrete-time trajectories of CSBPs using the same subordinator-based structure.

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arXiv2020

Compound vectors of subordinators and their associated positive Lévy copulas

Lévy copulas are an important tool which can be used to build dependent Lévy processes. In a classical setting, they have been used to model financial applications. In a Bayesian framework they have been employed to introduce dependent nonparametric priors which allow to model heterogeneous data. This paper focuses on introducing a new class of Lévy copulas based on a class of subordinators recently appeared in the literature, called \textit{Compound Random Measures}. The well-known Clayton Lévy copula is a special case of this new class. Furthermore, we provide some novel results about the underlying vector of subordinators such as a series representation and relevant moments. The article concludes with an application to a Danish fire dataset.

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arXiv2018

Bayesian nonparametric estimation of survival functions with multiple-samples information

In many real problems, dependence structures more general than exchangeability are required. For instance, in some settings partial exchangeability is a more reasonable assumption. For this reason, vectors of dependent Bayesian nonparametric priors have recently gained popularity. They provide flexible models which are tractable from a computational and theoretical point of view. In this paper, we focus on their use for estimating survival functions with multiple-samples information. Our methodology allows to model the dependence among survival times of different groups of observations and extend previous work to an arbitrary dimension . Theoretical results about the posterior behaviour of the underlying dependent vector of completely random measures are provided. The performance of the model is tested on a simulated dataset arising from a distributional Clayton copula.

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arXiv2017

Integrability conditions for Compound Random Measures

Compound random measures (CoRM's) are a flexible and tractable framework for vectors of completely random measure. In this paper, we provide conditions to guarantee the existence of a CoRM. Furthermore, we prove some interesting properties of CoRM's when exponential scores and regularly varying Lévy intensities are considered.

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