Algoritmos numéricos y filtros bayesianos para estimar modelos de efectos mixtos.

Parameter and state estimation in state – space models defined in the form of stochastic differential equations with mixed – effects is a challenging problem in the statistical community from a frequentist and Bayesian point of view. Since the observed data likelihood from state – space models is intractable in practical problems, pseudo – marginal methods represents a methodology to estimate unknown parameters and latent states in stochastic differential equation (SDE) with mixed – effects. However, the implementation of pseudo – marginal methods may require to simulate trajectories of SDE, this means to solve an SDE analytically in order to obtain the transition density. In most cases, SDEs do not have an explicit solution, therefore it is necessary to use approximate methods for discretization of SDEs such as Euler – Maruyama, diffusion bridge schemes, and Monte Carlo schemes. We compare the efficiency of the pseudo – marginal methods in simulated and real scenarios modeled by stochastic differential equation mixed – effects models (SDEMEMs). For the approximate simulation of the paths of the SDE, we consider three discretization schemes: Euler – Maruyama, Modified diffusion bridge and Residual diffusion bridge.

• Auteur principal: Barragán Ramírez, Gabriel Alberto (author)
• Format: masterThesis
• Langue: spa
• Publié: 2024
• Sujets: Algoritmo Metropolis - Hastings; Filtro de partículas; modelo estado - espacio; inferencia Bayesiana; efectos aleatorios
• Accès en ligne: http://dspace.unach.edu.ec/handle/51000/12502