Métodos Hamiltonian Monte Carlo para la estimación de modelos de series climáticas

Camón Fernández, Alejandro
Asín Lafuente, Jesús (dir.)

Universidad de Zaragoza, CIEN, 2022
Métodos Estadísticos department, Estadística e Investigación Operativa area

Graduado en Matemáticas

Abstract: This work presents a detailed explanation of the HMC algorithm used for bayesian inference and an application to estimate, in the bayesian framework, a new proposed autoregressive model for the maximum daily temperatures.
The proposed model is based on the previous work of Castillo-Mateo et al. (2022), where the time structure of mean was modeled. A more flexible estructure is considered modeling also the variance and including interaction terms to reflect a seasonal variability of trend and persistence. The model has easily interpretable terms, it is able to represent the short and long-term dynamics of the temperatures, specially in relation to the effect of a possible climate change. Also a procedure of selection of covariates is designed and all the estimation process is implemented using RStan library, in the R workspace.
Models are fitted to series in a database built with data obtained by 18 stations placed in Aragón and its surroundings during a period of over 60 years. The estimation with the HMC-NUTS algorithm is possible but computationally slow. The results show progress towards a more complete model, because both, a non-constant variance and the addition of seasonal-trend and seasonal-persistence interactions, are necessary in Aragón series.

Tipo de Trabajo Académico: Trabajo Fin de Grado