arXiv subjects

Sara Martino

Publications and source records attributed to Sara Martino.

21 records · Page 2Linked to original sources

arXiv2019

Integrated Nested Laplace Approximations (INLA)

This is a short description and basic introduction to the Integrated nested Laplace approximations (INLA) approach. INLA is a deterministic paradigm for Bayesian inference in latent Gaussian models (LGMs) introduced in Rue et al. (2009). INLA relies on a combination of analytical approximations and efficient numerical integration schemes to achieve highly accurate deterministic approximations to posterior quantities of interest. The main benefit of using INLA instead of Markov chain Monte Carlo (MCMC) techniques for LGMs is computational; INLA is fast even for large, complex models. Moreover, being a deterministic algorithm, INLA does not suffer from slow convergence and poor mixing. INLA is implemented in the R package R-INLA, which represents a user-friendly and versatile tool for doing Bayesian inference. R-INLA returns posterior marginals for all model parameters and the corresponding posterior summary information. Model choice criteria as well as predictive diagnostics are directly available. Here, we outline the theory behind INLA, present the R-INLA package and describe new developments of combining INLA with MCMC for models that are not possible to fit with R-INLA.

stat.CO↗

arXiv2015

Spatial Modelling of Temperature and Humidity using Systems of Stochastic Partial Differential Equations

This work is motivated by constructing a weather simulator for precipitation. Temperature and humidity are two of the most important driving forces of precipitation, and the strategy is to have a stochastic model for temperature and humidity, and use a deterministic model to go from these variables to precipitation. Temperature and humidity are empirically positively correlated. Generally speaking, if variables are empirically dependent, then multivariate models should be considered. In this work we model humidity and temperature in southern Norway. We want to construct bivariate Gaussian random fields (GRFs) based on this dataset. The aim of our work is to use the bivariate GRFs to capture both the dependence structure between humidity and temperature as well as their spatial dependencies. One important feature for the dataset is that the humidity and temperature are not necessarily observed at the same locations. Both univariate and bivariate spatial models are fitted and compared. For modeling and inference the SPDE approach for univariate models and the systems of SPDEs approach for multivariate models have been used. To evaluate the performance of the difference between the univariate and bivariate models, we compare predictive performance using some commonly used scoring rules: mean absolute error, mean-square error and continuous ranked probability score. The results illustrate that we can capture strong positive correlation between the temperature and the humidity. Furthermore, the results also agree with the physical or empirical knowledge. At the end, we conclude that using the bivariate GRFs to model this dataset is superior to the approach with independent univariate GRFs both when evaluating point predictions and for quantifying prediction uncertainty.

stat.AP↗

arXiv2015

Estimation of a non-stationary model for annual precipitation in southern Norway using replicates of the spatial field

Estimation of stationary dependence structure parameters using only a single realisation of the spatial process, typically leads to inaccurate estimates and poorly identified parameters. A common way to handle this is to fix some of the parameters, or within the Bayesian framework, impose prior knowledge. In many applied settings, stationary models are not flexible enough to model the process of interest, thus non-stationary spatial models are used. However, more flexible models usually means more parameters, and the identifiability problem becomes even more challenging. We investigate aspects of estimation of a Bayesian non-stationary spatial model for annual precipitation using observations from multiple years. The model contains replicates of the spatial field, which increases precision of the estimates and makes them less prior sensitive. Using R-INLA, we analyse precipitation data from southern Norway, and investigate statistical properties of the replicate model in a simulation study. The non-stationary spatial model we explore belongs to a recently introduced class of stochastic partial differential equation (SPDE) based spatial models. This model class allows for non-stationary models with explanatory variables in the dependence structure. We derive conditions to facilitate prior specification for these types of non-stationary spatial models.

stat.ME↗