An extended space approach for particle Markov chain Monte Carlo methods

In this paper we consider fully Bayesian inference in general state space models. Existing particle Markov chain Monte Carlo (MCMC) algorithms use an augmented model that takes into account all the variable sampled in a sequential Monte Carlo algorithm. This paper describes an approach that also uses sequential Monte Carlo to construct an approximation to the state space, but generates extra states using MCMC runs at each time point. We construct an augmented model for our extended space with the marginal distribution of the sampled states matching the posterior distribution of the state vector. We show how our method may be combined with particle independent Metropolis-Hastings or particle Gibbs steps to obtain a smoothing algorithm. All the Metropolis acceptance probabilities are identical to those obtained in existing approaches, so there is no extra cost in term of Metropolis-Hastings rejections when using our approach. The number of MCMC iterates at each time point is chosen by the used and our augmented model collapses back to the model in Olsson and Ryden (2011) when the number of MCMC iterations reduces. We show empirically that our approach works well on applied examples and can outperform existing methods.Comment: 35 pages, 2 figures, Typos corrected from Version

Generalized Information Criteria for Structured Sparse Models

Regularized m-estimators are widely used due to their ability of recovering a low-dimensional model in high-dimensional scenarios. Some recent efforts on this subject focused on creating a unified framework for establishing oracle bounds, and deriving conditions for support recovery. Under this same framework, we propose a new Generalized Information Criteria (GIC) that takes into consideration the sparsity pattern one wishes to recover. We obtain non-asymptotic model selection bounds and sufficient conditions for model selection consistency of the GIC. Furthermore, we show that the GIC can also be used for selecting the regularization parameter within a regularized $m$-estimation framework, which allows practical use of the GIC for model selection in high-dimensional scenarios. We provide examples of group LASSO in the context of generalized linear regression and low rank matrix regression

Spatial copula modeling of extreme crop insurance claims in Brazil

We use robustly estimated spatial R-vine copula models to assess spatial dependencies among extreme crop insurance claims. A truthful predictive model for simultaneous extreme losses is derived based on the linear structure found between copula parameters and distances between groups. Findings are compared to those from classical estimation of pair-copulas. Univariate fits of the excess-losses are based on the Generalized Pareto distribution. The dependence implied by the spatial component is captured by the Gumbel copulas in Tree 1, whereas a few atypical points are handled by robust inference which reveals that the influence of joint multivariate extreme outliers can not be neglected. Our findings are useful for crop insurance firms as well as for local authorities trying to minimize the effects of the natural disasters.Neste artigo utilizamos modelos de cópulas R-vine espaciais e estimação robusta para acessar as dependências entre os seguros relacionados à ocorrência de eventos extremos afetando as colheitas. Um modelo preditivo bastante eficiente para perdas extremas simultâneas é derivado com base na estrutura linear encontrada entre os parâmetros da cópula e as distâncias entre os grupos. Os achados são comparados com os da estimativa clássica de pair-copulas. Os ajustes univariados das perdas em excesso são feitos utilizando-se a distribuição generalizada de Pareto. A dependência espacial é capturada pelas cópulas tipo Gumbel na Árvore 1, enquanto alguns poucos pontos atípicos detectados pela inferência robusta revelam que a influência de extremos multivariados não pode ser negligenciada. Nossas descobertas são úteis para empresas de seguros agrícolas, bem como para autoridades locais que tentam minimizar os efeitos dos desastres naturais

Coastal aquifer hydrodynamics and salinity in response to the tide: case study in Lisbon, Portugal

The variability in dynamics and salinity of the coastal alluvial aquifer on which the city of Lisbon is located was evaluated. Such an evaluation was based on the analysis of level and groundwater electrical conductivity fluctuations depending on the tide in the Tagus River. The results obtained made it possible to recognize three sectors. First, a littoral sector where the variations in level and salinity are larger on the coast and decrease towards the innermost sections of the alluvial fan. Second, a sector close to the docks where there is greater dynamic and salinity variability than in the coastal sectors, as the excavations of the docks favour the tidal propagation towards the aquifer. And third, a sector located towards the apex of the alluvial fan associated with the dynamics of the stormwater channel. In this sector, the largest periodical water table fluctuations in the aquifer occur, since the freshwater that cannot drain towards the river enters the aquifer at high tide, causing a slight decrease in salinity content. On the basis of these results, conceptual models of hydrogeological behaviour were used to describe the spatial and temporal variations in the hydrodynamic and salinity characteristics of groundwater.Facultad de Ciencias Naturales y Muse