A SEIR model with time-varying coefficients for analysing the SARS-CoV-2 epidemic

In this study, we propose a time-dependent Susceptible-Exposed-Infected-Recovered (SEIR) model for the analysis of the SARS-CoV-2 epidemic outbreak in three different countries, the United States of America, Italy and Iceland using public data inherent the numbers of the epidemic wave. Since several types and grades of actions were adopted by the governments, including travel restrictions, social distancing, or limitation of movement, we want to investigate how these measures can affect the epidemic curve of the infectious population. The parameters of interest for the SEIR model were estimated employing a composite likelihood approach. Moreover, standard errors have been corrected for temporal dependence. The adoption of restrictive measures results in flatten epidemic curves, and the future evolution indicated a decrease in the number of cases

Application of hierarchical matrices in spatial statistics

Large datasets with irregularly spatial (or spatio-temporal) locations are difficult to handle in many applications of Gaussian random fields, such as maxi- mum likelihood estimation (MLE) and prediction. We aim to approximate covariance functions in a format that facilitates the computation of MLE and prediction with very large datasets using a hierarchical matrix approach. We present a numerical study where we compare this approach with the covariance tapering method

Central Limit Theorem for a conditionally centred functional of a Markov random field

We prove a CLT for empirical sums of a conditionally centred functional of a MRF on a non necessarly regular set of site. Since positive definiteness of the variance of the sums is crucial, we introduce the notion of conditionally separating partition and we give tools to verify such a positive definiteness. Exemples of Ising and gaussian MRF are studied

Modelling of discrete extremes through extended versions of discrete generalized Pareto distribution

The statistical modelling of integer-valued extremes such as large avalanche counts has received less attention than their continuous counterparts in the extreme value theory (EVT) literature. One approach to moving from continuous to discrete extremes is to model threshold exceedances of integer random variables by the discrete version of the generalized Pareto distribution. Still, the optimal threshold selection that defines exceedances remains a problematic issue. Moreover, within a regression framework, the treatment of the many data points (those below the chosen threshold) is either ignored or decoupled from extremes. Considering these issues, we extend the idea of using a smooth transition between the two tails (lower and upper) to force large and small discrete extreme values to comply with EVT. In the case of zero inflation, we also develop models with an additional parameter. To incorporate covariates, we extend the Generalized Additive Models (GAM) framework to discrete extreme responses. In the GAM forms, the parameters of our proposed models are quantified as a function of covariates. The maximum likelihood estimation procedure is implemented for estimation purposes. With the advantage of bypassing the threshold selection step, our findings indicate that the proposed models are more flexible and robust than competing models (i.e. discrete generalized Pareto distribution and Poisson distribution).Comment: 32 pages including supplementary materials, 11 figures including supplementary materials figures, 8 Tables including supplementary materials figure

On model-based clustering using quantile regression

Clustering general regression functions or curves can suffer from lack of robustness when we consider the usual Gaussian assumption. In this note we introduce a new model-based clustering method that tries to overcome this limitation

Clustering of bivariate satellite time series: a quantile approach

Clustering has received much attention in Statistics and Machine learning with the aim of developing statistical models and autonomous algorithms which are capable of acquiring information from raw data in order to perform exploratory analysis.Several techniques have been developed to cluster sampled univariate vectors only considering the average value over the whole period and as such they have not been able to explore fully the underlying distribution as well as other features of the data, especially in presence of structured time series. We propose a model-based clustering technique that is based on quantile regression permitting us to cluster bivariate time series at different quantile levels. We model the within cluster density using asymmetric Laplace distribution allowing us to take into account asymmetry in the distribution of the data. We evaluate the performance of the proposed technique through a simulation study. The method is then applied to cluster time series observed from Glob-colour satellite data related to trophic status indices with aim of evaluating their temporal dynamics in order to identify homogeneous areas, in terms of trophic status, in the Gulf of Gabes

Spatial clustering of time series using Bayesian quantile regression

A large research literature has developed methodologies for identifying clusters of units in a spatial setting. When we deal with longitudinal or temporal data, the proposed methods are mainly based on mean regression. However, the resulting classification could not be robust in presence of outliers, skewed distributions and/or heteroscedasticity. Furthermore, the researcher might be interested in classifying units according to whether certain thresholds are exceeded. We propose a model-based approach for clustering spatial units, that is based on median or, more in general, quantile regression. In this way, we want to cope better with the aforementioned issues. The spatial units are supposed to belong to a network. The model specification is hierarchical that allows a Bayesian inference based on Markov chain Monte Carlo methods. As an illustration and motivating example, we consider data on the sea surface temperature (SST) of the Mediterranean Sea. The dataset is a result of a model re-analysis that provides 251 time series of temperature in 1-degree gridded data covering the temporal window from 1982 to 2012. Specifying a quantile of interest (e.g. in ecology, is 0.9), we aim to identify areas with similar trends and cyclic patterns