Mathematics

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12 pages, 881 KiB

Open AccessArticle

Contributions from Spatial Models to Non-Life Insurance Pricing: An Empirical Application to Water Damage Risk

by Maria Victoria Rivas-Lopez, Roman Minguez-Salido, Mariano Matilla Garcia and Alejandro Echeverria Rey

Mathematics 2021, 9(19), 2476; https://doi.org/10.3390/math9192476 - 3 Oct 2021

Cited by 1 | Viewed by 2580

Abstract

This paper explores the application of spatial models to non-life insurance data focused on the multi-risk home insurance branch. In the pricing modelling and rating process, spatial information should be considered by actuaries and insurance managers because frequencies and claim sizes may vary [...] Read more.

This paper explores the application of spatial models to non-life insurance data focused on the multi-risk home insurance branch. In the pricing modelling and rating process, spatial information should be considered by actuaries and insurance managers because frequencies and claim sizes may vary by region and the premium should be different considering this rating variable. In addition, it is relevant to examine the spatial dependence due to the fact that the frequency of claims in neighbouring regions is often expected to be more closely related than those in regions far from each other. In this paper, a comparison between spatial models, such as spatial autoregressive models (SAR), the spatial error model (SEM), and the spatial Durbin model (SDM), and a non-spatial model has been developed. The data used for this analysis are for a home insurance portfolio located in Spain, from which we have selected peril of water coverage. Full article

(This article belongs to the Special Issue Spatial Statistics with Its Application)

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20 pages, 1950 KiB

Open AccessArticle

Fire Risk Sub-Module Assessment under Solvency II. Calculating the Highest Risk Exposure

by Elena Badal-Valero, Vicente Coll-Serrano and Jorge Segura-Gisbert

Mathematics 2021, 9(11), 1279; https://doi.org/10.3390/math9111279 - 2 Jun 2021

Cited by 2 | Viewed by 3149

Abstract

The European Directive 2009/138 of Solvency II requires adopting a new approach based on risk, applying a standard formula as a market proxy in which the risk profile of insurers is fundamental. This study focuses on the fire risk sub-module, framed within the [...] Read more.

The European Directive 2009/138 of Solvency II requires adopting a new approach based on risk, applying a standard formula as a market proxy in which the risk profile of insurers is fundamental. This study focuses on the fire risk sub-module, framed within the man-made catastrophe risk module, for which the regulations require the calculation of the highest concentration of risks that make up the portfolio of an insurance company within a radius of 200 m. However, the regulations do not indicate a specific methodology. This study proposes a procedure consisting of calculating the cluster with the highest risk and identifying this on a map. The results can be applied immediately by any insurance company, covered under the Solvency II regulations, to determine their maximum exposure to the catastrophic man-made risk of fire, instantly providing them with the necessary input for calibration of the solvency capital requirement. Full article

(This article belongs to the Special Issue Spatial Statistics with Its Application)

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40 pages, 1484 KiB

Open AccessArticle

A Review of Software for Spatial Econometrics in R

by Roger Bivand, Giovanni Millo and Gianfranco Piras

Mathematics 2021, 9(11), 1276; https://doi.org/10.3390/math9111276 - 2 Jun 2021

Cited by 68 | Viewed by 17047

Abstract

The software for spatial econometrics available in the R system for statistical computing is reviewed. The methods are illustrated in a historical perspective, highlighting the main lines of development and employing historically relevant datasets in the examples. Estimators and tests for spatial cross-sectional [...] Read more.

The software for spatial econometrics available in the R system for statistical computing is reviewed. The methods are illustrated in a historical perspective, highlighting the main lines of development and employing historically relevant datasets in the examples. Estimators and tests for spatial cross-sectional and panel models based either on maximum likelihood or on generalized moments methods are presented. The paper is concluded reviewing some current active lines of research in spatial econometric software methods. Full article

(This article belongs to the Special Issue Spatial Statistics with Its Application)

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16 pages, 2112 KiB

Open AccessArticle

Spatio-Temporal Traffic Flow Prediction in Madrid: An Application of Residual Convolutional Neural Networks

by Daniel Vélez-Serrano, Alejandro Álvaro-Meca, Fernando Sebastián-Huerta and Jose Vélez-Serrano

Mathematics 2021, 9(9), 1068; https://doi.org/10.3390/math9091068 - 10 May 2021

Cited by 8 | Viewed by 2892

Abstract

Due to the need to predict traffic congestion during the morning or evening rush hours in large cities, a model that is capable of predicting traffic flow in the short term is needed. This model would enable transport authorities to better manage the [...] Read more.

Due to the need to predict traffic congestion during the morning or evening rush hours in large cities, a model that is capable of predicting traffic flow in the short term is needed. This model would enable transport authorities to better manage the situation during peak hours and would allow users to choose the best routes for reaching their destinations. The aim of this study was to perform a short-term prediction of traffic flow in Madrid, using different types of neural network architectures with a focus on convolutional residual neural networks, and it compared them with a classical time series analysis. The proposed convolutional residual neural network is superior in all of the metrics studied, and the predictions are adapted to various situations, such as holidays or possible sensor failures. Full article

(This article belongs to the Special Issue Spatial Statistics with Its Application)

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18 pages, 656 KiB

Open AccessArticle

Spatiotemporal Econometrics Models for Old Age Mortality in Europe

by Patricia Carracedo and Ana Debón

Mathematics 2021, 9(9), 1061; https://doi.org/10.3390/math9091061 - 9 May 2021

Cited by 1 | Viewed by 2252

Abstract

In the past decade, panel data models using time-series observations of several geographical units have become popular due to the availability of software able to implement them. The aim of this study is an updated comparison of estimation techniques between the implementations of [...] Read more.

In the past decade, panel data models using time-series observations of several geographical units have become popular due to the availability of software able to implement them. The aim of this study is an updated comparison of estimation techniques between the implementations of spatiotemporal panel data models across MATLAB and R softwares in order to fit real mortality data. The case study used concerns the male and female mortality of the aged population of European countries. Mortality is quantified with the Comparative Mortality Figure, which is the most suitable statistic for comparing mortality by sex over space when detailed specific mortality is available for each studied population. The spatial dependence between the 26 European countries and their neighbors during 1995–2012 was confirmed through the Global Moran Index and the spatiotemporal panel data models. For this reason, it can be said that mortality in European population aging not only depends on differences in the health systems, which are subject to national discretion but also on supra-national developments. Finally, we conclude that although both programs seem similar, there are some differences in the estimation of parameters and goodness of fit measures being more reliable MATLAB. These differences have been justified by detailing the advantages and disadvantages of using each of them. Full article

(This article belongs to the Special Issue Spatial Statistics with Its Application)

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20 pages, 6606 KiB

Open AccessArticle

Regional Disparities and Spatial Dependence of Bankruptcy in Spain

by Manuel Rico, Santiago Cantarero and Francisco Puig

Mathematics 2021, 9(9), 960; https://doi.org/10.3390/math9090960 - 25 Apr 2021

Cited by 3 | Viewed by 2173

Abstract

Firm survival, bankruptcy, and turnaround are of great interest nowadays. Bankruptcy is the ultimate resource for a company to survive when it is affected by a severe decline. Thus, determinants of firm turnaround and survival in the context of bankruptcy are of interest [...] Read more.

Firm survival, bankruptcy, and turnaround are of great interest nowadays. Bankruptcy is the ultimate resource for a company to survive when it is affected by a severe decline. Thus, determinants of firm turnaround and survival in the context of bankruptcy are of interest to researchers, managers, and policy-makers. Prior turnaround literature has broadly studied firm-specific factors for turnaround success. However, location-specific factors remain relatively unstudied despite their increasing relevance. Thus, this paper aims to evaluate the existence of spatial dependence on the outcome of the bankruptcy procedure. Economic geography and business literature suggest that location matters and closer companies behave similarly to further ones. For this purpose, we designed a longitudinal analysis employing spatial correlation techniques. The analyses were conducted on a sample of 862 Spanish bankrupt firms (2004–2017) at a regional level (province). For overcoming the limitations of the broadly usually logistic model employed for the turnaround context, the Moran’s Index and the Local Association Index (LISA) were applied with gvSIG and GeoDa software. The empirical results show that the predictors GDP per capita and manufacturing specialization are related to higher bankruptcy survival rates. Both characteristics tend to be present in the identified cluster of provinces with better outcomes located in the North of Spain. We suggest that location broadly impacts the likelihood of the survival of a bankrupt firm, which can condition the strategic decision of locating in one region or another. Our findings provide policy-makers, managers, and researchers with relevant contributions and future investigation lines. Full article

(This article belongs to the Special Issue Spatial Statistics with Its Application)

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27 pages, 6963 KiB

Open AccessArticle

Evaluation Procedures for Forecasting with Spatiotemporal Data

by Mariana Oliveira, Luís Torgo and Vítor Santos Costa

Mathematics 2021, 9(6), 691; https://doi.org/10.3390/math9060691 - 23 Mar 2021

Cited by 13 | Viewed by 3867

Abstract

The increasing use of sensor networks has led to an ever larger number of available spatiotemporal datasets. Forecasting applications using this type of data are frequently motivated by important domains such as environmental monitoring. Being able to properly assess the performance of different [...] Read more.

The increasing use of sensor networks has led to an ever larger number of available spatiotemporal datasets. Forecasting applications using this type of data are frequently motivated by important domains such as environmental monitoring. Being able to properly assess the performance of different forecasting approaches is fundamental to achieve progress. However, traditional performance estimation procedures, such as cross-validation, face challenges due to the implicit dependence between observations in spatiotemporal datasets. In this paper, we empirically compare several variants of cross-validation (CV) and out-of-sample (OOS) performance estimation procedures, using both artificially generated and real-world spatiotemporal datasets. Our results show both CV and OOS reporting useful estimates, but they suggest that blocking data in space and/or in time may be useful in mitigating CV’s bias to underestimate error. Overall, our study shows the importance of considering data dependencies when estimating the performance of spatiotemporal forecasting models. Full article

(This article belongs to the Special Issue Spatial Statistics with Its Application)

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13 pages, 1293 KiB

Open AccessArticle

Gene Set Analysis Using Spatial Statistics

by Angela L. Riffo-Campos, Guillermo Ayala and Francisco Montes

Mathematics 2021, 9(5), 521; https://doi.org/10.3390/math9050521 - 3 Mar 2021

Viewed by 1819

Abstract

Gene differential expression consists of the study of the possible association between the gene expression, evaluated using different types of data as DNA microarray or RNA-Seq technologies, and the phenotype. This can be performed marginally for each gene (differential gene expression) or using [...] Read more.

Gene differential expression consists of the study of the possible association between the gene expression, evaluated using different types of data as DNA microarray or RNA-Seq technologies, and the phenotype. This can be performed marginally for each gene (differential gene expression) or using a gene set collection (gene set analysis). A previous (marginal) per-gene analysis of differential expression is usually performed in order to obtain a set of significant genes or marginal p-values used later in the study of association between phenotype and gene expression. This paper proposes the use of methods of spatial statistics for testing gene set differential expression analysis using paired samples of RNA-Seq counts. This approach is not based on a previous per-gene differential expression analysis. Instead, we compare the paired counts within each sample/control using a binomial test. Each pair per gene will produce a p-value so gene expression profile is transformed into a vector of p-values which will be considered as an event belonging to a point pattern. This would be the first component of a bivariate point pattern. The second component is generated by applying two different randomization distributions to the correspondence between samples and treatment. The self-contained null hypothesis considered in gene set analysis can be formulated in terms of the associated point pattern as a random labeling of the considered bivariate point pattern. The gene sets were defined by the Gene Ontology (GO) terms and Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways. The proposed methodology was tested in four RNA-Seq datasets of colorectal cancer (CRC) patients and the results were contrasted with those obtained using the edgeR-GOseq pipeline. The proposed methodology has proved to be consistent at the biological and statistical level, in particular using Cuzick and Edwards test with one realization of the second component and between-pair distribution. Full article

(This article belongs to the Special Issue Spatial Statistics with Its Application)

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12 pages, 1060 KiB

Open AccessArticle

Incorporating Biotic Information in Species Distribution Models: A Coregionalized Approach

by Xavier Barber, David Conesa, Antonio López-Quílez , Joaquín Martínez-Minaya , Iosu Paradinas and Maria Grazia Pennino

Mathematics 2021, 9(4), 417; https://doi.org/10.3390/math9040417 - 20 Feb 2021

Cited by 4 | Viewed by 2178

Abstract

In this work, we discuss the use of a methodological approach for modelling spatial relationships among species by means of a Bayesian spatial coregionalized model. Inference and prediction is performed using the integrated nested Laplace approximation methodology to reduce the computational burden. We [...] Read more.

In this work, we discuss the use of a methodological approach for modelling spatial relationships among species by means of a Bayesian spatial coregionalized model. Inference and prediction is performed using the integrated nested Laplace approximation methodology to reduce the computational burden. We illustrate the performance of the coregionalized model in species interaction scenarios using both simulated and real data. The simulation demonstrates the better predictive performance of the coregionalized model with respect to the univariate models. The case study focus on the spatial distribution of a prey species, the European anchovy (Engraulis encrasicolus), and one of its predator species, the European hake (Merluccius merluccius), in the Mediterranean sea. The results indicate that European hake and anchovy are positively associated, resulting in improved model predictions using the coregionalized model. Full article

(This article belongs to the Special Issue Spatial Statistics with Its Application)

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17 pages, 326 KiB

Open AccessArticle

An Autoregressive Disease Mapping Model for Spatio-Temporal Forecasting

by Francisca Corpas-Burgos and Miguel A. Martinez-Beneito

Mathematics 2021, 9(4), 384; https://doi.org/10.3390/math9040384 - 14 Feb 2021

Cited by 4 | Viewed by 1985

Abstract

One of the more evident uses of spatio-temporal disease mapping is forecasting the spatial distribution of diseases for the next few years following the end of the period of study. Spatio-temporal models rely on very different modeling tools (polynomial fit, splines, time series, [...] Read more.

One of the more evident uses of spatio-temporal disease mapping is forecasting the spatial distribution of diseases for the next few years following the end of the period of study. Spatio-temporal models rely on very different modeling tools (polynomial fit, splines, time series, etc.), which could show very different forecasting properties. In this paper, we introduce an enhancement of a previous autoregressive spatio-temporal model with particularly interesting forecasting properties, given its reliance on time series modeling. We include a common spatial component in that model and show how that component improves the previous model in several ways, its predictive capabilities being one of them. In this paper, we introduce and explore the theoretical properties of this model and compare them with those of the original autoregressive model. Moreover, we illustrate the benefits of this new model with the aid of a comprehensive study on 46 different mortality data sets in the Valencian Region (Spain) where the benefits of the new proposed model become evident. Full article

(This article belongs to the Special Issue Spatial Statistics with Its Application)

33 pages, 2090 KiB

Open AccessArticle

Comparing Bayesian Spatial Conditional Overdispersion and the Besag–York–Mollié Models: Application to Infant Mortality Rates

by Mabel Morales-Otero and Vicente Núñez-Antón

Mathematics 2021, 9(3), 282; https://doi.org/10.3390/math9030282 - 31 Jan 2021

Cited by 12 | Viewed by 3386

Abstract

In this paper, we review overdispersed Bayesian generalized spatial conditional count data models. Their usefulness is illustrated with their application to infant mortality rates from Colombian regions and by comparing them with the widely used Besag–York–Mollié (BYM) models. These overdispersed models assume that [...] Read more.

In this paper, we review overdispersed Bayesian generalized spatial conditional count data models. Their usefulness is illustrated with their application to infant mortality rates from Colombian regions and by comparing them with the widely used Besag–York–Mollié (BYM) models. These overdispersed models assume that excess of dispersion in the data may be partially caused from the possible spatial dependence existing among the different spatial units. Thus, specific regression structures are then proposed both for the conditional mean and for the dispersion parameter in the models, including covariates, as well as an assumed spatial neighborhood structure. We focus on the case of response variables following a Poisson distribution, specifically concentrating on the spatial generalized conditional normal overdispersion Poisson model. Models were fitted by making use of the Markov Chain Monte Carlo (MCMC) and Integrated Nested Laplace Approximation (INLA) algorithms in the specific context of Bayesian estimation methods. Full article

(This article belongs to the Special Issue Spatial Statistics with Its Application)

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25 pages, 6883 KiB

Open AccessArticle

by Gabriel Riutort-Mayol, Virgilio Gómez-Rubio, José Luis Lerma and Julio M. del Hoyo-Meléndez

Mathematics 2020, 8(12), 2141; https://doi.org/10.3390/math8122141 - 1 Dec 2020

Cited by 3 | Viewed by 2144

Abstract

Rock art paintings present high sensitivity to light, and an exhaustive evaluation of the potential color degradation effects is essential for further conservation and preservation actions on these rock art systems. Microfading spectrometry (MFS) is a technique that provides time series of stochastic [...] Read more.

Rock art paintings present high sensitivity to light, and an exhaustive evaluation of the potential color degradation effects is essential for further conservation and preservation actions on these rock art systems. Microfading spectrometry (MFS) is a technique that provides time series of stochastic observations that represent color fading over time at the measured points on the surface under study. In this work, a reliable and robust modeling framework for a short and greatly fluctuating observation dataset collected over the surfaces of rock art paintings located on the walls of Cova Remigia in Ares del Maestrat, Castellón, Spain, is presented. The model is based on a spatially correlated spline-based time series model that takes into account prior information in the form of model derivatives to guarantee monotonicity and long-term saturation for predictions of new color fading estimates at unobserved locations on the surface. The correlation among the (spatially located) time series is modeled by defining Gaussian process (GP) priors over the spline coefficients across time series. The goal is to obtain a complete spatio-temporal mapping of color fading estimates for the study area, which results in very important and useful information that will potentially serve to create better policies and guidelines for heritage preservation and sustainable rock art cultural tourism. Full article

(This article belongs to the Special Issue Spatial Statistics with Its Application)

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