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This is the pre-peer reviewed version of the following article: Ameijeiras‐Alonso, J, Lagona, F, Ranalli, M, Crujeiras, RM. A circular nonhomogeneous hidden Markov field for the spatial segmentation of wildfire occurrences. Environmetrics. 2019; 30:e2501. https://doi.org/10.1002/env.2501, which has been published in final form at https://doi.org/10.1002/env.2501. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions Motivated by studies of wildfire seasonality, we propose a nonhomogeneous hidden Markov random field to model the spatial distribution of georeferenced fire occurrences during the year, by representing occurrence times as circular data. The model is based on a mixture of Kato–Jones circular densities, whose parameters vary across space according to a latent nonhomogeneous Potts model, modulated by georeferenced covariates. It allows us to segment fire occurrences according to a finite number of latent classes that represent the conditional distributions of the data under specific periods of the year, simultaneously accounting for unobserved heterogeneity and spatial autocorrelation. Further, it parsimoniously accommodates specific features of wildfire occurrence data such as multimodality, skewness, and kurtosis. Due to the numerical intractability of the likelihood function, estimation of the parameters is based on composite likelihood methods. It reduces to a computationally efficient expectation–maximization algorithm that iteratively alternates the maximization of a weighted composite likelihood function with weights updating. The proposal is illustrated in a study of wildfire occurrences in the Iberian Peninsula during a decade Jose Ameijeiras‐Alonso and Rosa M. Crujeiras gratefully acknowledge the support of Project MTM2016‐76969‐P (Spanish State Research Agency, AEI), co‐funded by the European Regional Development Fund (ERDF), IAP network from Belgian Science Policy. Part of the research was carried out by Jose Ameijeiras‐Alonso during his visit to University of Roma Tre, supported by Grants BES‐2014‐071006 and EEBB‐I‐17‐12716 from the Spanish Ministry of Economy, Industry and Competitiveness. Francesco Lagona is supported by the 2015 PRIN supported project “Environmental processes and human activities: capturing their interactions via statistical methods”, funded by the Italian Ministry of Education, University and Scientific Research NON

A novel segmentation method is proposed for the analysis of bivariate times eries of intensities and angles that often occur in environmental applications. The model is based on a mixture of copula-based cylindrical distributions,whose parameters evolve according to a latent Markov chain.The model parsimoniously accommodates typical features of cylindrical time series such as circular-linear correlation, multimodality, skewness and temporal auto-correlation. A computationally efficient Expectation-Maximization algorithm is described to estimate the parameters and a parametric bootstrap routine is exploited to compute confidence intervals. These methods are illustrated on cylindrical time series of wave heights and directions in the Adriatic sea.

We describe a mixed-effects model for non-negative continuous cross-sectional data in a two-part modelling framework. A potentially endogenous binary variable is included in the model specification and association between the outcomes is modeled through a (discrete) latent structure. We show how model parameters can be estimated in a finite mixture context, allowing for skewness, multivariate association between random effects and endogeneity. The model behavior is investigated through a large-scale simulation experiment. The proposed model is computationally parsimonious and seems to produce acceptable results even if the underlying random effects structure follows a continuous parametric (e.g. Gaussian) distribution. The proposed approach is motivated by the analysis of a sample taken from the Medical Expenditure Panel Survey. The analyzed outcome, i.e. ambulatory health expenditure, is a mixture of zeros and continuous values. The effects of socio-demographic characteristics on health expenditure are investigated and, as a by-product of the estimation procedure, two subpopulations (i.e. high and low users) are identified.

A new hidden Markov model is proposed for the analysis of cylindrical time series, i.e. bivariate time series of intensities and angles. It allows to segment cylindrical time series according to a finite number of regimes that represent the conditional distributions of the data under specific environmental conditions. The model parsimoniously accommodates for circular-linear correlation, multimodality, skewness and temporal autocorrelation. A computationally efficient Expectation-Maximization algorithm is described to estimate the parameters and a parametric bootstrap routine is provided to compute confidence intervals. These methods are illustrated on cylindrical time series of wave heights and directions.

A regression model for correlated circular data is proposed by assuming that samples of angular measurements are drawn from a multivariate von Mises distribution with mean and concentration parameters that depend on covariates through suitable link functions. The model accommodates for heteroscedasticity, unstructured correlation, and specific autoregressive correlation structures. Inference is based on a Monte Carlo approximation of the log-likelihood, due to the intractability of the normalizing constant. The model is illustrated on two case studies: a longitudinal study of animal orientation and a study on the spatial distribution of sea current directions.

A von Mises Markov random field model is introduced for the analysis of spatial series of angles. Because the likelihood function of the model is unknown up to a normalizing constant, two inferential procedures are proposed for parameter estimation. The first one is based on the maximization of a pseudo-likelihood function and provides a computationally convenient, consistent, although inefficient estimator. The second one is based on the maximization of a Monte Carlo Markov Chain approximation of the likelihood and is more efficient than the pseudo-likelihood estimator, although computationally more expensive. The model is illustrated on a spatial series of sea currents directions.

A Non-Homogeneous Hidden Markov Model for the Analysis of Multi-Pollutant Exceedances Data

A principal motivation for the research reported in this paper is to seek to understand what consequences can result from an erroneous specification of the lattice topology when an autoregressive spatial model is employed for inferential purposes. The first part of the discussion concerns impacts of such a specification error on the resulting dependence structure among data in SAR and CAR models. Although some ideas on this matter can be found in popular monographs about spatial statistics (Cliff and Ord 1981; Griffith 1988; Cressie 1993; Guyon 1995), the problem does not seem to have been attacked directly in the literature, two exceptions being Griffith (1995) and Griffith and Lagona (1997). In this paper an additional step is made in this direction, extensively using the theory of power series for matrices (see, for instance, Cooke 1950) and basic graph theory (see, for instance, Ore 1960). The second part of the discussion concerns impacts of a misspecified lattice topology on the quality of popular estimation procedures for SAR and CAR models. Because estimator quality can be measured by sampling distribution properties, unbiasedness and efficiency are considered here as basic measures of it. For this problem, a useful starting point is furnished by Oksanen (1991), and Cordey and Griffith's (1993) work is extended here. Much of the finite sample mathematical statistics summarized in this paper is numerically demonstrated in Griffith (1995). And, the Jacobian work outlined in Griffith and Sone (1995) is exploited to attain selected analytical results.

Multivariate spatial count data are often segmented by unobserved space-varying factors that vary across space. In this setting, regression models that assume space-constant covariate effects could be too restrictive. Motivated by the analysis of cause-specific mortality data, we propose to estimate space-varying effects by exploiting a multivariate hidden Markov field. It models the data by a battery of Poisson regressions with spatially correlated regression coefficients, which are driven by an unobserved spatial multinomial process. It parsimoniously describes multivariate count data by means of a finite number of latent classes. Parameter estimation is carried out by composite likelihood methods, that we specifically develop for the proposed model. In a case study of cause-specific mortality data in Italy, the model was capable to capture the spatial variation of gender differences and age effects.

International audience; The Political Legislation Cycle theory predicts a peak of legislative production in the pre-electoral period, when legislators focus on voters’ welfare to be reelected. This paper verifies the theory on South Korean legislative production (1948–2016); it is the first test of the theory in a country undergoing a process of democratization, thus providing evidence relevant also for the conditional political cycles literature. Two insofar untested hypotheses are verified: 1) peaks of legislative production should increase with the degree of democracy; 2) as the party system and the mechanisms of legislative checks and balances develop, the PLC should become more evident in bills of legislative rather than executive's initiative. A hurdle model estimated on both laws of parliamentary proposal and of government assignment lends empirical support to both hypotheses, with the noticeable feature that PLC in Korea appear more in the form of an upward trend than of pre-electoral peaks. © 2021 Elsevier B.V.

Toroidal time series are temporal sequences of bivariate angular observations that often arise in environmental and ecological studies. A hidden semi- Markov model is proposed for segmenting these data according to a finite number of latent classes, associated toroidal densities. The model conveniently integrates circular correlation, multimodality and temporal auto-correlation. A computationally efficient EM algorithm is proposed for parameter estimation. The proposal is illustrated on a time series of wind and sea wave directions.

Population ageing is one of the most important demographic phenomena of this century. Driven by fertility decline and the continuing extension of the life expectancy, the process of population ageing has not been uniform across time and space. Italy has one of the oldest populations in the world. The combination of a very old population and large territorial differences has made Italy an interesting laboratory for studying population ageing. The purpose of this paper is to study how population ageing developed between 2002 and 2014 across different geographical areas within Italy. We analyse patterns of population ageing across the five major socio-economic regions using the 110 provinces of Italy as our spatial units of analysis. We use a statistical model that integrates patterns of variation of population ageing data by accounting for autocorrelation in space and time. The results indicate that the provincial age structures tend to converge and demonstrate the importance of considering the role of space in studies of population ageing.

A hidden Markov model is proposed for segmenting cylindrical time series according to a finite number of latent classes, associated with copula-based cylindrical densities. It provides a parsimonious and computationally tractable approach that integrates circular–linear correlation, multimodality and temporal auto-correlation.

Cylindrical hidden Markov fields are proposed as a parsimonious strategy to analyze spatial cylindrical data, i.e. bivariate spatial series of angles and intensities. These models are mixtures of copula-based bivariate densities, whose parameters vary across space according to a latent Markov random field. They enable segmentation of spatial cylindrical data within a finite number of latent classes that represent the conditional distributions of the data under specific environmental conditions, simultaneously accounting for spatial auto-correlation.

Motivated by studies of wildfire seasonality, we propose a nonhomogeneous hidden Markov random field to model the spatial distribution of georeferenced fire occurrences during the year, by representing occurrence times as circular data. The model is based on a mixture of Kato–Jones circular densities, whose parameters vary across space according to a latent nonhomogeneous Potts model, modulated by georeferenced covariates. It allows us to segment fire occurrences according to a finite number of latent classes that represent the conditional distributions of the data under specific periods of the year, simultaneously accounting for unobserved heterogeneity and spatial autocorrelation. Further, it parsimoniously accommodates specific features of wildfire occurrence data such asmultimodality, skewness, and kurtosis. Due to the numerical intractability of the likelihood function, estimation of the parameters is based on composite likelihood methods. It reduces to a computationally efficient expectation–maximization algorithm that iteratively alternates the maximization of a weighted composite likelihood function with weights updating. The proposal is illustrated in a study of wildfire occurrences in the Iberian Peninsula during a decade.

Toroidal time series are temporal sequences of bivariate angular observations that often arise in environmental and ecological studies. A hidden Markov model is proposed for segmenting these data according to a finite number of latent classes, associated with copula-based toroidal densities. The model conveniently integrates circular correlation, multimodality and temporal auto-correlation. A computationally efficient EM algorithm is proposed for parameter estimation. The proposal is illustrated on a time series of wind and sea wave directions.

Beltrán-Sánchez et al . based their comment on misleading calculations of the maximum survival age. With realistic numbers of people attaining age 105 and the estimated plateau, the Jeanne Calment record is indeed plausible.