Theories about biological limits to life span and evolutionary shaping of human longevity depend on facts about mortality at extreme ages, but these facts have remained a matter of debate. Do hazard curves typically level out into high plateaus eventually, as seen in other species, or do exponential increases persist? In this study, we estimated hazard rates from data on all inhabitants of Italy aged 105 and older between 2009 and 2015 (born 1896-1910), a total of 3836 documented cases. We observed level hazard curves, which were essentially constant beyond age 105. Our estimates are free from artifacts of aggregation that limited earlier studies and provide the best evidence to date for the existence of extreme-age mortality plateaus in humans.

The identification of sea regimes from environmental multivariate times series is complicated by the mixed linear-circular support of the data, by the occurrence of missing values, by the skewness of some variables, and by the temporal autocorrelation of the measurements. We address these issues simultaneously by a hidden Markov approach, and segment the data into pairs of toroidal and skew elliptical clusters by means of the inferred sequence of latent states. Toroidal clusters are defined by a class of bivariate von Mises densities, while skew elliptical clusters are defined by mixed linear models with positive random effects. The core of the classification procedure is an EM algorithm accounting for missing measurements, unknown cluster membership, and random effects as different sources of incomplete information. Moreover, standard simulation routines allow for the efficient computation of bootstrap standard errors. The proposed procedure is illustrated for a multivariate marine time series, and identifies a number of wintertime regimes in the Adriatic Sea

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Summary   Motivated by segmentation issues in studies of sea current circulation, we describe a hidden Markov random field for the analysis of spatial cylindrical data, i.e. bivariate spatial series of angles and intensities. The model is based on a mixture of cylindrical densities, whose parameters vary across space according to a latent Markov field. It enables segmentation of the data within a finite number of latent classes that represent the conditional distributions of the data under specific environmental conditions, simultaneously accounting for unobserved heterogeneity and spatial auto‐correlation. Further, it parsimoniously accommodates specific features of environmental cylindrical data, such as circular–linear correlation, multimodality and skewness. Because of the numerical intractability of the likelihood function, estimation of the parameters is based on composite likelihood methods and essentially reduces to a computationally efficient expectation–maximization algorithm that iteratively alternates the maximization of a weighted composite likelihood function with weights updating. These methods are tested on simulations and exploited to segment the sea surface of the Gulf of Naples by means of meaningful circulation regimes.

A new hidden Markov model is proposed for the analysis of cylindrical time series, that is, bivariate time series of intensities and angles. It allows us 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\ud that samples of angular measurements are drawn from a multivariate\ud von Mises distribution with mean and concentration parameters that depend\ud on covariates through link functions. The model can flexibly accommodate\ud heteroscedasticity, unstructured correlation, and specific autoregressive correlation\ud structures. Because the computation of the normalizing constant of the\ud multivariate von Mises distribution is unfeasible, inference is based on a computationally\ud tractable Monte Carlo approximation of the log-likelihood. These\ud methods are illustrated by fitting a number of regression models in two case\ud studies: a longitudinal study of animal orientation, involving multiple time\ud series of directional observations, and a study of marine currents, involving a\ud spatial series of sea current directions

Summary. The production of legislative acts is affected by multiple sources of latent heterogeneity, due to multilevel and multivariate unobserved factors that operate in conjunction with observed covariates at all the levels of the data hierarchy. We account for these factors by estimating a multilevel Poisson regression model for repeated measurements of bivariate counts of executive and ordinary legislative acts, enacted under multiple Italian governments, nested within legislatures. The model integrates discrete bivariate random effects at the legislature level and Markovian sequences of discrete bivariate random effects at the government level. It can be estimated by a computationally feasible expectation-maximization algorithm. It naturally extends a traditional Poisson regression model to allow for multiple outcomes, longitudinal dependence and multilevel data hierarchy. The model is exploited to detect multiple cycles of legislative supply that arise at multiple timescales in a case-study of Italian legislative production.

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