Information matrix for hidden Markov models with covariates

For a general class of hidden Markov models that may include time-varying covariates, we illustrate how to compute the observed information matrix, which may be used to obtain standard errors for the parameter estimates and check model identifiability. The proposed method is based on the Oakes’ identity and, as such, it allows for the exact computation of the information matrix on the basis of the output of the expectation-maximization (EM) algorithm for maximum likelihood estimation. In addition to this output, the method requires the first derivative of the posterior probabilities computed by the forward-backward recursions introduced by Baum and Welch. Alternative methods for computing exactly the observed information matrix require, instead, to differentiate twice the forward recursion used to compute the model likelihood, with a greater additional effort with respect to the EM algorithm. The proposed method is illustrated by a series of simulations and an application based on a longitudinal dataset in Health Economics

Testing for positive association in contingency tables with fixed margins

An exact conditional approach is developed to test for certain forms of positive association between two ordinal variables (e.g. positive quadrant dependence, total positivity of order 2). The approach is based on the use of a test statistic measuring the goodness-of-(t of the model formulated according to the type of positive association of interest. The nuisance parameters, corresponding to the marginal distributions of the two variables, are eliminated by conditioning the inference on the observed margins. This, in turn, allows to remove the uncertainty on the conclusion of the test, which typically arises in the unconditional context where the null distribution of the test statistic depends on such parameters. Since the multivariate generalized hypergeometric distribution, which results from conditioning, is normally intractable, Markov chain Monte Carlo methods are used to obtain maximum likelihood estimates of the parameters of the constrained model. The Pearson\u2019s chi-squared statistics is used as a test statistic; a p-value forthis statistic is computed through simulation, when the data are sparse, or exploiting the asymptotic theory based on the chi-bar squared distribution. The extension of the present approach to deal with bivariate contingency tables, strati(ed according to one or more explanatory discrete variables, is also outlined. Finally, three applications based on real data are presented

Bayesian inference for marginal models under equality and inequality constraints

We develop a Bayesian framework for making inference on a class of marginal models for categorical variables, which is formulated through equality and/or inequality constraints on generalized logits, generalized log-odds ratios and similar higher-order interactions. A Markov chain Monte Carlo (MCMC) algorithm is used for parameters estimation and for computing the Bayes factor between competing models. The approach is illustrated through the application to a well-known dataset on social mobility

The use of mixtures for dealing with non-normal regression errors

In many situations, the distribution of the error terms of a linear regression model departs significantly from normality. It is shown, through a simulation study, that an effective strategy to deal with these situations is fitting a regression model based on the assumption that the error terms follow a mixture of normal distributions. The main advantage, with respect to the usual approach based on the least-squares method is a greater precision of the parameter estimates and confidence intervals. For the parameter estimation we make use of the EM algorithm, while confidence intervals are constructed through a bootstrap method

A historical perspective on vascular plants endemic to Italy

A Historical Perspective on Vascular Plants Endemic to Italy. According to a recent review, Italian endemic vascular flora is made up by 1371 specific and subspecific taxa. Focussing on these taxa, in this paper we analyse the frequency of the names' authorities, the type and frequency of specific/infraspecific epithets, and their change over time. The most represented authorities, accounting for about 20% of the name descriptions, are Salvatore Brullo (1947-), Giovanni Gussone (1787-1866) and Michele Tenore (1780-1861). Geographical epithets are the most represented in the dataset. Despite a very slow increase in taxa description in the period 1929-1964, in the last decades we encountered an exponential increase, highlighting for the generalized use of new techniques as a tool to describe new species and for the increasing exploration of poorly known areas, but also for the urgent need to reconsider the past, present and future concept od species

A spatio-temporal model based on discrete latent variables for the analysis of COVID-19 incidence

We propose a model based on discrete latent variables, which are spatially associated and time specific, for the analysis of incident cases of SARS-CoV-2 infections. We assume that for each area the sequence of latent variables across time follows a Markov chain with initial and transition probabilities that also depend on latent variables in neighboring areas. The model is estimated by a Markov chain Monte Carlo algorithm based on a data augmentation scheme, in which the latent states are drawn together with the model parameters for each area and time. As an illustration we analyze incident cases of SARS-CoV-2 collected in Italy at regional level for the period from February 24, 2020, to January 17, 2021, corresponding to 48 weeks, where we use number of swabs as an offset. Our model identifies a common trend and, for every week, assigns each region to one among five distinct risk groups