Showing papers by "Francesco Bartolucci published in 2021"

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

Abstract: 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.

A multivariate statistical approach to predict COVID-19 count data with epidemiological interpretation and uncertainty quantification.

Abstract: For the analysis of COVID-19 pandemic data, we propose Bayesian multinomial and Dirichlet-multinomial autoregressive models for time-series of counts of patients in mutually exclusive and exhaustive observational categories, defined according to the severity of the patient status and the required treatment. Categories include hospitalized in regular wards (H) and in intensive care units (ICU), together with deceased (D) and recovered (R). These models explicitly formulate assumptions on the transition probabilities between these categories across time, thanks to a flexible formulation based on parameters that a priori follow normal distributions, possibly truncated to incorporate specific hypotheses having an epidemiological interpretation. The posterior distribution of model parameters and the transition matrices are estimated by a Markov chain Monte Carlo algorithm that also provides predictions and allows us to compute the reproduction number R t . All estimates and predictions are endowed with an accuracy measure obtained thanks to the Bayesian approach. We present results concerning data collected during the first wave of the pandemic in Italy and Lombardy and study the effect of nonpharmaceutical interventions. Suitable discrepancy measures defined to check and compare models show that the Dirichlet-multinomial model has an adequate fit and provides good predictive performance in particular for H and ICU patients.

Modelling Nonstationary Spatial Lag Models with Hidden Markov Random Fields

Abstract: One of the basic assumptions in spatial statistic is second-order stationarity, which implies homogeneity and isotropy. However, when using a spatial random field framework to model socio-economical or epidemiological data – just to mention two examples – it is often unreasonable to believe that the relationship between variables could be modelled as a realization of a unique stationary process. In order to provide a more realistic representation, we introduce a latent process which drives the value of the coefficients in a Cliff-Ord-type spatial autoregressive linear model identifying groups of observations with a similar behaviour. The latent process evolves as a Hidden Markov Random Field. This structure allows the topology of the problem to be taken into account when identifying groups. A simulation exercise is performed to investigate the influence of parameter values – estimated via a Markov chain Monte Carlo procedure – on the accuracy of the results. Criteria to perform model comparison in order to establish the optimal number of clusters are also provided. A case study referred to hedonic house prices in Boston illustrates the advantages of the proposed modelling strategy.

Exploring the dependencies among main cryptocurrency log-returns: A hidden Markov model

Abstract: A multivariate hidden Markov model is proposed to explain the price evolution of Bitcoin, Ethereum, Ripple, Litecoin, and Bitcoin Cash. The observed daily log-returns of these five major cryptocurrencies are modeled jointly. They are assumed to be correlated according to a variance-covariance matrix conditionally on a latent Markov process having a finite number of states. For the purpose of comparing states according to their volatility, we estimate specific variance-covariance matrix varying across states. Maximum likelihood estimation of the model parameters is carried out by the Expectation-Maximization algorithm. The hidden states represent different phases of the market identified through the estimated expected values and volatility of the log-returns. We reach interesting results in detecting these phases of the market and the implied transition dynamics. We also find evidence of structural medium term trend in the correlations of Bitcoin with the other cryptocurrencies.

Reflections on Murray Aitkin's contributions to nonparametric mixture models and Bayes factors

Abstract: We describe two interesting and innovative strands of Murray Aitkin's research publications, dealing with mixture models and with Bayesian inference. Of his considerable publications on mixture mod...

A bivariate finite mixture growth model with selection

Abstract: A model is proposed to analyze longitudinal data where two response variables are available, one of which is a binary indicator of selection and the other is continuous and observed only if the first is equal to 1. The model also accounts for individual covariates and may be considered as a bivariate finite mixture growth model as it is based on three submodels: (i) a probit model for the selection variable; (ii) a linear model for the continuous variable; and (iii) a multinomial logit model for the class membership. To suitably address endogeneity, the first two components rely on correlated errors as in a standard selection model. The proposed approach is applied to the analysis of the dynamics of household portfolio choices based on an unbalanced panel dataset of Italian households over the 1998–2014 period. For this dataset, we identify three latent classes of households with specific investment behaviors and we assess the effect of individual characteristics on households’ portfolio choices. Our empirical findings also confirm the need to jointly model risky asset market participation and the conditional portfolio share to properly analyze investment behaviors over the life-cycle.

Estimating the size of a closed population by modeling latent and observed heterogeneity

Abstract: We describe a new class of capture-recapture models for closed populations when individual covariates are available. The novelty consists in combining a latent class model where the marginal weights and the conditional distributions given the latent may depend on covariates, with a model for the marginal distribution of the available covariates. In addition, a general formulation for the conditional distributions given the latent which allows serial dependence is provided. An efficient algorithm for maximum likelihood estimation is presented, asymptotic results are derived, and a procedure for constructing likelihood based confidence intervals for the population total is presented. Two examples with real data are used to illustrate the proposed approach.

Recursive Computation of the Conditional Probability Function of the Quadratic Exponential Model for Binary Panel Data

Abstract: We propose a general recursive algorithm for the computation of the conditional probability function of the quadratic exponential model for binary panel data given the total of the responses, which is a sufficient statistic for the individual intercept parameter. This recursion permits to implement conditional and pseudo-conditional maximum likelihood estimators of the parameters of this model, and related models such as the dynamic logit model, even when one or more statistical units are observed at many occasions. In this way we solve a typical problem in dealing with distributions with a complex normalizing constant. The advantage in terms of computational load with respect to standard techniques is assessed by simulation and illustrated by an application based on a popular dataset about brand loyalty.

Maximum likelihood estimation of hidden Markov models for continuous longitudinal data with missing responses and dropout

Abstract: We propose an inferential approach for maximum likelihood estimation of the hidden Markov models for continuous responses. We extend to the case of longitudinal observations the finite mixture model of multivariate Gaussian distributions with Missing At Random (MAR) outcomes, also accounting for possible dropout. The resulting hidden Markov model accounts for different types of missing pattern: (i) partially missing outcomes at a given time occasion; (ii) completely missing outcomes at a given time occasion (intermittent pattern); (iii) dropout before the end of the period of observation (monotone pattern). The MAR assumption is formulated to deal with the first two types of missingness, while to account for informative dropout we assume an extra absorbing state. Maximum likelihood estimation of the model parameters is based on an extended Expectation-Maximization algorithm relying on suitable recursions. The proposal is illustrated by a Monte Carlo simulation study and an application based on historical data on primary biliary cholangitis.