Parsimonious hidden Markov models for matrix-variate longitudinal data

Hidden Markov models (HMMs) have been extensively used in the univariate and multivariate literature. However, there has been an increased interest in the analysis of matrix-variate data over the recent years. In this manuscript we introduce HMMs for matrix-variate balanced longitudinal data, by assuming a matrix normal distribution in each hidden state. Such data are arranged in a four-way array. To address for possible overparameterization issues, we consider the eigen decomposition of the covariance matrices, leading to a total of 98 HMMs. An expectation-conditional maximization algorithm is discussed for parameter estimation. The proposed models are firstly investigated on simulated data, in terms of parameter recovery, computational times and model selection. Then, they are fitted to a four-way real data set concerning the unemployment rates of the Italian provinces, evaluated by gender and age classes, over the last 16 years.publishedVersio

Electron Spin Resonance dosimetry using organic compounds (alanine and ammonium tartrate) for mixed neutron-gamma fields

Alongside with the development of Neutron Capture Therapy (NCT) and the use of thermal neutrons for radiotherapeutic purposes, many efforts have been devoted to the characterization of the beam in order to optimize therapy procedures. Reliable dose measurements should be able to determine the various (neutrons and photonic) components of the mixed beam usually employed for therapy. This paper studies the effect of additives such as boric and gadolinium nuclei on the sensitivity of neutron organic (alanine and ammonium tartrate) dosimeters analyzed through Electron Spin Resonance (ESR) technique (Marrale, 2014). These dosimeters were exposed to a mixed (neutron-gamma) field mainly composed of thermal neutrons. The choice of 10B and 64Gd as nuclei additives is due to their very high capture cross section for thermal neutrons. Also, after the nuclear reaction with thermal neutrons are emitted particles, which in turn release their energy in the vicinity of the reaction site (Marrale, 2008). The irradiation with mixed field (neutron-gamma) were performed within the thermal column of the TRIGA reactor, University of Pavia. Dosimeters readout was performed through the Electron Spin Resonance spectrometer Bruker ECS106 located at the Laboratory of Dosimetry ESR / TL of the Department of Physics and Chemistry - University of Palermo. We found that the addition of Gadolinium allows to largely increase the sensitivity of the dosimeters for thermal neutrons. In particular, a low concentration (5% by weight) of gadolinium oxide leads to an improvement of the sensitivity of neutrons more than 10 times. In addition, for this low content of gadolinium the photon tissue equivalence is not heavily reduced. This experimental analyses are compared with computational analyses carried out by means of Monte Carlo simulations performed with the MCNP (Monte Carlo N-Particle) transport code. A good agreement was observed for alanine dosimeters

Mode mixture of unimodal distributions for insurance loss data

DATA AVAILABILITY : The real datasets used in this manuscript are publicly available in the CASdatasets package for the R statistical software.Insurance loss data have peculiar features that can rarely be accounted for by simple parametric distributions. Thus, in this manuscript, we first introduce a new type of location mixture model: the mode mixture. By using convenient mode-parameterized hump-shaped distributions, we present a family of eight mode mixture of unimodal distributions. Then, we fit these models to two real insurance loss datasets, where they are evaluated in terms of goodness of fit and ability to reproduce classical risk measures. We extend the comparisons to existing models based on mode-parameterized hump-shaped distributions. Lastly, using simulated data, we further investigate the performance of the estimated risk measures of our models.The National Research Foundation (NRF) of South Africa (SA), , the DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa and the Department of Research and Innovation at the University of Pretoria (SA).http://link.springer.com/journal/104792025-05-29hj2024StatisticsSDG-01:No povert

Two new matrix-variate distributions with application in model-based clustering

Two matrix-variate distributions, both elliptical heavy-tailed generalization of the matrix-variate normal distribution, are introduced. They belong to the normal scale mixture family, and are respectively obtained by choosing a convenient shifted exponential or uniform as mixing distribution. Moreover, they have a closed-form for the probability density function that is characterized by only one additional parameter, with respect to the nested matrix-variate normal, governing the tail-weight. Both distributions are then used for model-based clustering via finite mixture models. The resulting mixtures, being able to handle data with atypical observations in a better way than the matrix-variate normal mixture, can avoid the disruption of the true underlying group structure. Different EM-based algorithms are implemented for parameter estimation and tested in terms of computational times and parameter recovery. Furthermore, these mixture models are fitted to simulated and real datasets, and their fitting and clustering performances are analyzed and compared to those obtained by other well-established competitors

On the Use of the Matrix-Variate Tail-Inflated Normal Distribution for Parsimonious Mixture Modeling

Recent advances in the matrix-variate model-based clustering literature have shown the growing interest for this kind of data modelization. In this framework, finite mixture models constitute a powerful clustering technique, despite the fact that they tend to suffer from overparameterization problems because of the high number of parameters to be estimated. To cope with this issue, parsimonious matrix-variate normal mixtures have been recently proposed in the literature. However, for many real phenomena, the tails of the mixture components of such models are lighter than required, with a direct effect on the corresponding fitting results. Thus, in this paper we introduce a family of 196 parsimonious mixture models based on the matrix-variate tail-inflated normal distribution, an elliptical heavy-tailed generalization of the matrix-variate normal distribution. Parsimony is reached by applying the well-known eigen-decomposition of the component scale matrices, as well as by allowing the tailedness parameters of the mixture components to be tied across groups. An AECM algorithm for parameter estimation is presented. The proposed models are then fitted to simulated and real data. Comparisons with parsimonious matrix-variate normal mixtures are also provided