ABSTRACT
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.
ABSTRACT
A correct modelization of the insurance losses distribution is crucial in the insurance industry. This distribution is generally highly positively skewed, unimodal hump-shaped, and with a heavy right tail. Compound models are a profitable way to accommodate situations in which some of the probability masses are shifted to the tails of the distribution. Therefore, in this work, a general approach to compound unimodal hump-shaped distributions with a mixing dichotomous distribution is introduced. A 2-parameter unimodal hump-shaped distribution, defined on a positive support, is considered and reparametrized with respect to the mode and to another parameter related to the distribution variability. The compound is performed by scaling the latter parameter by means of a dichotomous mixing distribution that governs the tail behavior of the resulting model. The proposed model can also allow for automatic detection of typical and atypical losses via a simple procedure based on maximum a posteriori probabilities. Unimodal gamma and log-normal are considered as examples of unimodal hump-shaped distributions. The resulting models are firstly evaluated in a sensitivity study and then fitted to two real insurance loss datasets, along with several well-known competitors. Likelihood-based information criteria and risk measures are used to compare the models.
ABSTRACT
PURPOSE: To evaluate the efficacy of a new surgical technique in reducing inferior oblique muscle overaction. METHODS: Anterior transposition and myectomy of the inferior oblique muscle represent the gold-standard treatment in dissociated vertical deviation, including cases in which a simultaneous inferior oblique muscle overaction is also present. A new surgical procedure that consists of suturing the muscle to the sclera at the Gobin point with tendon sparing using a micro-incision to minimize the related tissue trauma and induce a faster recovery was developed. RESULTS: Two of 8 patients with essential infant esotropia had a complete resolution of the elevation in adduction with no residual vertical imbalance. All patients experienced an improvement in lateral incomitance. CONCLUSIONS: The new "equatorial scleral anchor" surgical procedure gives a similarly good outcome when compared with the classic inferior oblique anterior transposition technique, with the advantages being simple, safe, reversible, and modular in terms of suturing.
