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In the mare, foaling is a critical unpredictable event due to a wide range of gestational length and the absence of clear signs of impending parturition. To predict foaling, pH, inversion sodium potassium and increase of calcium concentration in mammary secretions are used. The aim of this study was to find how many days are left until parturition knowing mare's age (A) and parity (P) combined with ultrasonographic measurements of the fetal orbit in Standardbred mares with normal pregnancy. Eighty healthy Standardbred mares with normal pregnancy were hospitalized for attended delivery. Information about mare's age, parity and breeding date were recorded at admission. Transrectal ultrasonography were routinely performed at admission and every 10 days until parturition using a B-mode real time portable unit equipped with a 5-7.5 MHz linear transducer. The images of the fetal orbit were acquired when cornea, anterior and posterior chamber, vitreous body, lens and optic nerve were visible. Longitudinal diameter (LD) was considered as the distance between the two ocular poles, within the vitreous body; transverse diameter (TD), perpendicular to LD and bisecting the lens, was measured as the distance between cornea and retina. At delivery, length of pregnancy and gestational age at each exam were registered. For each ultrasound examination, days before parturition (DBP) were calculated. Seventy-eight Standardbred mares with normal pregnancies were included in the study. Mares' mean age was 9 ± 5 years old (range 4-20 years) and mean gestation length was 341 ± 7 days (range 327-366 days). Thirty-three mares were primiparous and 45 mares were multiparous. Data were analyzed using a regression tree: P, A, LD and TD were used as covariates. DBP was used as the variable of interest. Nine terminal nodes were identified based on the selected covariates. The first split is produced by the TD: fetuses with TD greater or equal than 2.97 cm are further split according to LD, with a threshold of 3.28 cm. The next split is dictated by A; after a further split on LD, the first terminal node is built, containing 34 fetuses with average DBP equal to 10 days. If the A is ≥ 9.5 years a further split is on P: when mares are multiparous, the TD built two different nodes. Since prediction of mare's foaling date is an important factor in stud farm management, the regression model developed may help the veterinarian to estimate the DBP in Standardbred mares with normal pregnancy.

This paper addresses two crucial issues in multiple linear regression analysis: (i) error terms whose distribution is non-normal because of the presence of asymmetry of the response variable and/or data coming from heterogeneous populations; (ii) selection of the regressors that effectively contribute to explaining patterns in the observations and are relevant for predicting the dependent variable. A solution to the first issue can be obtained through an approach in which the distribution of the error terms is modelled using a finite mixture of Gaussian distributions. In this paper we use this approach to specify a Bayesian linear regression model with non-normal errors; furthermore, by embedding Bayesian variable selection techniques in the specification of the model, we simultaneously perform estimation and variable selection. These tasks are accomplished by sampling from the posterior distributions associated with the model. The performances of the proposed methodology are evaluated through the analysis of simulated datasets in comparison with other approaches. The results of an analysis based on a real dataset are also provided. The methods developed in this paper result to perform well when the distribution of the error terms is characterised by heavy tails, skewness and/or multimodality.

Model-based clustering is a technique widely used to group a collection of units into mutually exclusive groups. There are, however, situations in which an observation could in principle belong to more than one cluster. In the context of next-generation sequencing (NGS) experiments, for example, the signal observed in the data might be produced by two (or more) different biological processes operating together and a gene could participate in both (or all) of them. We propose a novel approach to cluster NGS discrete data, coming from a ChIP-Seq experiment, with a mixture model, allowing each unit to belong potentially to more than one group: these multiple allocation clusters can be flexibly defined via a function combining the features of the original groups without introducing new parameters. The formulation naturally gives rise to a 'zero-inflation group' in which values close to zero can be allocated, acting as a correction for the abundance of zeros that manifest in this type of data. We take into account the spatial dependency between observations, which is described through a latent conditional autoregressive process that can reflect different dependency patterns. We assess the performance of our model within a simulation environment and then we apply it to ChIP-seq real data.

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Dynamic processes are crucial in many empirical fields, such as in oceanography, climate science, and engineering. Processes that evolve through time are often well described by systems of ordinary differential equations (ODEs). Fitting ODEs to data has long been a bottleneck because the analytical solution of general systems of ODEs is often not explicitly available. We focus on a class of inference techniques that uses smoothing to avoid direct integration. In particular, we develop a Bayesian smooth‐and‐match strategy that approximates the ODE solution while performing Bayesian inference on the model parameters. We incorporate in the strategy two main sources of uncertainty: the noise level of the measured observations and the model approximation error. We assess the performance of the proposed approach in an extensive simulation study and on a canonical data set of neuronal electrical activity.

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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