Monte Carlo integration with variance reduction by means of control variates can be implemented the ordinary least squares estimator for intercept in a multiple linear regression model integrand as response and covariates. Even without special knowledge on integrand, significant efficiency gains obtained if variate space is sufficiently large. Incorporating large number procedure may however re...

We show that by employing a distribution over random matrices, the matrix variate Gaussian Gupta & Nagar (1999), for the neural network parameters we can obtain a non-parametric interpretation for the hidden units after the application of the “local reprarametrization trick” (Kingma et al., 2015). This provides a nice duality between Bayesian neural networks and deep Gaussian Processes Damianou...

In 1949, 126 coalminers, chosen to cover the whole radiological range of coalworkers' pneumoconiosis, were subjected to a battery of physiological tests of lung function, clinical investigations, and anthropometry. During the ensuing 12 years 40 of these men died. An analysis of the original measurements was carried out in an attempt to identify the particular features of the disturbance of lun...

The evolution of the 4-variate probability distribution of the diameter at the breast height, total height, crown base height, and crown width against the age in a forest stand is of great interest to forest management and the evaluation of forest resources. This paper focuses on the Vasicek type 4-variate fixed effect stochastic differential equation (SDE) to quantify the dynamic of tree size ...

Given a random n-variate degree-d homogeneous polynomial f , we study the following problem: