Bayesian inference for the multivariate Normal is most simply instantiated using a Normal-Wishart prior over the mean and covariance. Predictive densities then correspond to multivariate T distributions, and the moments from the marginal densities are provided analytically or via Monte-Carlo sampling. We show how this textbook approach is applied to a simple two-dimensional example.

This paper establishes a sufficient condition for Turing’s formulae of various orders to have asymptotic multivariate normality. As an application, a consistent estimator of the tail under a discrete power tail model is also described.

Classes of shape mixtures of independent and dependent multivariate skew-normal distributions are considered and some of their main properties are studied. If interpreted from a Bayesian point of view, the results obtained in this paper bring tractability to the problem of inference for the shape parameter, that is, the posterior distribution can be written in analytic form. Robust inference fo...

the Normal Distribution's familiar "bell curve". The latter term can be interpreted as a description of squared of distance (x  between some value of x who's probability is being assessed (along the x axis), and  the center of the probability density distribution, "standardized" by the distribution's known variance 2. It should be noted that f(x) only depends on this single scalar range var...

1 General case 1.1 Cumulative distribution function 1.2 A counterexample 1.3 Normally distributed and independent 2 Bivariate case 3 Affine transformation 4 Geometric interpretation 5 Correlations and independence 6 Higher moments 7 Conditional distributions 8 Fisher information matrix 9 Kullback-Leibler divergence 10 Estimation of parameters 11 Entropy 12 Multivariate normality tests 13 Drawin...

In this paper, we seek for a single best representative of a set of statistical multivariate normal distributions. To define the “best” center, we consider either minimizing the average or the maximum relative entropy of the center to the given set of normal distributions. Since the relative entropy is an asymmetric divergence, this yields the notion of leftand right-sided, and symmetrized entr...

Problems of regression smoothing and curve fitting are addressed via predictive inference in a flexible class of mixture models. Multidimensional density estimation using Dirichlet mixture models provides the theoretical basis for semi-parametric regression methods in which fitted regression functions may be deduced as means of conditional predictive distributions. These Bayesian regression fun...

This paper 1 deals with the normal density of n dependent random variables. This is a function of the form : ce ?x T Ax where A is an n n positive deenite matrix, x is the n?vector of the random variables and c is a suitable constant. The rst problem we consider is the (approximate) evaluation of the integral of this function over the positive orthant Z 1 x1=0 Z 1 x2=0 ... Z 1 xn=0 ce ?x T Ax :...