where c = (2π) is a constant and |y| = d. The j’th row of Bi is the regression vector for the j’th component of y given that Q = i. We consider tying and various constraints on the covariance matrix in order to reduce the number of free parameters. We will allow any of the variables to be hidden — we will replace observed values with expected values conditioned on evidence, as in EM. We express...

This paper considers two flexible classes of omnibus goodness-of-fit tests for the inverse Gaussian distribution. The test statistics are weighted integrals over the squared modulus of some measure of deviation of the empirical distribution of given data from the family of inverse Gaussian laws, expressed by means of the empirical Laplace transform. Both classes of statistics are connected to t...

PESC computes a Gaussian approximation to the NFCPD (main text, Eq. (11)) using Expectation Propagation (EP) (Minka, 2001). EP is a method for approximating a product of factors (often a single prior factor and multiple likelihood factors) with a tractable distribution, for example a Gaussian. EP generates a Gaussian approximation by approximating each individual factor with a Gaussian. The pro...

Linear inverse Gaussian problems is traditionally solved using least squares based inversion. The center of the posterior Gaussian probability distribution is often chosen as the solution to such problems, while the solution is in fact the posterior Gaussian probability distribution itself. We present an algorithm, based on direct sequential simulation, which can be used to efficiently draw sam...

There is strong evidence to suggest that data recorded from magnetoencephalography (MEG) follows a non-Gaussian distribution. However, existing standard methods for source localisation model the data using only second order statistics, and therefore use the inherent assumption of a Gaussian distribution. In this paper, we present a new general method for non-Gaussian source estimation of statio...

Variance estimation and ranking methods are developed for stochastic processes modeled by Gaussian mixture distributions. It is shown that the variance estimate from a Gaussian mixture distribution has the same properties as a variance estimate from a single Gaussian distribution based on a reduced number of samples. Hence, well known tools of variance estimation and ranking of single Gaussian ...

Figure 1.1: Visualization of Tensors of different orders. gained popularity in parameter estimation for a variety of problems. In this lecture, the focus is on how they may be used in estimating the parameters of Gaussian Mixture Models and Hidden Markov Models. In a Gaussian mixture model, there are k unknown n-dimensional multivariate Gaussian distributions. Samples are generated by first pic...

In this paper, we propose a new speech probability distribution, two-sided generalized gamma distribution (GΓD) for an efficient parametric characterization of speech spectra. GΓD forms a generalized class of parametric distributions including the Gaussian, Laplacian and Gamma probability density functions (pdf’s) as special cases. All the parameters associated with the GΓD are estimated by the...