An approach is proposed for computing the percentile points of the maximum of k independent Student’s t random variables. A simple program in R (a freely downloadable statistical software) is presented and its performance compared with other known approaches. Similar programs are presented for computing the percentile points of the componentwise maximum of k-variate t and k-variate normal vecto...

A direct corollary of the fundamental theorem of algebra is that p(x) can be factorized over the complex domain into a product an(x − r1)(x − r2) · · · (x − rn), where an is the leading coefficient and r1, r2, . . . , rn are all of its n complex roots. We will look at how to find roots, or zeros, of polynomials in one variable. The solution of multi-variate polynomials can often be transformed ...

In stationary subspace analysis (SSA) one assumes that the observable p-variate time series is a linear mixture of k-variate nonstationary and (p−k)-variate series. The aim then to estimate unmixing matrix which transforms observed multivariate onto components. classical approach data are projected subspaces by minimizing Kullback–Leibler divergence between Gaussian distributions, method only d...

Abstract. Factorisation (also known as “factor separation”) is widely used in the analysis of numerical simulations. It allows changes properties a system to be attributed multiple variables associated with that system. There are many possible factorisation methods; here we discuss three previously proposed factorisations have been applied field climate modelling: linear factorisation, Stein an...

Modern datasets are becoming heterogeneous. To this end, we present in this paper MixedVariate Restricted Boltzmann Machines for simultaneously modelling variables of multiple types and modalities, including binary and continuous responses, categorical options, multicategorical choices, ordinal assessment and category-ranked preferences. Dependency among variables is modeled using latent binary...

This paper introduces a novel class of Bayesian models for multivariate time series analysis based on a synthesis of dynamic linear models and graphical models. The synthesis uses sparse graphical modelling ideas to introduce structured, conditional independence relationships in the time-varying, cross-sectional covariance matrices of multiple time series. We define this new class of models and...