This paper considers multiple regression model with multivariate spherically symmetric errors to determine optimal β-expectation tolerance regions for the future regression vector (FRV) and future residual sum of squares (FRSS) by using the prediction distributions of some appropriate functions of future responses. The prediction distribution of the FRV, conditional on the observed responses, i...

CIRANO Le CIRANO est un organisme sans but lucratif constitué en vertu de la Loi des compagnies du Québec. Le financement de son infrastructure et de ses activités de recherche provient des cotisations de ses organisations-membres, d'une subvention d'infrastructure du Ministère du Développement économique et régional et de la Recherche, de même que des subventions et mandats obtenus par ses équ...

This paper considers the robust and efficient implementation of Gaussian process regression with a Student-t observation model, which has a non-log-concave likelihood. The challenge with the Student-t model is the analytically intractable inference which is why several approximative methods have been proposed. Expectation propagation (EP) has been found to be a very accurate method in many empi...

We detail a Bayesian interpolation procedure for linearin-the-parameter models which combines both effective complexity control and robustness to outliers. Robustness is obtained by adopting a Student-t noise distribution, defined hierarchically in terms of an inverse-Gamma prior distribution over individual Gaussian observation variances. Importantly, this hierarchical definition enables pract...

In this paper, we briefly review the basics of copula theory and the problem of estimating Value at Risk (VaR) of portfolio composed by several assets. We present two VaR estimation models in which each return series is assumed to follow AR(1)-GARCH(1, 1) model and the innovations are simultaneously generated using Gaussian copula and Student t copula. The presented models are applied to estima...

In this paper, we provide a statistical analysis of the Stochastic Volatility (SV) models using full Bayesian approach. Student-t distribution is chosen as an alternative to the normal distribution for modelling white noise. Bayesian computation of the SV models completely relies on the Markov chain Monte Carlo methods. In particular, to speed up the efficiency of the Gibbs sampling scheme, we ...

The Chronicle learned today t h a t Monday's recommendation to ihe President from the Student FacultyAdm in lstraition Committee suggested an administrative rei-interpretation of present policy on University group usage of segregated facilities. "Hie present policy was recommended by the University Policy and Planning Advisory Committee in September and imtmediately accepted by President Dougla...

Hierarchical models for L studies, domains or experiments often assume that the study means have a common normal population distribution. However, modeling normal sampling distributions with a normal population distribution may overstate the level of exchangeability of the studies. Using heavy tailed population distributions, in particular t distributions, provide some protection from combining...

I explicitly work out closed form solutions for the optimal hedging strategies (in the sense of Bouchaud and Sornette) in the case of European call options, where the underlying is modeled by (unbiased) iid additive returns with Student-t distributions. The results may serve as illustrative examples for option pricing in the presence of fat tails.

We propose a model for natural images in which the probability of an image is proportional to the product of the probabilities of some filter outputs. We encourage the system to find sparse features by using a Studentt distribution to model each filter output. If the t-distribution is used to model the combined outputs of sets of neurally adjacent filters, the system learns a topographic map in...