The aim of this paper is to define a new family of probability density functions (MR pdf) based on the multiresolution analysis theory. Each function of this family can be seen as a particular type of density mixture. The MR pdf has advantages of estimation over the conventional mixtures and it is suitable to model a large variety of square integrable probability density functions. The flexibil...

The problem is that of sequential probability forecasting for finite-valued time series. The data is generated by an unknown probability distribution over the space of all one-way infinite sequences. It is known that this measure belongs to a given set C, but the latter is completely arbitrary (uncountably infinite, without any structure given). The performance is measured with asymptotic avera...

This paper establishes that every random utility discrete choice model (RUM) has a representation that can be characterized by a choice-probability generating function (CPGF) with speci c properties, and that every function with these speci c properties is consistent with a RUM. The choice probabilities from the RUM are obtained from the gradient of the CPGF. Mixtures of RUM are characterized b...

This paper describes a general scheme for accomodating different types of conditional distributions in a Bayesian network. The algorithm is based on the polytree algorithm for Bayesian network inference, in which “messages” (probability distributions and likelihood functions) are computed. The posterior for a given variable depends on the messages sent to it by its parents and children, if any....

In this paper, I redefine the prices derived in Ross’ Recovery Theorem (Ross, 2015) using a multivariate Markov chain rather than a univariate one. I employ a mixture transition distribution where the proposed states depend on the level of the S&P 500 index and its options’ implied volatilities. I include volatility because the transition path between states depends on the propensity of an unde...

We introduce the mixture of Gaussian processes (MGP) model which is useful for applications in which the optimal bandwidth of a map is input dependent. The MGP is derived from the mixture of experts model and can also be used for modeling general conditional probability densities. We discuss how Gaussian processes -in particular in form of Gaussian process classification, the support vector mac...

Definition A Gaussian Mixture Model (GMM) is a parametric probability density function represented as a weighted sum of Gaussian component densities. GMMs are commonly used as a parametric model of the probability distribution of continuous measurements or features in a biometric system, such as vocal-tract related spectral features in a speaker recognition system. GMM parameters are estimated ...

An important and common problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. As this problem concerns the selection of significant genes from a large pool of candidate genes, it needs to be carried out within the framework of multiple hypothesis testing. In this paper, we focus on the use of mixture models to handle the mult...

Simultaneously testing a collection of null hypotheses about a data generating distribution based on a sample of independent and identically distributed observations is a fundamental and important statistical problem involving many applications. In this article we propose a new resampling based multiple testing procedure asymptotically controlling the probability that the proportion of false po...

Considering the probabilistic approach to practical problems we are increasingly confronted with the need to estimate unknown multivariate probability density functions from large high-dimensional databases produced by electronic devices. The underlying densities are usually strongly multimodal and therefore mixtures of unimodal density functions suggest themselves as a suitable approximation t...