In this chapter, we will provide an overview of the current status of research involving Bayesian inference in wavelet nonparametric problems. In many statistical applications, there is a need for procedures to (i) adapt to data and (ii) use prior information. The interface of wavelets and the Bayesian paradigm provide a natural terrain for both of these goals.

Methods We retrospectively analyzed the clinical files of all pediatric pts treated with omalizumab from December 2009 to July 2013. The evaluated parameters included: adverse reactions to omalizumab, clinical evolution, Asthma Control Test (ACT) and Severity Scoring of Atopic Dermatitis (SCORAD) score evolution and medication decrease. Statistical significance was defined by a p value in the a...

Multivariate longitudinal data are common in medical, industrial and social science research. However, statistical analysis of such data in the current literature is restricted to linear or parametric modeling, which is inappropriate for applications in which the assumed parametric models are invalid. On the other hand, all existing nonparametric methods for analyzing longitudinal data are for ...

Parametric and nonparametric methods have been developed for purposes of predicting phenotypes. These methods are based on retrospective analyses of empirical data consisting of genotypic and phenotypic scores. Recent reports have indicated that parametric methods are unable to predict phenotypes of traits with known epistatic genetic architectures. Herein, we review parametric methods includin...

Finalement, je tiensà remercier ma famille et mes amis pour leur soutien et, tout simple-ment, pour leur présencè a mes côtés en toutes circonstances.

We consider extensions of the famous GARCH(1, 1) model where the recursive equation for the volatilities is not specified by a parametric link but by a smooth autoregression function. Our goal is to estimate this function under nonparametric constraints when the volatilities are observed with multiplicative innovation errors. We construct an estimation procedure whose risk attains the usual con...

This paper reviews Bayesian Nonparametric methods and discusses how parametric predictive densities can be constructed using nonparametric ideas.