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Dependent Dirichlet Priors and Optimal Linear Estimators for Belief Net Parameters
Dependent Dirichlet Priors Optimal Linear Estimators Belief Net Parameters
2012/9/19
A Bayesian belief network is a model of a joint distribution over a finite set of vari-ables, with a DAG structure representing im-mediate dependencies among the variables.For each node, a table of pa...
Hierarchical array priors for ANOVA decompositions
array-valued data Bayesian estimation cross-classi ed data factorial design MANOVA penalized regression tensor Tucker product sparse data.
2012/9/17
ANOVA decompositions are a standard method for describing and estimating heterogeneity among the means of a response variable across levels of multiple categorical factors. In such a decomposition, th...
The use of systems of stochastic PDEs as priors for multivariate models with discrete structures
Gaussian distribution multivariate stochastic PDEs discrete structures
2012/9/17
A challenge in multivariate problems with discrete structures is the inclusion of prior information that may di er in each separate structure. A particular example of this is seismic amplitude versus ...
Bayesian inference with rescaled Gaussian process priors
Rate of convergence Bayesian inference nonparametric density estimation nonparametric regression classification
2009/9/16
We use rescaled Gaussian processes as prior models for functional parameters in nonparametric statistical models. We show how the rate of contraction of the posterior distributions depends on the scal...
Lower bounds for posterior rates with Gaussian process priors
Bayesian nonparametrics Gaussian process priors Lower bounds
2009/9/16
Upper bounds for rates of convergence of posterior distributions associated to Gaussian process priors are obtained by van der Vaart and van Zanten in [van der Vaart and van Zanten, Rates of contracti...
Kullback Leibler property of kernel mixture priors in Bayesian density estimation
Bayesian density estimation Dirichlet process, kernel mixture KullbackLeibler property posterior consistency
2009/9/16
Positivity of the prior probability of Kullback-Leibler neighborhood around the true density, commonly known as the Kullback-Leibler property, plays a fundamental role in posterior consistency. A popu...