Bayesian kernel mixtures for counts

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Presentation transcript:

Bayesian kernel mixtures for counts Antonio Canale & David B. Dunson Presented by Yingjian Wang Apr. 29, 2011

Outline Existed models for counts and their drawbacks; Univariate rounded kernel mixture priors; Simulation of the univariate model; Multivariate rounded kernel mixture priors; Experiment with the multivariate model;

Modeling of counts Mixture of Poissons: a) Not a nonparametric way; b) Only accounts for cases where the variance is greater than the mean;

Modeling of counts (2) DP mixture of Poissons/Multinomial kernel: a) It is non-parametric but, still has the problem of not suitable for under-disperse cases; b) If with multinomial kernel, the dimension of the probability vector is equal to the number of support points, causes overfitting.

Modeling of counts (3) DP with Poisson base measure: a) There is no allowance for smooth deviations from the base; Motivation: The continuous densities can be accurately approximated using Gaussian kernels. Idea: Use kernels induced through rounding of continuous kernels.

Univariate rounded kernel

Univariate rounded kernel (2) Existence: Consistence: (the mapping g(.) maintains KL neighborhoods.)

Examples of rounded kernels Rounded Gaussian kernel: Other kernels: log-normal, gamma, Weibull densities.

Eliciting the thresholds

A Gibbs sampling algorithm

Experiment with univariate model Two scenarios: Two standards: Results:

Extension to multivariate model

Telecommunication data Data from 2050 SIM cards, with multivariate: yi=[yi1, yi2, yi3, yi4, yi5], Compare the RMG with generalized additive model (GAM):