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Bayesian kernel mixtures for counts

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;

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Bayesian kernel mixtures for counts

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

  2. 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;

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

  4. 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.

  5. 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.

  6. Univariate rounded kernel

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

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

  9. Eliciting the thresholds

  10. A Gibbs sampling algorithm

  11. Experiment with univariate model • Two scenarios: • Two standards: • Results:

  12. Extension to multivariate model

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

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