Abstract:
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We consider the problem of estimating probability distribution of event chance based on binary or multinomial observations of the event at some random data points in the domain of the covariates. For each given data point x in the domain, the contribution of each random observed data points to x is evaluated using some non-parametric approach. The cumulative contributions from all random observations to x can then be considered as the local sample size and the corresponding observed binary or multinomial response are applied to estimate the distribution of the local event chance. If a Beta or Dirichlet prior distribution is assumed, then the corresponding posterior distribution is also Beta or Dirichlet and the parameters can be updated easily. We compared our new method with more traditional indicator Kriging method with simulations. The proposed method has a direct application in constructing Gibbs sampler in multinomial non-parametric latent class regression analyses. The method is applied in estimating disease etiology.
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