in real world data, often (always to me) happen that for modelling count data

  • Poisson
  • Negative binomial
  • multinomial
  • dirichlet-multinomial

probability distribution, are not robust to outliers, as they don't have long tails. A lot have been proposed in this matter


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However often these problems arise, when implementing those functions in a Bayesian inference model

1) The likelihood calculation doesn't have a closed form, and it's calculation in computationally prohibitive

2) It is not clear how to generate random variables

3) The implementation with mean parameter (for regression) does not exist or does not work (nominal mean is not read mean)

Thus the question is:

Does anybody have worked/implemented a functional implementation for any of these robust count functions? With likelihood calculation and random number generation process?



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