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Having the poisson gamma model: $$\lambda\sim Gamma(\alpha,\beta)$$ $$N|\lambda \sim Poiss(\lambda)$$

the expectation of N is $$E(N)=E(E(N|\lambda))=E(\lambda)=\frac{\alpha}{\beta}$$

Is there some literature, where I can learn, how to work with such concepts? E.g. what is $E(E(N\lambda))$?

Rafael
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  • One question. Do you want to learn how to treat with conditional expectations, or how to treat with Poisson processes? – kolobokish Oct 06 '19 at 13:54
  • I would be interested in how to treat with conditional expectations. In particular, the Poisson-Gamma model. – Rafael Oct 06 '19 at 14:09
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    I can recommend a book by Kingman "Poisson Processes". For conditional expectation there are tones of literature which contain conditional expectation. The most easy introduction I have seen was written "Elementary Stochastic Calculus" (by Thomas Mikosch). A good book you to look through would be the one by Taylor and Karlin, "An introduction to stochastic modelling". You may want to take a look at the following chapters ("Conditioning of random variable" and "Spatial Poisson processes" as far as I remember). – kolobokish Oct 06 '19 at 18:28
  • I would also like to mention my favorite lecture notes. A very thorough work by Amir Dembo named "Stochastic processes". – kolobokish Oct 06 '19 at 18:30
  • Thank you very much for your recommendations. – Rafael Oct 10 '19 at 19:55

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