42 - Prior predictive distribution for Gamma prior to Poisson likelihood

This video provides a derivation of the prior predictive distribution - a negative binomial - for when there is a Gamma prior to a Poisson likelihood.
If you are interested in seeing more of the material on Bayesian statistics, arranged into a playlist, please visit: • Bayesian statistics: a... Unfortunately, Ox Educ is no more. Don't fret however as a whole load of new youtube videos are coming soon, along with a book that accompanies the series: www.amazon.co.uk/gp/product/1... Alternatively, for more information on this video series and Bayesian inference in general, visit: ben-lambert.com/bayesian-lect... For more information on econometrics and Bayesian statistics, see: ben-lambert.com/

[@Johnnyboycurtis]

If you derived the posterior from the last lecture, for a new predictive value, you would have p(x_new | lambda) p(lambda| x). This would use the posterior vs just a prior, which is generally what you want/need.

[@SpartacanUsuals]

Hi, thanks for your comment - yes there are two ways to derive the posterior predictive density. Best, Ben

[@shimaasadk9830]

thanks alot for this video it was very useful for me .
could you help me in other types of prior like reference prior and matching prior

[@wenqian4926]

Thanks a lot！

[@jrippee05]

I could be wrong but that first term that you called the likelihood doesn't look like the likelihood.

[@biswaspankaj286]

that is not the likelihood you are correct