# How to use the posterior distribution of one model as a prior distribution for another model

**URL:** <https://discourse.pymc.io/t/how-to-use-the-posterior-distribution-of-one-model-as-a-prior-distribution-for-another-model/13956>\
**Category:** General\
**Created:** [March 7, 2024, 8:48am UTC](https://discourse.pymc.io/t/how-to-use-the-posterior-distribution-of-one-model-as-a-prior-distribution-for-another-model/13956 "2024-03-07T08:48:37Z")\
**Posts on this page:** 1\
**Showing post:** 14

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**Author:** ![perrette](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/perrette/32/4637_2.png) [@perrette](https://discourse.pymc.io/u/perrette)\
**Post date:** [April 4, 2024, 12:12pm UTC](https://discourse.pymc.io/t/how-to-use-the-posterior-distribution-of-one-model-as-a-prior-distribution-for-another-model/13956/14 "2024-04-04T12:12:20Z")

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FYI I added additional thoughts to my original thread: [How best to use a posterior sample as a prior for a future integration in another model? - #14 by perrette](https://discourse.pymc.io/t/how-best-to-use-a-posterior-sample-as-a-prior-for-a-future-integration-in-another-model/8650/14)

Basically, I take inspiration from two articles on copulas ([here](https://twiecki.io/blog/2018/05/03/copulas/) and [there](https://www.pymc.io/projects/examples/en/latest/howto/copula-estimation.html)), and suggest to a) transform the marginal posterior distributions from modelA into normal distributions, b) model the normalized parameters as a MvNormal distribution (and transform back) in modelB. In the case of a long-tailed LogNormal distribution, this is simple (it involves shifting and taking the logarithm), and in the general case it is more complicated but doable provided a parameterized distribution can fit the marginal (and the copula example can be applied: transform to uniform to normal and back with cdf and inverse cdf).

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