Is it right to use as a prior the output from another analysis with a larger dataset?

General
1

Hello.

If I want to fit an bayesian model to a small dataset… Can I first apply that model to a large dataset and use its output as prior for the small one?

For example I want to fit a regression model to see if smoking has an effect on cancer but I only have 30 observations.
What if I first apply the model to a public health service database with 1 million observations and use its output as the prior for my small experiment?

2

You can do that if you choose conjugate priors. If you don’t have a conjugate prior, then the result won’t be in closed form and you won’t be able to turn it into a prior.

The problem you will have with 1 million prior observations and 30 new observations is that the 30 new observations won’t do anything. The resulting inference will be what you get from the total 1,000,030 observations.

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