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I'm looking for advice on how best to go about setting an informative prior for the Bayesian Lasso and BART (I'm applying these in R using the rjags and bartMachine packages)

I have 3 proteomics datasets, each measuring the same 123 proteins for patients and controls. I want to train a Bayesian model on dataset 2, using a prior distribution based on knowledge gained from dataset 1, and then test the performance of the Bayesian model in predicting patients from controls in dataset 3.

At the moment, I'm applying a ridge regression model to dataset 1, and obtaining the regression coefficients for all 123 proteins.

My initial idea is to try and use these regression coefficients to centre a prior on beta.

Could this work? Does anyone have any advice regarding creating an informed prior based on results from past experiments?

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    $\begingroup$ You may want to narrow this down somehow so that it isn't as open-ended. As is, people may feel that it is too broad to be answerable here. $\endgroup$
    – gung - Reinstate Monica
    Commented Jul 14, 2017 at 14:27
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    $\begingroup$ (Take this idea with a grain of salt because I haven't thought about it too carefully). For your new dataset 2, recenter the response using $X\beta$ where $\beta$ are the coefficients obtained from dataset 1, and then fit the usual lasso. Zeros in the lasso coefficients will indicate you can use the original ridge estimates, and non-zeros will indicate a non-zero additive term in the coefficient. $\endgroup$
    – Greenparker
    Commented Jul 14, 2017 at 15:46

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The posterior you get from the first regression fit will produce the prior for the next fit. Ridge is just a Bayes update, but of course you need to be mindful when choosing (or estimating) $\sigma $ and $\lambda.$ A normal-inverse gamma model can be used to update also the variance; but not sure how that works with $ \lambda. $ Look up Bayesian Lasso.... Likely you would need to use a Gibbs sampler for a full Bayes solution, but this should be fairly straight forward for the ridge case.

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