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I'd like to combine Bayesian and non-parametric (e.g. XGBoost) models, with the goal of getting a probability distribution over my target variable rather than a point estimate. I have a prior, and I have some non-parametric models that produce reasonable results. My best guess is something like fit a simple Bayesian regression model and use the non-parametric model estimates as inputs.

Is there a more effective or more principled way to do this though?

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    $\begingroup$ Possibly bootstrapping? Could fit a variety of models on bootstrapped resamples of the data and report the distribution of predicted values. $\endgroup$
    – Arthur
    Commented Nov 17, 2022 at 18:35
  • $\begingroup$ Could you give us more details? What is the prior? $\endgroup$
    – Tim
    Commented Nov 17, 2022 at 18:58
  • $\begingroup$ as @Arthur suggested, if what you are after is a probability of the target distribution then just run bootstrap samples.That is a principled, simple way of getting a probability distribution. $\endgroup$
    – seanv507
    Commented Nov 17, 2022 at 21:12
  • $\begingroup$ What about this: proceedings.mlr.press/v22/kim12/kim12.pdf ? $\endgroup$
    – Karel Macek
    Commented Nov 18, 2022 at 16:16
  • $\begingroup$ If you're looking for a Bayesian version of tree models, your answer is BART. $\endgroup$
    – Durden
    Commented Mar 13 at 23:37

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