Projectpred, BMA, variable selection and joint posterior probabilities

Apologies if this is the wrong forum.

I’m interested in using Aki Vehtari’s projectpred (Projection predictive variable selection – A review and recommendations for the practicing statistician) for variable selection, but I’m particularly interested in the joint posterior probabilities (JPP) rather than the marginal posterior probabilities (MPP). Does anyone have any experience or ideas on whether this is possible? My use case is a very simple logistic regression (similar to the bodyfat example linked).

Thanks in advance,

Rich

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This is definitely the right forum - tagging @AlejandroCatalina who should know more (I personally unfortunately don’t know much about projpred).

Thanks @martinmodrak for tagging.

Can you elaborate your idea a bit more @datarichard ?

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Projpred is not providing marginal posterior probabilities. It’s providing the best projection mode for each model size (conditional how well the search thorugh the model space works). The model size selection is based on cross-validated log score.

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