Using probability scores from a random forest

I've the following problem. I've a data set that tries to predict whether a given buy event will happen or not (0/1) when a customer sees a certain product, and I've features created for both the customer and the product (I'm excluding the nature of the data set and related matters to keep things simple). I build a classifier (R's random Forest) and conclude the following.

             Actual
0   1
Predicted
0   0.97 0.03
1   0.13 0.87


Separately, I've the priors for the probability of a given product being sold. i.e. number of customers buying a certain product divided by number of customers who got to view that product. My question is two fold

1) When I run the model for a given customer and product combination, I get a probability estimate of buy (given by predict function with type="prob"). How do I blend this with the prior knowledge of the sell through rate of the product? 2) Is this even the right approach to take?

• To keep things simple I would just add the sell through rate of the product to your X variables. Bayesian updating seems to be what you're asking about, but that would only make sense if you were continually retraining your forest to constantly incorporate new data. Even then I don't know if random forest and bayesian updating really work well together. Oct 20, 2014 at 14:00
• Why not build a Bayesian logistic regression model, where you can incorporate the prior information into the likelihood function? The prior probabilities can be specified using beta distributions for example and that's basically adding a few successes or failures in the training set. However, there's a lack of way of incorporating that into a random forest model. A weighted blending might be the way to go. Feb 16, 2017 at 17:43