Am I correct in understanding there is no way to be using actual data as a prior rather than choosing a distribution that best fits that data ?
It seems like an additional step that adds inaccuracies while it might not be necessary?
Or am I missing something (fundamental) here.
Im currently struggling to model my historical data so that I can use it as an informative prior and this got me wondering if I would be able to use the actual data rather than some fitted distribution.
You can see here: Updating priors — PyMC example gallery
And here:
Out of the two I’d trust the second much more.
In addition to @twiecki 's comment, just one addition: if I understand you correctly, you are planning to model something, and you have historical data to inform some of this model’s parameters – is that right? In that case, perhaps the best way to go would be to model the historical data and the new data jointly in a single model, rather than fitting the historical data and then summarising its results in a prior for a second model. The main drawback of doing this could be a hit on speed, as you’re now fitting a larger model. But that would avoid the difficulties of having to summarise the posterior of a previous model to be a prior for the second.