I have two probability density functions such that 1 = ∫ a b pdf 1...
I have two probability density functions such that
which represent the same underlying process (i.e. obtained from different measurements).
I am more confident in the values of for values of where and more confident in values of where . Is it possible to combine these pdfs to one while keeping this "confidence" scheme in mind? (Assuming that I have only access to the pdfs - not an assumption on the underlying process).
I can definitely "average/combine" the pdfs as a whole, but is it possible to be more confident in a section? The value of a range of the pdf is really meaningless without knowing the rest of the distribution, so I'm unsure if I can really proceed post-measurement.