ajtulloch

I think the mathematical concept that you are looking for is that of the dual space. Essentially if you have a vector space V, you can construct a dual space V* where the elements of the dual space are functions taking elements of V to the underlying field F, and under certain conditions these spaces are isomorphic (the same) - so there is a 1:1 correspondence between elements of the vector space and the functions in the dual space.

One way to view this formula is to use the fact that the Beta distribution is a conjugate prior for the binomial distribution.

Essentially if you have a Beta(a, b) prior then your prior mean is a/(a+b) and after observing n samples from a Bernoulli distribution that are all positive, your posterior is Beta(a+n, b) with posterior mean (a+n)/(a+n+b). So in your example you effectively have a Beta(0, x) prior and x (“suspicious”/“gullible”) is directly interpreted as the strength of your prior!

TF32 is not IEEE-754 float32, it is a reduced precision format designed for machine learning usecases. The correct specsheet number for FP32 (and FP64 which is the relevant precision here) throughput on H100 is more like 60TFLOP/s, so your number is off by roughly an order of magnitude.