Use prior distributions in calculating kernel score

[ArtPoon]

Prior distributions specified as strings in JSON, references to scipy.stats objects.

[ArtPoon]

scipy.stats distributions are bloody confusing and the documentation is absolute garbage difficult to comprehend.

• lognorm(shape, scale=x). For some reason I have had no success in specifying shape with a keyword. Based on this StackOverflow post, this first positional argument seems to correspond to sdlog. Thus, setting it to a very small value (0.0001) gives you a tight distribution around the mean (scale). Setting lognorm(0.5, scale=10000) gives an IQR of about 7000 to 15,000, and a 95% CI of about 4000 to 27,000. lognorm(1.0, scale=0.01) gives an IQR of about 0.005 to 0.02 and a 95% CI of about 0.001 to .07. Note that loc shifts the distribution like any other continuous distribution.
• norm(loc, scale). This has been more straightforward. loc is simply the offset that determines the mean and scale is the standard deviation.
• uniform(loc, scale). This is where the reuse of keyword arguments gets a bit obtuse. loc is the lower limit and scale is the range. Thus, uniform(10, 20) samples points uniformly from the range (10, 30).
• beta(alpha, beta). alpha and beta are positional arguments. loc and scale can be used to shift and rescale the distribution, respectively.