nu > 0 about conjugatepriors.jl

[krylea]

(I should clarify this is referring to the NormalGamma distribution)

[mschauer]

Hm, with nu = 0, this is not a proper distribution and one cannot sample anymore from it, compare

ConjugatePriors.jl/src/normalgamma.jl

Line 48 in 8e3a6a7

mu = rand(Normal(d.mu, sqrt(1./(tau2*d.nu))))

The originating package Distribution.jl in general only supports proper distributions. As priors, improper distributions still make sense. What to do?

[sourish-cmi]

If you choose nu=0 the marginal prior distribution for location parameter for the Normal Gamma model would be Cauchy distribution. This is a proper distribution for which mean and variance do not exist. However, because prior is a proper distribution, the posterior distribution turns out to be just fine. That is why even if you use nu=0 the simulation works fine. It is not an accident. You can look into Andrew Gelman's book. He gave a beautiful explanation about this (Chapter 2).

Ref: Bayesian Data Analysis (By Andrew Gelman and etal.) Second Ed.

https://www.amazon.in/Bayesian-Analysis-Chapman-Statistical-Science/dp/1439840954/ref=sr_1_1?crid=20GZF006GVZ5E&keywords=bayesian+data+analysis+gelman&qid=1642527457&sprefix=bayesian+data+analysis+ge%2Caps%2C345&sr=8-1