Further features for rhine-bayes

[turion]

Leftovers from https://github.com/turion/rhine/pull/186#issue-1371220322:

• [ ] Ornstein-Uhlenbeck
• [ ] Gamma process
• [ ] Poisson process

[reubenharry]

I implemented what I assume is a Bernoulli process-like thing using ClExcept (i.e. switching at random times from True to False), which seems to work ok. Not sure if that should be in the library too.

[turion]

I implemented what I assume is a Bernoulli process-like thing using ClExcept (i.e. switching at random times from True to False), which seems to work ok. Not sure if that should be in the library too.

That sounds great!

[turion]

Not sure anymore about Bernoulli processes. Isn't that just the same as constMCl $ bernoulli p? I.e. at every tick we throw a coin?

[turion]

Gamma process

Wikipedia says:

The process is a pure-jump increasing Lévy process with intensity measure ν ( x ) = γ x − 1 exp ⁡ ( − λ x ) , for all positive x x. Thus jumps whose size lies in the interval [ x , x + d x ) occur as a Poisson process with intensity ν ( x ) d x .

I'm surprised by the dx. I would have expected the intensity to be simply ν ( x ).

[reubenharry]

Ah, I meant a switching process (don't know the proper name) where a bool value flips its value at random points (but then stays at the same value until the next random point at which it flips).

[turion]

Ok, if the switching is memoryless, then this sounds a lot like a Poisson process where we throw an exception for every event. See https://github.com/turion/rhine/pull/218, it should be possible to implement it using the Poisson process from there, and standard exception throwing.