Log of modified_bessel_first_kind

[nikunj410]

I am working on a custom pdf that uses {\displaystyle {}_{1}F_{1}(a,2a,x)} that can be represented in terms of Bessel Functions as follows

{\displaystyle {}_{1}F_{1}(a,2a,x)=e^{x/2}\,{}_{0}F_{1}\left(;a+{\tfrac {1}{2}};{\tfrac {x^{2}}{16}}\right)=e^{x/2}\left({\tfrac {x}{4}}\right)^{1/2-a}\Gamma \left(a+{\tfrac {1}{2}}\right)I_{a-1/2}\left({\tfrac {x}{2}}\right).}

The current Stan implementation of the Bessel function does not accept non-integer orders.
Ideally, I would have used the {\displaystyle {}_{1}F_{1}} directly, but the function is currently not available in stan either.

Is there a possibility of having this function for users in the near future?

Confluent hypergeometric functions to estimate population size and detection probability from spatially replicated counts

I am modeling spatial population dynamics which consist of two layers. The inner layer is the population abundance of the species which is modeled using an a spatial population dynamics model. The outer layer is the observation process. Here is the brief description of the model Assuming count data y_{x,t,j}\sim \text{Binomial}(n_{x,t,j}, \theta), were x is the patch location, t is time, j is the replicate sampling ID, and \theta is the detection probability. We assume \theta \sim \text{Beta…