Prior on real<lower=0,upper=1> with half mass in 0

Modeling
1

Greetings,

I am trying to implement Joint Species Models where the variance covariance of regression coefficients is informed by a correlation matrix derived from species phylogenies. One parameter that needs to be estimated is

real<lower=0,upper=1> rho;

which measures the strength of the phylogenetic signal. Ovaskainen et al. in their software HMSC https://www.helsinki.fi/en/researchgroups/statistical-ecology/hmsc use for this parameter the following prior:
with probability 0.5, rho = 0,
with probability 0.5, rho ~ Uniform(0,1).

the idea behind this is to allow rho to be zero for the case when phylogeny does not influence parameter estimates.

Is there a way to define a prior in Stan that will behave similarly?
I have tried a beta with lots of mass near zero but it is not quite the same.

2

Check out the mixture modelling section of the Stan User’s Guide.

3

ah!

So it was as simple as

target += log_sum_exp(log(0.5) + beta_lpdf(rho|1, 1000), log(0.5) +  beta_lpdf(rho|1, 1));

thank you!

1 Like
4

Actually, now that I think about it you should look at the section on zero inflation, which will show you how to use a conditional and avoid the beta_lpdf(rho|1, 1000) bit (which I presume was your hack to convey certainty of a value at zero).

5

Also, this bit is going to be constant regardless of rho, so you can compute it once in the transformed data section and just add it here.