I would like to ask you questions about choosing non-informative prior of N.
(I decided to go first with non-informative prior of N since I thought non-informative should be a starting point in general...)
I realized N should be following discrete uniform distribution to do so, with two paremeters; a and b. (a for the smallest possible natural number, b the biggest possible natural number.)
Then I naively assumed a should be at least bigger than survey sample size n_a (1000) and the biggest ambulance attended overdoses (the vector of U_t).
Then for b, I just set it two times of the real value of N as b just because I have no better idea...
Q1.
I would like to ask you if this approach looks fine.
I read from the the Gelman's book that a different parameterization can lead different prior condition (one may believe a prior is non-informative but it can be actually super informative), but I guess it's not the case here...?
Q2.
In pymc3, I can actually implement the uniform(a,b), where a is the maximum number of our data set, and b is 20000 (two times of the real value of N).
But in JAGS, I feel like it's not possible to set a as such with default function?
what I found in JAGS is dcat() function, with an argument p as a vector of probability.
I assume that will give us discrete uniform which always starts from 0. (0,1,2,3, ... , b as support.)
If I want to construct such discrete uniform with nonzero a, should I make my own function?
Dear Prof. Paul Gustafson,
I hope you are doing well.
I would like to ask you questions about choosing non-informative prior of N. (I decided to go first with non-informative prior of N since I thought non-informative should be a starting point in general...)
I realized N should be following discrete uniform distribution to do so, with two paremeters; a and b. (a for the smallest possible natural number, b the biggest possible natural number.) Then I naively assumed a should be at least bigger than survey sample size n_a (1000) and the biggest ambulance attended overdoses (the vector of U_t). Then for b, I just set it two times of the real value of N as b just because I have no better idea...
Q1. I would like to ask you if this approach looks fine. I read from the the Gelman's book that a different parameterization can lead different prior condition (one may believe a prior is non-informative but it can be actually super informative), but I guess it's not the case here...?
Q2. In pymc3, I can actually implement the uniform(a,b), where a is the maximum number of our data set, and b is 20000 (two times of the real value of N). But in JAGS, I feel like it's not possible to set a as such with default function? what I found in JAGS is dcat() function, with an argument p as a vector of probability. I assume that will give us discrete uniform which always starts from 0. (0,1,2,3, ... , b as support.) If I want to construct such discrete uniform with nonzero a, should I make my own function?
Thanks in advance!
Best, Tom