Hierarchical Binomial with weights to priors

Questions
1

I’m trying to model a proportion statistic for each area. My input data frame has:

var1: total of times a sampled person has said yes to a question for each area (num successes)
var2: total number of sampled person for each area (trial_sizes)

With the total of ~ 6400 rows, for each row I want an estimate of the expected proportion of people saying yes. My model is as follows:

with pm.Model() as model:
   u = pm.Uniform('u', lower=0.0, upper=1.0)
   log_v = pm.Exponential('log_v', lam=1.5)
   v = pm.Deterministic('v', tt.log(log_v))

   alpha = pm.Deterministic('alpha', u*v)
   beta = pm.Deterministic('beta', v*(1-u))
    
   p_output = pm.Beta("p_output", alpha=alpha, beta=beta, shape=prop_data.shape[0])

   r = pm.Binomial("r", n = use_data.trial_sizes.values,
                        p = p_output, 
                        observed = use_data.loc[:,var1].values)
trace = pm.sample(draws=5000, tune=2500, njobs=4)

I’m trying to incorporate weights to each p_output as the population sizes of each area is different, its effect on the global mean proportion would be different (i.e. high proportion in small areas has less effect than a high proportion in bigger areas). Is there a way in pyMC3 to incorporate this?

Many thanks,

2

I presume there is a difference between “population size” and “trial size;” and I also assume that you have a var3 which is “population size”. The easiest thing to do is use pm.Deterministic to take the population-weighted average

w = use_data.loc[:,var3].values
mean_prop = pm.Deterministic('mean_proportion', tt.sum(w*p_output)/tt.sum(w))
1 Like
3

Many thanks!