Positive samples

Questions
1

Is there a way where I can ensure that the samples drawn from the distribution belong to positive side only? For example,

    mu1 = 3
    sd1 = 1
    mu2 = 1
    sd2=0.5
    param1 = pm.Normal('param1_{0}'.format(index), mu=mu1, sd=sd1)
    param2 = pm.Normal('param2_{0}'.format(index), mu=mu1, sd=sd1)
    param3 = pm.Normal('param3_{0}'.format(index), mu=mu2, sd=sd2)
    param4 = pm.Normal('param4_{0}'.format(index), mu=mu2, sd=sd2)
    offset = pm.Normal('offset_{0}'.format(index), mu=mu2, sd=sd2)
    
# Likelihood
alpha = tt.abs_(param1*ON_shared + param2*OFF_shared + offset)
beta = tt.abs_(param3*ON_shared + param4*OFF_shared)
mu = pm.math.log(alpha)
s = tt.abs_(tt.power(beta, -1))

final = pm.Logistic('final_{0}'.format(index), mu=mu, s=s, observed=pm.math.log(data))

    step =  pm.NUTS([param1, param2, param3, param4, offset])
trace = pm.sample(trace_length, step = step, tune = 500)
print(pm.summary(trace))

Generally the summary after few iteration leads to the params having negative means. I want to avoid that by specifying explicitly not to sample negative values. Can this be done?

2

This is usually done by restricting your prior, for example use a HalfNormal instead of Normal, or use a pm.Bound to bound your distribution and create a bounded random variable.