Question about ppc and waic

Questions
1

I have read arviz.plot_ppc and pymc3.waic(although it is out-of-date).
I still cannot understand the usage of ppc, and this is my code.

    r_CH4_obs = r_2 + r_3 + r_4
    r_CO_obs = - r_3 - r_4 + r_1
    r_CO2_obs = - r_2 + r_4 - r_1
    ##Likelihood function
    r_CH4_likehood = pm.Normal('r_CH4_likehood',mu = r_CH4_obs, sd = sigma, observed = r0_CH4)
    r_CO_likehood = pm.Normal('r_CO_likehood',mu = r_CO_obs, sd = sigma, observed = r0_CO)
    r_CO2_likehood = pm.Normal('r_CO2_likehood',mu = r_CO2_obs, sd = sigma, observed = r0_CO2)

Here is my likelihood.

from scipy import optimize
with Tk_PL_ab_3478:
    map_estimate = pm.find_MAP()
    print(map_estimate)
    step = pm.NUTS()
    #prior = pm.sample_prior_predictive()
    trace_Tk_PL_ab_3478 = pm.sample(draws = 10000, tune = 10000, cores = 2, start = map_estimate, step = step)
    #posterior_predictive = pm.sample_posterior_predictive(trace_PL_in_134)
    prior_check = pm.sample_prior_predictive(samples = 500)
    ppc = pm.sample_posterior_predictive(trace_Tk_PL_ab_3478, var_names=["r_CH4_likehood","r_CO_likehood","r_CO2_likehood"])

And here is my sampling codes.

import arviz as az
az.plot_ppc(Tk_PL_ab_3478, var_names=["r_CH4_likehood","r_CO_likehood","r_CO2_likehood"],group ={'posterior'})

When I use plot_ppc,

ppc
ppc1370×286 74.9 KB

TypeError: Data must include log_likelihood in sample_stats occurred.

How can I deal with my codes?

Another question is about waic, used for model comparison. But in this case, I cannot run waic due to multi-likelihood. How can I use waic and loo with multi-likelihood?

waic
waic1122×467 197 KB

Finally, in old version of pymc3, model comparsion method like dic is availble but now I cannot use it. Any other model comparison methods, like Baysian factors? or anything else?

Thank you!

2

For insight on how to calculate WAIC and on how to deal with multiple likelihoods, I’d refer you to this really great answer by @OriolAbril.

3

I has read the answer, but it seems that I cannot understand the transfer from pymc3 to arviz, as a result of which, I cannot make WAIC sense.