Unexplained NAN In Jupiter Notebook

Questions
1

Hello everyone, I’m having a problem with initializing my model in Jupyter notebooks. I am building a simple model for modeling the spreading of COVID-19, and am using a dataset from The Covid Tracking Project. I have the following model:

def sampleMCMC(data, pop):

# splitting data into infections and time as numpy arrays
dataDeath = data['death'].to_numpy()
time = np.linspace(0,len(data)-1, len(data))

# establishing model
with pm.Model() as model:
    
    # create population number priors
    error = pm.Normal('error', mu=0, sigma=pop/1000)
    i0 = pm.Poisson('i0', mu=pop/100 + error)
    s0 = pm.Deterministic('s0', pop - i0)
    
    # create starting values based on data, does not inform inference but starts at a reasonable value
    # start beta as average of positive-to-test and positive-to-population
    beta_start = float((data['positive'].iloc[-1]/data['total'].iloc[-1] + data['positive'].iloc[-1]/pop) / 2)
    # start gamma as average of recovered-to-positive and recovered-to-population
    gamma_start = float((data['recovered'].iloc[-1]/data['total'].iloc[-1] + data['recovered'].iloc[-1]/pop) / 2)
    # start rho as average of death-to-positive and death-to-population
    rho_start = float((data['death'].iloc[-1]/data['positive'].iloc[-1] + data['death'].iloc[-1]/pop) / 2)
    
    # creating priors for beta, gamma, and rho
    beta = pm.InverseGamma('beta', mu=.05, sigma=.5, testval=beta_start)
    gamma = pm.InverseGamma('gamma', mu=.047, sigma=.5, testval=gamma_start)
    rho = pm.TruncatedNormal('rho', mu=.036, sigma=.1, lower=0, upper=1, testval=rho_start)

    # create number of removed based on analytic solution and above parameters
    sirRem = pm.Deterministic('sirRem',
        pop - ((s0 + i0)**(beta/(beta - gamma)))*
        (s0 + i0*tt.exp(time*(beta - gamma)))**(-gamma/(beta - gamma)))
    # create number of deaths as a fraction of number of removed
    sirDeath = pm.Deterministic('sirDeath', rho*sirRem)
    
    # create variance prior
    sigma = pm.HalfCauchy('sigma', beta=4)
    
    # create likelihood with modelled counts and observed counts
    obsDeath = pm.TruncatedNormal('obsDeath', mu=sirDeath, sigma=sigma,
                                 lower=0, upper=pop, observed=dataDeath)

    # specifying model conditions
    step=pm.NUTS(target_accept=.99)
    start=pm.find_MAP()
    init="advi+adapt_diag"
    
    print(model.check_test_point())
    
    # execute sampling
    model_trace = pm.sample(draws=500, tune=500, step=step, start=start, init=init, chains=8)
    
    # plot results
    pm.plot_trace(model_trace, var_names=('i0','beta','gamma','rho','sigma'))
    pm.plot_posterior(model_trace, var_names=('i0','beta','gamma','rho','sigma'))

# return posterior samples and other information
return model_trace

This is the most recent of many many many iterations, and I’m quite happy with how it’s performing on data for about half the states in the US. For many of the other states, however, I get stuck in the following place:

Screen Shot 2020-07-24 at 3.54.25 PM
Screen Shot 2020-07-24 at 3.54.25 PM706×198 23.2 KB

I find this error really weird because none of my variables themselves are nan, but I get that “logp = nan” next to the progress bar. I’m at a loss for why this doesn’t work for some states. It works like a charm for others.

Any help would be greatly appreciated!