Negative initial value for Gamma prior

Questions v5
1

I am following the Survival Analysis tutorial (with some of my own made up data)

coords = {"intervals": intervals}

with pm.Model(coords=coords) as model:
    lambda0 = pm.Gamma("lambda0", 0.1, 0.1, dims="intervals")

    beta = pm.Normal("beta", 0, sigma=0.001)

    lambda_ = pm.Deterministic("lambda_", T.outer(T.exp(beta * np.log(traindf.days_since_last_order+0.01)), lambda0))
    mu = pm.Deterministic("mu", exposure * lambda_)

    obs = pm.Poisson("obs", mu, observed=death)

However I get the error:

Logp initial evaluation results:
{'lambda0': -18.2, 'beta': -59886.4, 'obs': -inf}

I’m not sure why would a Gamma prior (my lambda0) obtain a negative value, if a Gamma distribution is strictly non-negative?

I’m probably missing something obvious…

Thanks for the help in advance.

2

As the message says, this is reporting the log probability (logp) of the initial value for beta under your specified prior

My guess is that np.log(traindf.days_since_last_order+0.01)) is allowed to be negative (indeed you add 0.01, so i guess there are zeros and log(0.01) < 0. So mu is negative, and the Poisson is undefined.

You should use pm.math.exp(mu) instead of just mu in the Possion. Reading a bit more carefully, I see you exponentiation inside the outer product, but it’s probably safer to work entirely in the latent space until the last moment

3

Not sure how I missed that…as I said, I’m missing something obvious, thanks :slight_smile: Maybe it is because I expected Pymc to return the initial values that caused the problem, not the log-probabilities, but I should have read the message more carefully.

I don’t think mu is negative because I take the exponent of beta * np.log(traindf.days_since_last_order+0.01) and then the outer product with lambda0 which is also positive?

I hear you though about maybe keeping the transformations to the end, and staying in the latent space as far as possible.

4

You can try model.debug() to help track down why obs is getting impossible values. It could also be a problem in death

5

So it seems that initial parameters evaluate to a mu that is pretty much zero, and hence the error. I will play with better priors with prior predictive distribution, but to test the theory I simply added a small constant to mu and it fit perfectly.

And yes, model.debug(verbose=True) came in handy.

Thanks for the help!

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