Help with fitting Gamma Distribution

Hi all,
New to pymc3 so thanks in advance for your patience.

I have a Poisson process that gives me the following distribution.
I would like to fit a gamma distribution and use the distributions of the alpha and beta parameters.

I can get the alpha and beta parameters from but would like the distributions of these parameters.

Any advice on how to respecify this model?

Using the parameterizations for gamma here:

My model:

model = pm.Model()

with model:
# Prior distribution for mu.
mu = pm.Gamma('mu', alpha=100, beta=1.0/5)

# Prior distribution for sigma
sigma = pm.Exponential('sigma', 100.0)

# Parametrization for the (alpha) shape parameter.
alpha =  mu**2/sigma**2

# Parametrization for the scale parameter.
beta = mu/sigma**2  

y_obs = pm.Gamma('y_obs', alpha=alpha, beta=beta, observed=df['bw'].values)

trace = pm.sample(draws=2000)


ValueError: Bad initial energy: inf. The model might be misspecified.

May be it is due to the division by sigma which has an exponential prior and during the sampling it may sample 0s (which leads to division by 0 --> inf).

Instead of Exponential try using an prior that behave according to the expected behavior.

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The main problem is that the Gamma distribution can only have positive observed values, that is no observed can be equal to zero. I suggest you just change the values of the observed from 0 to 1e-3. That, along with what @Nadheesh said about the exponential having is most likely value equal to zero, should help you.

Thanks! I realize I used a 1e-4 offset in my scipy implementation and forgot to apply that in my model above!

Thanks all for the feedback above. for zero values, I added 1e-4.

Here’s the working model:

model = pm.Model()

with model: 

# alpha
alpha = pm.Exponential('alpha', 10)

# beta
beta = pm.Exponential('beta', 100)

g = pm.Gamma('g', alpha=alpha, beta=beta, observed=bw)
trace = pm.sample(2000)
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