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PyMC3 has excellent functionality for dealing with Bayesian regressions, so I've been trying to leverage that to run a Bayesian Gamma Regression using PyMC3 where the likelihood would be Gamma.

From what I understand, running any sort of Bayesian Regression in PyMC3 requires the pymc3.glm.GLM() function, which takes in a model formula in Patsy form (e.g. y ~ x_1 + x_2 + ... + x_m), the dataframe, and a distribution.

However, the issue is that the pymc3.glm.GLM() function requires a pymc3..families object (https://github.com/pymc-devs/pymc3/blob/master/pymc3/glm/families.py) for the distribution. But the Gamma distribution doesn't show up as one of the families built into the package so I'm stuck. Or is the Gamma function family hidden somewhere? Would appreciate any help in this matter!

For context: I have a dataframe of features [x_1, x_2, ..., x_m] (call it X) and a target variable (call it y). This is the code I have prepared so far, but just need to figure out how to get the Gamma distribution in as my likelihood.

import pymc3 as pm

# Combine X and y into a single dataframe
patsy_DF = X
patsy_DF['y'] = y

# Get Patsy Formula 
all_columns = "+".join(X.columns)
patsy_formula = "y~" + all_columns

# Instantiate model
model = pm.Model()

# Construct Model
with model:
    # Fit Bayesian Gamma Regression
    pm.glm.GLM(patsy_formula, df_dummied, family=pm.families.Gamma())
        # !!! ... but pm.families.Gamma() doesn't exist ... !!!

    # Get MAP Estimate and Trace
    map_estimate = pm.find_MAP(model=model)
    trace = pm.sample(draws=2000, chains=3, start = map_estimate)

# Get regression results summary (coefficient estimates, 
pm.summary(trace).round(3)
quant_fin
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  • Correct, the `GLM` function doesn't have implemented support for gamma distribution. You'll have to explicitly write out the gamma regression model. – merv Feb 10 '19 at 17:45
  • It may also be worth noting that R has better support for these types of models. For example, the `rstanarm` package has [an example of Bayesian Gamma Regression](https://cran.r-project.org/web/packages/rstanarm/vignettes/continuous.html#gamma-regression-example). Personally, I use PyMC3 or Stan when I need the flexibility of arbitrarily complex hierarchical models, but tend to defer back to R when doing more standard regression analyses. – merv Feb 14 '19 at 16:11

0 Answers0