Bayesian Survival Analysis with PyMC: Modelling Customer Churn

The approach you've described for handling censored data in a survival analysis model using PyMC3 leverages the pm.Potential function to incorporate partial information about observations that are not fully observed. This method allows us to include censored data points in our likelihood calculation without needing to specify their exact outcome, which is crucial when dealing with right-censored or interval-censored data.

Here's a more detailed breakdown of how this works:

1. Understanding Censoring

• Right-Censoring: This occurs when the event of interest (e.g., customer churn) has not occurred by the end of the observation period, but we know it will happen at some point in the future.
• Interval-Censoring: This is more complex and involves knowing that an event happened within a specific time interval.

2. Gumbel Distribution as a Transformation

The Gumbel distribution is used here because it provides a convenient transformation of the Weibull distribution, which is commonly used in survival analysis for its flexibility in modeling different types of hazard rates (increasing, decreasing, or constant).

• The relationship between Weibull and Gumbel distributions: [ Y = \log T

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