Build and evaluate donation propensity model

You are asked to build a model that maximizes the expected net revenue generated by solicitations. The cost structure is: reaching someone online costs $1 per person; attending the gala costs $100 per attendee, plus a fixed venue expense of $20,000. The outcomes are the probability that a person donates and the amount they give.

Tasks:

1. Propose either a two-stage model (conversion and donation amount) or a direct model of expected revenue. Describe the features, how you would handle sparse or categorical variables, what leakage risks arise, and how you would treat heavily skewed donation amounts (for example, log transforms or zero-truncated models).
2. Define the profit-optimized threshold policy for the online channel—solicit versus suppress—and the invitation policy for the gala, which has a capacity of 100. Show how predicted probabilities and amounts are converted into expected marginal profit and used to rank donors.
3. Explain calibration and why it matters when optimizing profit; choose a method (such as Platt scaling or isotonic regression) and an evaluation plot.
4. Describe how to evaluate a policy offline when historical assignments were not random. Include inverse propensity weighting or doubly robust estimators, along with the assumptions they require.
5. If you instead model uplift, or treatment effect, for the online campaign, define the objective, suitable metrics (such as Qini coefficient or uplift AUC), and how you would protect against targeting bias that deprives low-budget donors of engagement.

Overview: This question tests a data scientist's ability in profit-focused predictive modeling: conversion and donation-amount modeling, sparse and categorical feature handling, calibration and uplift estimation, and offline policy evaluation under selection bias.

See the full data scientist interview experience where this question appeared.