Model comment counts and detect anomalies
Company: Meta
Role: Data Scientist
Category: Statistics & Math
Difficulty: hard
Interview Round: Onsite
Comment counts per post are heavy-tailed. You observe mean=4 and variance=50 at the post-day level. (a) Test whether a Poisson model is appropriate; if not, propose a negative binomial or discrete lognormal and outline parameter estimation. (b) Compare fits via likelihood ratio or Vuong tests and report which tail behavior each captures. (c) Define robust monitoring metrics (e.g., trimmed mean, P50, Gini) and control limits to detect manipulation (e.g., purchased comments). (d) Given a sudden 3× increase in the 99th percentile but stable P50, propose a rule to trigger investigation while minimizing false alarms.
Overview: This question evaluates competency in statistical modeling of heavy-tailed count data, model selection and comparison, and the formulation of robust monitoring metrics for anomaly detection, testing both theoretical understanding and applied data-science skills.
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