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Estimate unbiased ad scores with many reviewers

Last updated: Mar 29, 2026

Quick Overview

This question evaluates a candidate's skills in hierarchical and mixed-effects modeling, latent-variable estimation, debiasing rater severity and scale, model identifiability, and uncertainty quantification including BLUPs or Bayesian posterior inference.

  • Medium
  • Google
  • Statistics & Math
  • Data Scientist

Estimate unbiased ad scores with many reviewers

Company: Google

Role: Data Scientist

Category: Statistics & Math

Difficulty: Medium

Interview Round: Technical Screen

You have 1,000 ads and 100 reviewers; each reviewer rates 100 ads on a 1–10 scale with incomplete overlap. Specify a mixed-effects model to estimate latent ad quality while debiasing reviewer severity and scale, e.g., yij = μ + qi (ad effect) + bj (reviewer intercept) + εij, with optional reviewer-specific scale or slope. State identifiability constraints, justify which effects are fixed vs random, and describe how to obtain BLUPs or Bayesian posteriors with uncertainty. Address heteroskedasticity, missingness, and rater drift. Propose validation (leave-one-reviewer-out, posterior predictive checks, ICC) and a principled way to rank ads with uncertainty-aware intervals.

Quick Answer: This question evaluates a candidate's skills in hierarchical and mixed-effects modeling, latent-variable estimation, debiasing rater severity and scale, model identifiability, and uncertainty quantification including BLUPs or Bayesian posterior inference.

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|Home/Statistics & Math/Google

Estimate unbiased ad scores with many reviewers

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Google
Oct 13, 2025, 9:49 PM
MediumData ScientistTechnical ScreenStatistics & Math
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You have 1,000 ads and 100 reviewers; each reviewer rates 100 ads on a 1–10 scale with incomplete overlap. Specify a mixed-effects model to estimate latent ad quality while debiasing reviewer severity and scale, e.g., yij = μ + qi (ad effect) + bj (reviewer intercept) + εij, with optional reviewer-specific scale or slope. State identifiability constraints, justify which effects are fixed vs random, and describe how to obtain BLUPs or Bayesian posteriors with uncertainty. Address heteroskedasticity, missingness, and rater drift. Propose validation (leave-one-reviewer-out, posterior predictive checks, ICC) and a principled way to rank ads with uncertainty-aware intervals.

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