TL;DR
Bayesian Estimation with Conjugate Priors: A canonical quantitative trading interview question at intermediate difficulty. Commonly asked at Two Sigma, Citadel, DE Shaw, Jane Street, Point72.
By Valenke Exam Prep Team·Last updated 2026-06-01
intermediateStatistical Inference & Estimation
Bayesian Estimation with Conjugate Priors
Asked at: Two Sigma, Citadel, DE Shaw, Jane Street, Point72
Problem
A coin has unknown bias . Your prior is (mildly favoring a fair coin). You flip the coin 10 times and observe 7 heads.
(a) What is the posterior distribution of ?
(b) What is the Bayesian point estimate (posterior mean)?
(c) Compare this to the MLE. Why do they differ?
(d) Find a 90% credible interval for .
(e) After 1000 more flips, 680 are heads. Update the posterior. How has the prior's influence changed?
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