Designing a Bayesian Classifier for Case Analysis

# Designing a Bayesian Classifier for Case Analysis The preserved interview report says only that a Bayesian classifier was implemented and then exercised on different cases. For this practice discussion, explicitly assume a binary decision with labeled historical examples, sometimes-missing evidence, changeable priors, and unequal error costs. These are working assumptions for the exercise, not facts supplied by the source. Explain how the classifier is estimated, how a posterior becomes a decision, and how you would detect failed assumptions. ### Constraints & Assumptions - The practice target is binary and its labels may be imbalanced. - Features may be categorical or discretized numeric observations. - Missingness is not automatically uninformative; state whether the fact that a feature is absent carries evidence. - False positives and false negatives may have different costs. - Do not assume conditional independence without stating and testing it. ### Clarifying Questions to Ask - What inputs, labels, and outputs did the original exercise define? - Is the required output a calibrated probability, a class label, or both? - Which error is more costly, and may the threshold vary by case? - Can priors or missingness patterns change between training and deployment? ### Part 1 — Model and estimation Describe the prior, likelihood, posterior, smoothing, and any conditional-independence assumption used in the practice model. #### What This Part Should Cover - A mathematically correct application of Bayes' rule - A defensible likelihood model for each stated feature type - Smoothing for unseen values - An explicit treatment of informative versus uninformative missingness ### Part 2 — Decisions for changing cases Explain how a changed prior, stronger or contradictory evidence, missing evidence, and asymmetric error costs affect the posterior or decision threshold. #### What This Part Should Cover - Posterior odds or log-odds reasoning - Evidence that raises or lowers the score - Cost-sensitive threshold selection - Separation of estimated probability from the final action ### Part 3 — Validation and failure analysis Propose checks for discrimination, calibration, drift, and violations of the chosen likelihood assumptions. #### What This Part Should Cover - Metrics appropriate for imbalance and decision cost - Calibration diagnostics rather than accuracy alone - Slice analysis for correlated features and missingness patterns - Monitoring for prior and likelihood drift ```hint Separate preserved facts from practice assumptions State the model and missingness assumptions first, derive the posterior second, and apply a decision threshold only after the probability is available. ``` ### What a Strong Answer Covers - A source-bounded explanation that labels every added case dimension as an assumption - A coherent chain from data assumptions to posterior probabilities and decisions - Correct handling of unseen values and informative missingness - Evaluation that includes calibration, operating points, and deployment drift ### Follow-up Questions 1. How would you update predictions if the deployment prior changes but class-conditional likelihoods remain stable? 2. What symptoms suggest correlated features are being double-counted? 3. How would you model the fact that a feature is missing when missingness itself predicts the class?