Capstone projects

Capstone philosophy

A Bayesian capstone should not be judged only by whether a model runs. A strong project must show:

  • a coherent scientific question;
  • defensible prior design;
  • a justified computational strategy;
  • substantive diagnostics;
  • predictive or decision-relevant conclusions;
  • reproducible code and narrative.

Standard deliverables

Every project should include:

  1. A two-to-four page proposal.
  2. A reproducible code repository or Quarto report.
  3. Prior predictive checks before final fitting.
  4. Posterior diagnostics and model criticism.
  5. Sensitivity analysis.
  6. A final report with uncertainty-aware conclusions.

Reusable templates are provided at:

Project 1: hierarchical Bayesian regression on grouped data

Question. How much variation exists within and between groups, and when does partial pooling improve predictive performance?

Suggested data. Education, health, ecological, or sports data with natural grouping.

Core model.

  • varying intercepts;
  • varying slopes;
  • alternative hyperpriors for group-level scales.

Required analysis.

  • compare complete pooling, no pooling, and partial pooling;
  • interpret shrinkage;
  • study centered versus non-centered parameterizations;
  • evaluate predictive performance with PSIS-LOO.

Project 2: Bayesian hidden Markov model for longitudinal behavior

Question. Can latent behavioral states explain irregular longitudinal observations?

Suggested data. Animal movement, user engagement, wearable activity, or panel response data.

Core model.

  • hidden state transition matrix;
  • emission model appropriate to the measurement scale;
  • forward-backward recursions or Stan-compatible marginalization where feasible.

Required analysis.

  • derive state-update logic;
  • fit the model and interpret transition probabilities;
  • diagnose label-switching or weak identifiability;
  • compare with simpler non-HMM alternatives.

Project 3: Dirichlet-Multinomial model for compositional counts

Question. How do prior concentration and overdispersion affect inference for compositional count data?

Suggested data. Microbiome, topic counts, vote shares, or ecological composition.

Core model.

  • multinomial likelihood;
  • Dirichlet prior or hierarchical extension;
  • optional covariate-dependent composition model.

Required analysis.

  • derive posterior and posterior predictive forms where conjugacy applies;
  • study prior concentration sensitivity;
  • compare multinomial versus Dirichlet-multinomial fit.

Project 4: Bayesian Logistic regression with prior sensitivity

Question. How sensitive are posterior effect estimates and decisions to prior choices in binary outcome modeling?

Suggested data. Clinical outcomes, approval decisions, churn, or admissions data.

Core model.

  • logistic regression with weakly informative Gaussian or Student-\(t\) priors;
  • optional hierarchical extension.

Required analysis.

  • compare at least three prior families or scales;
  • evaluate calibration and predictive metrics;
  • discuss separation and regularization.

Project 5: Gaussian process regression

Question. How do kernel assumptions shape posterior uncertainty and predictive smoothness?

Suggested data. Time-indexed or spatially indexed smooth response data.

Core model.

  • GP prior with squared exponential, Mat{'e}rn, or periodic kernels;
  • hyperpriors on length-scale and marginal variance.

Required analysis.

  • derive the conditional posterior predictive mean and covariance;
  • study kernel sensitivity;
  • diagnose extrapolation failure and computational scaling.

Project 6: mixture model and label switching study

Question. What inferential pathologies emerge in finite mixtures, and how can they be handled?

Suggested data. Height mixtures, gene expression, image features, or income subpopulations.

Core model.

  • finite Gaussian mixture or latent class model;
  • symmetric versus asymmetric priors on components.

Required analysis.

  • document label switching explicitly;
  • compare identifiable summaries and relabeling strategies;
  • discuss posterior multimodality and prior influence.

Project 7: HMC diagnostics case study

Question. What do HMC pathologies reveal about model geometry?

Suggested data. Any hierarchical or weakly identified model with a known funnel or curvature issue.

Core model.

  • centered and non-centered versions;
  • progressively tuned adapt_delta and max_treedepth.

Required analysis.

  • compare divergences, ESS, \(\hat{R}\), and E-BFMI;
  • interpret geometry rather than merely increasing tuning parameters;
  • propose model redesigns and justify them.

Evaluation rubric

Criterion Weight What earns a high score
Scientific framing 15 Clear question, relevant data, explicit assumptions
Prior design 15 Thoughtful and justified prior specification
Computation 20 Stable implementation and well-explained algorithms
Diagnostics 20 Deep use of PPC, chain diagnostics, and sensitivity
Interpretation 20 Careful uncertainty communication and substantive insight
Reproducibility 10 Organized code, documented environment, clear report
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