Bayesian Statistics - Students seminar and Grades

Students seminar

List and names here.

Bayesian nonparametrics

  • Thomas S Ferguson. A Bayesian analysis of some nonparametric problems. The Annals of Statistics, pages 209–230, 1973.

  • Thomas S Ferguson. Prior distributions on spaces of probability measures. The Annals of Statistics, pages 615–629, 1974.

  • Jayaram Sethuraman. A constructive definition of Dirichlet priors. Statistica Sinica, pages 639–650, 1994.

  • Peter Muller and Riten Mitra. Bayesian nonparametric inference–why and how. Bayesian Analysis, 8(2), 2013.

Bayesian deep learning

  • Gal, Yarin, and Zoubin Ghahramani. "Dropout as a Bayesian approximation: Representing model uncertainty in deep learning." In international conference on machine learning, pp. 1050-1059. 2016.

  • Kendall and Gal. What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?

Applications

  • Taylor-Rodriguez, D., Kaufeld, K., Schliep, E. M., Clark, J. S., & Gelfand, A. E. (2017). Joint species distribution modeling: dimension reduction using Dirichlet processes. Bayesian Analysis, 12(4), 939-967.

  • Hore, S., Johannes, M., Lopes, H., McCulloch, R. and Polson, N., 2010. Bayesian computation in finance. Frontiers of Statistical Decision Making and Bayesian Analysis, pp.383-396.

Variable selection, regularisation

  • Edward I George. The variable selection problem. Journal of the American Statistical Association, 95(452):1304–1308, 2000.

  • Trevor Park and George Casella. The Bayesian lasso. Journal of the American Statistical Association, 103(482):681–686, 2008.

  • Feng Liang, Rui Paulo, German Molina, Merlise A Clyde, and Jim O Berger. Mixtures of g-priors for Bayesian variable selection. Journal of the American Statistical Association, 2012.

About priors

  • Persi Diaconis and Donald Ylvisaker. Conjugate priors for exponential families. The Annals of Statistics, 7(2):269–281, 1979.

  • Persi Diaconis and Donald Ylvisaker. Quantifying prior opinion. Bayesian Statistics, 2:133–156, 1985

  • Robert E Kass and Larry Wasserman. The selection of prior distributions by formal rules. Journal of the American Statistical Association, 91(435):1343–1370, 1996.

Markov chains, sampling-based approches, Bayesian bootstrap

  • Persi Diaconis and David Freedman. de Finetti’s theorem for Markov chains. The Annals of Probability, pages 115–130, 1980.

  • Albert Y Lo. A Bayesian bootstrap for a finite population. The Annals of Statistics, pages 1684–1695, 1988.

  • Alan E Gelfand and Adrian FM Smith. Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85(410):398–409, 1990.

  • Peter J Green. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82(4):711–732, 1995.

Linear Regression, Time Series

  • Dennis V Lindley and Adrian FM Smith. Bayes estimates for the linear model. Journal of the Royal Statistical Society: Series B (Statistical Methodology), pages 1–41, 1972.

  • Arnold Zellner. Bayesian and non-Bayesian analysis of the regression model with multivariate Student-t error terms. Journal of the American Statistical Association, 71(354):400–405, 1976.

  • Siddhartha Chib and Edward Greenberg. Bayes inference in regression models with ARMA(p,q) errors. Journal of Econometrics, 64(1-2):183– 206, 1994.

  • Steven L Scott and Hal R Varian. Predicting the present with Bayesian structural time series. International Journal of Mathematical Modelling and Numerical Optimisation, 5(1-2):4–23, 2014.

Grades

The final grade on 20 will consist of

  • 10 points for 'Contrôle continu'

    • you are asked to solve 10 exercises from Peter Hoff's book (Bayes stat) and/or Ghoshal and van der Vaart book (Bayes nonparametric stat, from chapters 4. Dirichlet Processes, 5. Dirichlet Process Mixtures and 14. Discrete Random Structures). From as many different chapters in total as possible.

      • 5 exercises for November 30.

      • 5 exercises for January 15.

Send the exercises by email. You can type them on LaTeX, possibly using knitr or RMarkdown especially if you intend to code in R. Scanned handwritten notes are fine as well.

  • 10 points for for the study of a research article:

    • 10 points for a presentation, which should stress the main contribution(s) of the article. Presentation will most likely be of about 12 to 15 minutes, with some 5 minutes of questions at the end.

    • possibly 2 bonus points for an optional written report of the article (max two pages): this report should aim at mimicking a referee report. See here for some useful hints: NIPS Reviewer best practices, Institute of Mathematical Statistics - Guidelines for Referees.

References

Evaluation criteria for the seminar

Slides quality

5: Structure is excellent

4: Structure is good, there are minor suggestions

3: Correct global organisation, but some details lack of clarity.

2: Navigating requires some effort. Lack of structure; some parts are confusing.

1: Student does not seem to spend more than 5 mins on that

0: No slides


Clarity of the explanation/speech

5: Everything is as clear as blue sky, excellent

4: Clear overall, minor problems

3: Lack of clarity in details, but the idea explanation is understandable

2: Following requires some effort, some parts are confusing

1: Student doesn’t seem to know what they is talking about

0: Doesn’t know what to say. At all.


The paper understanding, answers to questions

5: Outstanding depth of analysis and validation process, excellent answers.

4: Very good depth in analysis, but some points remain to be investigated with more care.

3: Satisfying analysis, some potential mistakes or methodological errors in application, validation or interpretation.

2: Weaknesses in analysis, with some lack of depth.

1: Some poor understanding of the topic.

0: Total misunderstanding.