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### dhr.dr. B.J.K. (Bas) Kleijn

• Faculteit der Natuurwetenschappen, Wiskunde en Informatica
Korteweg-de Vries Instituut
Science Park 107
Science Park 107  Amsterdam
Kamernummer: F3.30
Postbus  94248
1090 GE  Amsterdam
• B.J.K.Kleijn@uva.nl
T: 0205256064
T: 0205255217

### Bayesian Statistics

Course code ST406046

### Lecturers

dr. B.J.K. Kleijn

### Course description and goals

To understand the basic properties of Bayesian methods; to be able to apply this knowledge to statistical questions; to know the extent (and limitations) of conclusions based thereon. Frequentist statistics is based on the assumption that the observation is random and its distribution is unknown but fixed. Bayesian statistical methods are based on the principle that both observations and distributions are random. A Bayesian procedurerequires specification of a statistical model with a so-called prior distribution; the posterior distribution is a version of the prior that is corrected by the observation. In this course, we introduce Bayesian methods for a variety of statistical problems starting with some basic examples. We consider basic properties of the procedure, choice of the prior by objective and subjective criteria, Bayesian inference, some decision theory and some model selection. In addition, non-parametric Bayesian modelling is considered, posterior asymptotic behaviour is discussed, e.g. posterior consistency, rates of contraction and the posterior limit shape and the Bernstein-Von Mises theorem..

### Lecture Notes

Below you find links to the May 2011 version of the lecture notes for this course. This version of the notes is to be used for the exams in June 2011. The appendix on Measure Theory is still being edited, so nothing there is definitive. The main material (Chapters 1-3) is complete, including exercise sections at the end of each chapter. Later chapters, on Bayesian asymptotic statistics, are not available yet, but are covered in the Hilversum Spring school notes, 2006.

Below is a presentation on Bayesian asymptotics, as presented at the "14th Meeting of AiOs in Stochastics", Hilversum, The Netherlands, 8-10 May 2006.

#### 2014

• van der Pas, S. L., Kleijn, B. J. K., & van der Vaart, A. W. (2014). The horseshoe estimator: Posterior concentration around nearly black vectors. Electronic Journal of Statistics, 8(2), 2585-2618. DOI: 10.1214/14-EJS962 [details] [PDF]
• Ritov, Y., Bickel, P. J., Gamst, A. C., & Kleijn, B. J. K. (2014). The Bayesian Analysis of Complex, High-Dimensional Models: Can It Be CODA? Statistical Science, 29(4), 619-639. DOI: 10.1214/14-STS483 [details] [PDF]

#### 2012

• Kleijn, B. J. K., & van der Vaart, A. W. (2012). The Bernstein-Von-Mises theorem under misspecification. Electronic Journal of Statistics, 6, 354-381. DOI: 10.1214/12-EJS675 [details] [PDF]
• Bickel, P. J., & Kleijn, B. J. K. (2012). The semiparametric Bernstein-von Mises theorem. The Annals of Statistics, 40(1), 206-237. DOI: 10.1214/11-AOS921 [details] [PDF]

#### 2008

• Bickel, P., Kleijn, B., & Rice, J. (2008). Event-weighted tests for detecting periodicity in photon arrival times. Astrophysical Journal, 685(1), 384-389. DOI: 10.1086/590399 [details]
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