Bayesian statistics

2022/2023
Programme:
Mathematics, Second Cycle
Year:
1 ali 2 year
Semester:
first or second
Kind:
optional
Group:
M5
ECTS:
6
Language:
slovenian, english
Hours per week – 1. or 2. semester:
Lectures
2
Seminar
1
Tutorial
2
Lab
0
Content (Syllabus outline)

Bayesian models with one and more parameters. Connection with standard statistical methods. Hierachical models. Testing of models and sensitivity analysis. Bayesian design of experiment.
Bayesian approach to evidence synthesis of multiple surveys, power priors, analysis of dependence of synthesis analysis on previous surveys.
Introduction into regression analysis. Analysis of variance and covariance. Hypothesis testing via Bayes factor, complexity and fit. Posterior probabilities of hypotheses – models, and influence of priors on them, training sample.
More on posterior probabilities, estimating parameters, central credibility interval, the importance of conjugated distributions. Gibbs sampler, convergence of estimates, algorithm Metropolis-Hastings. Posterior simulations. Some other specific models of Bayesian anlysis.

Readings

A. Gelman, J.B.Carlin, H.S. Stern, D.B. Rubin: Bayesian Data Analysis. Chapman&Hall, 1995.
H. Hoijtink: Bayesian Data Analysis. In: R.E. Millsap and A. Maydeu-Olivares, The SAGE Handbook of Quantitative Methods in Psychology. London: SAGE, 2009.
I. Ntzoufras: Bayesian Modeling Using WinBUGS. New York: Wiley, 2009.

Objectives and competences

Basic knowledge of Bayesian statistics is acquired.
Bayesian methods are of great importance in practice. Therefore, experts with practical knowledge will present their experience in class.

Intended learning outcomes

Knowledge and understanding:
Understanding of basic concepts of Bayesian statistics.

Learning and teaching methods

Lectures, exercises, seminar type homework, homework that require the use of statistical packages, consultations

Assessment

Type (examination, oral, coursework, project):
Exercise-based exam.
Theoretical knowledge exam.
Grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

Jaka Smrekar:
SMREKAR, Jaka. Homotopy type of space of maps into a K(G,n). Homology, homotopy, and applications, ISSN 1532-0073, 2013, vol. 15, no. 1, str. 137-149. [COBISS-SI-ID 16643929]
SMREKAR, Jaka. Turning a self-map into a self-fibration. Topology and its Applications, ISSN 0166-8641. [Print ed.], 2014, vol. 167, str. 76-79. [COBISS-SI-ID 16943705]
SMREKAR, Jaka. Homotopy type of mapping spaces and existence of geometric exponents. Forum mathematicum, ISSN 0933-7741, 2010, vol. 22, no. 3, str. 433-456. [COBISS-SI-ID 15638105]

Mihael Perman:
PERMAN, Mihael, WELLNER, Jon A. An excursion approach to maxima of the Brownian bridge. Stochastic Processes and their Applications, ISSN 0304-4149. [Print ed.], 2014, vol. 124, iss. 9, str. 3106-3120.
PERMAN, Mihael. A decomposition for Markov processes at an independent exponential time. Ars mathematica contemporanea, ISSN 1855-3966. [Tiskana izd.], 2017, vol. 12, no. 1, str. 51-65.
PERMAN, Mihael, ZALOKAR, Ana. Optimal hedging strategies in equity-linked products. Journal of Computational and Applied Mathematics, ISSN 0377-0427. [Print ed.], 2018, vol. 344, str. 601-607.