IMM Pakistan Student 2021 - 2022
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IMM Pakistan / 2024 - 2025
Probability and Statistical Analysis (M1)
TEACHING TEAM
Content
Course description
Dr. Rugerri will be teaching half of the course, which is focused on Bayesian Statistics. In particular, the following topics will be covered: Bayes Theorem, Prior elicitation, Conjugate priors, Bayesian estimators, Credible intervals, Hypothesis testing, Bayes factor, Markov Chain Monte Carlo simulation, Hierarchical models, Linear regression, Logistic regression, Markov chains, Poisson processes
Prof. Dabo-Niang will cover the fundamentals of statistics. In particular, the following topic will be covered:
1) DESCRIPTIVE STATISTICS, EXPLORATORY DATA ANALYSIS
- Summarising quantities (sample mean/median/mode/variance)
- Box-plot, scatter plot, histograms, stem-and-leaf
2) DISTRIBUTION OF SAMPLING STATISTICS AND PARAMETER ESTIMATION
- Sample mean
- Central limit theorem
- Sample varianve
- Method of moments estimation
- Maximum likelihood estimation
- Confidence intervals
3) PROPERTIES OF THE ESTIMATORS
- Consistency
- Distorsion
- UMVUE
- Sufficient statistics
4) HYPOTHESIS TESTING
- Significance levels
- Tests Concerning the Mean of a Population
- Testing the Equality of Means of Two Populations
- Hypothesis Tests Concerning the Variance of a Normal Population
- Hypothesis Tests in Bernoulli Populations
5) LINEAR REGRESSION
- Simple linear regression
- Multiple Linear Regression
- Analysis of variance
Materials
References
References
References for the half of the course that is taught by Dr. Ruggeri:
- Albert, J. (2009). Bayesian Computation with R. Springer.
- Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D., Vehtari, A. & Rubin, D.B. (2021). Bayesian Data Analysis (3rd ed.). Chapman and Hall/CRC. Freely available from https://sites.stat.columbia.edu/gelman/book/
- Rios Insua, D., Ruggeri, F. & Wiper, M.P. (2012). Bayesian Analysis of Stochastic Process Models. Wiley.
References for the half of the course taught by Prof. Dabo-Niang:
- Ross, Sheldon M. Introduction to probability and statistics for engineers and scientists. Academic press, 2020.
- Hastie, T., Tibshirani, R., & Friedman, J. (2009). An introduction to statistical learning. With Applications to R. Second edition. https://www.statlearning.com
- Agresti, A., & Kateri, M. (2021). Foundations of statistics for data scientists: with R and Python. Chapman and Hall/CRC.
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ADMISSIONS
Applicants Are Divided Into Two Groups: "International Applicants" Who Have Foreign Citizenship And "Pakistani Applicants" Who Either Hold Pakistani Citizenship, Have Dual Citizenship, Or Are Pakistanis Residing Outside The Country.
