Train students to make them capable of understanding and applying the fundamental concepts of probability and statistics in the field of data analysis; Various probability density functions (PDF) and cumulative distribution functions (CDF) and their use will be explained; how to calculate and interpret conditional and joint probabilities. The Law of Large Numbers and the Central Limit Theorem will be explained with applications to real-world problems. Fundamental objectives will be the understanding and application of Bayesian Statistics as well as the understanding and implementation of parameter estimation through the maximum likelihood principle. The quality of fit of statistical models will be discussed. Additionally, methods of Machine Learning for data analysis will be introduced. Effective communication of results and statistical interpretations will also be introduced.
teacher profile teaching materials
1. Review of Fundamental Statistical Concepts:
Probability distributions, random variables, and sampling distributions.
Descriptive statistics and data visualization.
Introduction to statistical inference.
2. Parameter Estimation: Method of Moments:
Principles and applications of the method of moments.
Comparison with other estimation methods.
3. Parameter Estimation: Maximum Likelihood Estimation (MLE):
Likelihood functions and their properties.
Derivation and properties of maximum likelihood estimators.
Applications of MLE in various statistical models.
4. Properties of Estimators:
Unbiasedness, efficiency, and consistency of estimators.
Mean squared error and other measures of estimator performance.
5. Confidence Intervals:
Construction and interpretation of confidence intervals.
Confidence intervals for different parameters and distributions.
Relationship between confidence intervals and hypothesis testing.
6. Hypothesis Testing:
Formulation of null and alternative hypotheses.
Type I and Type II errors, and power of a test.
Common hypothesis tests (e.g., t-tests, chi-square tests,…).
P-values.
7. Bayesian Statistics:
Bayes' theorem and its applications.
Prior and posterior distributions.
Bayesian inference and parameter estimation.
Comparison of Bayesian and frequentist approaches.
8. Advanced Topics (on request)
“Bayesian Reasoning in Data Analysis” – G. D’Agostini (Springer)
"Introduction to Statistics and Data Analysis" - C. Heumann, M. Schomaker, Shalabh (Springer)
"Statistical Methods for Data Analysis" - L. Lista (Springer)
Slides used during lectures
Programme
Course Topics:1. Review of Fundamental Statistical Concepts:
Probability distributions, random variables, and sampling distributions.
Descriptive statistics and data visualization.
Introduction to statistical inference.
2. Parameter Estimation: Method of Moments:
Principles and applications of the method of moments.
Comparison with other estimation methods.
3. Parameter Estimation: Maximum Likelihood Estimation (MLE):
Likelihood functions and their properties.
Derivation and properties of maximum likelihood estimators.
Applications of MLE in various statistical models.
4. Properties of Estimators:
Unbiasedness, efficiency, and consistency of estimators.
Mean squared error and other measures of estimator performance.
5. Confidence Intervals:
Construction and interpretation of confidence intervals.
Confidence intervals for different parameters and distributions.
Relationship between confidence intervals and hypothesis testing.
6. Hypothesis Testing:
Formulation of null and alternative hypotheses.
Type I and Type II errors, and power of a test.
Common hypothesis tests (e.g., t-tests, chi-square tests,…).
P-values.
7. Bayesian Statistics:
Bayes' theorem and its applications.
Prior and posterior distributions.
Bayesian inference and parameter estimation.
Comparison of Bayesian and frequentist approaches.
8. Advanced Topics (on request)
Core Documentation
“A Modern Introduction to Probability and Statistics” – F.M. Dekking, C. Kraaikamp, H.P Lopuhaä, L. E. Meester (Springer_“Bayesian Reasoning in Data Analysis” – G. D’Agostini (Springer)
"Introduction to Statistics and Data Analysis" - C. Heumann, M. Schomaker, Shalabh (Springer)
"Statistical Methods for Data Analysis" - L. Lista (Springer)
Slides used during lectures
Attendance
Attendance is not required; however, it is recommended to improve the understanding of the subject matter.Type of evaluation
Students are required to complete a project, which may be done in groups and is graded on a scale of thirty. This evaluation can be supplemented by an oral exam.