Statistical Analysis

Python is one of the most versatile and widely used scripting languages. Its clean and uncluttered syntax as well as its straightforward design greatly contribute to this success and make it an ideal language for programming education. Its application ranges from web development to scientific computing. Especially in the fields of data science and artificial intelligence, it is the most common programming language supported by all major data-handling and analytical frameworks. This course provides a thorough introduction to the language and its main features, as well as insights into rationale and application within important libraries related to data science and artificial intelligence and important adjacent concepts such as environments, testing, and version control.

Kursinhalte

• Introduction to Python
  • Data Structures
  • Functions
  • Flow Control
  • Input / Output
  • Modules and Packages
• Classes and Inheritance
  • Scopes and Namespaces
  • Classes and Inheritance
  • Iterators and Generators
• Python Important Libraries
  • Standard Python Library
  • Scientific Calculations
  • Machine Learning Libraries
  • Data Visualization
  • Accessing Databases
• Errors and Exceptions
  • Syntax Errors
  • Handling and Raising Exceptions
  • User-Defined Exceptions
• Working with Python
  • Virtual Environments
  • Managing Packages
  • Unit and Integration Testing
  • Documenting Code
• Version Control
  • Introduction to Version Control
  • Version Control with GIT

Fakten zum Modul: Niveau: Master · Unterrichtssprache: English · 5 ECTS-Punkte · Modulprüfung: Hausarbeit

Modern techniques to analyze data and derive predictions for future events are deeply rooted in mathematical techniques.

Kursinhalte

• Calculus
  • Differentiation
  • Integration
  • Partial Differentiation
  • Vector Analysis
• Integral Transformations
  • Convolution
  • Complex Numbers
  • Fourier Series
  • Fourier Transformation
• Vector Algebra
  • Scalars and Vectors
  • Addition and Subtraction of Vectors
  • Multiplication of Vectors, Vector Product, Scalar Product
• Vector Calculus
  • Differentiation of Vectors
  • Integration of Vectors
  • Scalar and Vector Fields
  • Vector Operators
• Matrices and Vector Spaces
  • Basic Matrix Algebra and Systems of Linear Equations
  • Transpose, Trace, Determinant, and Inverse of a Matrix
  • Eigenvalues, Eigenvectors, and Diagonalization
  • Tensors
• Information Theory
  • Mean Squared Error (MSE) and Simple Linear Regression
  • Area Under the ROC Curve and Gini Index
  • Entropy
  • Cross Entropy

Fakten zum Modul: Niveau: Master · Unterrichtssprache: English · 5 ECTS-Punkte · Modulprüfung: Examen, 90 Minuten

Nearly all processes in nature and technical or scientific scenarios are not deterministic but stochastic. Therefore, these processes must be described in terms of probabilities and probability density distributions.

Kursinhalte

• Introduction to Statistics
  • Probability Theory
  • Kolmogorov Axioms
  • Probability Distributions
  • Samples and Statistics
  • Problems of Dimensionality
  • Principal Component Analysis and Discriminant Analysis
• Descriptive Statistics
  • Mean, Median, Mode, Quantiles
  • Variance, Skewness, Kurtosis
• Important Probability Distributions and Their Applications
  • Binomial and Negative Binomial Distribution
  • Gaussian or Normal Distribution
  • Poisson, Gamma-Poisson and Exponential Distribution
  • Weibull Distribution
  • Transformed Random Variables
• Bayesian Statistics
  • Bayes' Rule
  • Estimating the Prior, Benford's Law and Jeffrey's Rule
  • Conjugate Priors
  • Bayesian and Frequentist Approach
• Data Visualization
  • General Principles of Dataviz/Visual Communication
  • 1D, 2D Histograms
  • Box Plot, Violin Plot
  • Scatter Plot, Scatter Plot Matrix, Profile Plot
  • Bar Chart
• Parameter Estimation
  • Maximum Likelihood
  • Ordinary Least Squares
  • Expectation Maximization (EM)
  • Lasso and Ridge Regularization
  • Propagation of Uncertainties
• Hypothesis Testing
  • Error of 1st and 2nd Kind
  • Multiple Hypothesis Tests
  • p-Value

Fakten zum Modul: Niveau: Master · Unterrichtssprache: English · 5 ECTS-Punkte · Modulprüfung: Workbook

Statistical inference and causal analysis are crucial tools for analyzing and understanding data on a fundamental level. This course starts with an introduction to Bayesian inference and Bayesian networks which use probabilities to describe statistical problems and introduce probabilistic modelling which allows the specification of Bayesian statistical models in code.

Kursinhalte

• Statistical Inference
  • Bayesian inference
  • Bayesian networks
  • Probabilistic modelling
• Introduction to Causality
  • Correlation vs causation
  • Granger causality
  • Directed Acyclic Graphs (DAG)
  • Elements of causal graphs: collider, chain, fork
  • D – separation
• Interventions
  • Seeing vs doing
  • Conditional independence
  • Confounders & counterfactuals
  • Causal inference vs randomized controlled trials
• Do-calculus
  • Front- & backdoor criterion
  • Three rules of do-calculus
• Fallacies
  • Mediation fallacy
  • Collider bias
  • Simpson’s & Berkson’s Paradox
  • Imputing missing values: causal vs data-driven view

Fakten zum Modul: Niveau: Master · Unterrichtssprache: English · 5 ECTS-Punkte · Modulprüfung: Workbook