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Lecture notes of MORE
Contents
Fundamentals
Covariance and Correlation
Multivariate Gaussian distribution
Minimal concepts of graph theory
Monte Carlo methods and MCMC
Monte Carlo simulation
Markov chain Monte Carlo sampling
Introduction to non-stationarity
Data Exploration
Statistical Modelling under the Non Stationary assumptions
The detrending approach
The integrated approach
Return Period Under the Nonstationary Assumption
Bivariate Copulas
Multivariate Data Exploration
Bivariate Copulas
Copula Families
Tail Dependence
Fitting Copulas
Goodness-of-Fit Methods for Copulas
AND and OR Hazard Scenarios
Non-parametric Bayesian Networks
Definition
Correlations in NPBNs
Semantics of NPBNs
Tutorial py-Banshee
Vine-copulas
Regular vines
Vine copulas
Estimation
Data Assimilation
Analytical Filtering
The Gaussian special case
The Kalman Filter
Example Lemniscate
Example Satellite
Ensemble Filtering
Ensemble Kalman Filter
Pseudo-algorithm
Example
State-vector augmentation
Particle Filter
Importance sampling
Resampling
Pseudo-algorithm
Example
The curse of dimensionality
Grand Prix
Grand Prix 2024
Structured Expert Judgment
Questionnaire
Calibration score
Information score
Aggregation of expert opinions
References
Repository
Open issue
Index
