Lectures

Zoom link: https://dartmouth.zoom.us/j/9608147464

Introduction

• Uncertainty and data-driven qunatification
• Review of probability (last update: Jan 11, 2021)
• Information Theory

Statistical Inference

• Parametric inference
• Nonparametric inference
• Bayesian inference

Random Sampling

• Monte Carlo
• Importance sampling; Matlab/Python Code
• Markov chain Monte Carlo; Matlab/Python Code

Special Topics

• Hilbert Space
• Smoothing using Orthogonal Functions
• Midterm

Stochastic Processes

• Brownian Motion
• Stochastic Differential Equations
• Stationary Stochastic Process

Polynomial Chaos

• Karhunen-Loeve Expansion
• Generalized Polynomial Chaos
• Review

Data Assimilation

• Kalman Filter; (Matlab code)
• Approximate Gaussian Filters I
• Approximate Gaussian Filters II

Advanced Data Assimilation

• Ensemble Square Root Filter
• Particle Filter (particle filter Matlab code for Lorenz 63)
• Localization and Inflation

Challenges of High-dimensional Spaces

• Sampling in High-dimensional Spaces
• Data Assimilation in High-dimensional Spaces
• Summary