Inference from Data and Models: A Foundation in State Estimation

How do we extract meaningful insights from real-world observations when our data is noisy and incomplete? This course provides a clear, step-by-step introduction to the core principles of data inference, state estimation, and mathematical modeling. You will transition from analyzing raw data to building, testing, and refining predictive models that reflect physical and mathematical realities. In this course, you will: 1. Understand the foundational concepts of statistical inference, probability distributions, and parameter estimation. 2. Combine observational data with mathematical models using linear and non-linear regression. 3. Apply state estimation and data assimilation methods to track dynamic systems over time. 4. Analyze model uncertainty and quantify the reliability of your predictions. 5. Explore modern computational approaches to inverse problems and system identification. Starting with essential definitions and probability theory, the course guides you through state estimation, inverse problems, and modern data-model integration workflows. This course is designed for beginners in data science, engineering, and environmental sciences who want to understand how models and data work together, requiring no advanced prerequisites. Start mastering the art of model-based inference today.