Observation Theory: Parameter Estimation

This module introduces the concept of estimation and its necessity in various fields. It covers generic sources of uncertainty in observations and key concepts such as deterministic vs. stochastic parameters, random vs. systematic errors, precision vs. accuracy, bias, and probability distribution functions as metrics of randomness.

This module focuses on developing a systematic approach to translate real-life problems into mathematical models. It covers the creation of observation-equation systems, including vectors of observations and unknown parameters, linear functional relations, and stochastic characteristics of observations.

This module introduces the concept of (weighted) least squares estimation (WLSE). It covers the mathematical logic behind LSE and its main properties, teaching learners how to find estimates that predict observations as closely as possible.

This module explores the concept of Best Linear Unbiased Estimation (BLUE). It covers BLUE's theory and implications, as well as its relation to other estimators such as WLSE, maximum likelihood, and minimum variance estimators.

This module discusses how uncertainty in observations propagates to the uncertainty of estimates. It introduces the concept of error propagation and its application in specifying estimate precision, inferring confidence intervals, and describing the expected variability of estimation results.

This final module introduces probabilistic decision-making processes and statistical hypothesis testing for validating estimation results. It covers methods to verify the validity of chosen mathematical models and techniques to detect and identify model misspecifications.