To get the most out of this course, students should have a solid foundation in the following areas: 

- Linear Algebra: Matrix algebra, vector spaces, matrix inversion, trace, determinants, and positive semi-definite matrices. 

- Probability & Multivariate Statistics: Joint, marginal, and conditional distributions, expectation, variance, covariance, correlation, and multivariate normal distributions. Statistical Inference: Parameter estimation, likelihood functions, and Maximum Likelihood Estimation (MLE). 

- Basic Calculus: Partial derivatives, optimization of functions, and multiple integrals. 

- Programming Skills: Basic proficiency in R or Python for matrix manipulation, spatial data handling, and probabilistic simulation. 

In earth sciences, natural resource evaluation, and environmental studies, probabilistic models are essential for predicting spatial phenomena and quantifying uncertainties arising from sparse sampling, measurement errors, or indirect observations. Because spatial observations cannot be considered independent, standard statistical and machine learning approaches are often ill-suited and lack interpretability. This course provides a mathematical introduction to the modeling of spatially correlated data through probabilistic methods, offering a foundational grounding in linear geostatistics and spatial statistics. 

General introduction and probability reminders. Random function models, Inference, Prediction (Kriging and simulations) 

Evaluation based on a mini-project