Courses

Course material for USC PM522b Statistical Inference, USC PM569 Spatial Statistics and USC PM566 Introduction to Health Data Science.

Statistical Inference:

Course text Casella and Berger Statistical Inference, 2nd ed. 2002

• Slides 1: Random sampling, sampling distributions, order statistics.
• Slides 2: Sufficiency principle (sufficient, minimal sufficient, complete sufficient statistics), ancillary statistics, Basu's Theorem, Likelihood principle.
• Slides 3: Methods for finding point estimators including maximum likelihood, numerical methods for maximum likelihood, moment generating functions, method of moments.
• Slides 4: Evaluating estimators -- bias, MSE, MVUE
• Slides 5: Hypothesis testing and interval estimation
• Slides 6: Asymptotic evaluations -- consistency, effeciency, robustness, asymptotic LRT, asymptotic interval estimates, bootstrap.
• Slides 7: ANOVA and linear regression

Spatial Statistics:

• Introduction: spatial data and spatial data types
• Geostatistics 1: spatial semivariance and covariance
• Geostatistics 2: fitting semivariogram and covariance functions
• Geostatistics 3: kriging and spatial interpolation
• Areal 1: neighbourhoods and adjacency
• Areal 2: global and local measures of association
• Areal 3: spatial autoregressive models
• Point pattern 1: Poisson processes and complete spatial randomness
• Point pattern 2: Point process modeling and cluster detection
• Point pattern 3: Markov modeling and inhibition processes

Data Science:

• Check out the course here