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