# Outline

After the foundational material is presented (roughly the first third of the class), I will introduce a large variety of statistical models and methods.  I will choose these based on what makes sense from a pedagogical perspective at first, but as the semester goes on I will choose more and more material based on students interest and class projects.

For more information on the content of the class, see the detailed lecture notes online, which gives a general outline.  Here's another version of some of the material:

### Foundations

• What is statistics?
• What is political methodology?
• Models and a language of inference
• The role of simulation
•   To solve probability problems
•    to evaluate estimators
•    to compute features of probability distributions
•    to transform statistical results into quantities of interest
• Stochastic components (normal, log-normal, Bernoulli, Poisson, etc)
• The relationship between stochastic and systematic components and data generation processes
• Systematic components (linear, logit, etc.)
• Uncertainty and Inference
•   Probability as a model of uncertainty
•   Probability distributions, theory, discrete, continuous, examples
• Inference
•   Inverse probability problems
•   The likelihood theory of inference
•   The Bayesian theory of inference
•   Detailed example: Forecasting presidential elections
• Properties of maximum likelihood estimation (finite sample, asymptotic, etc.)
• Precision of likelihood estimates

### Specific Topics

We will not get to all these topics, and the list of topics we do cover will likely include others than those listed here, depending on student interest.

• Discrete regression models
• Binary variables
• Interpreting functional forms
• Ordinal variables
• Grouped uncorrelated binary variables
• Event count models --- Correlated and uncorrelated events; over and under dispersion.
• Basic time series models
• Basic multiple equation models, including identification
• Multinomial choice models
• Models for selection bias, censoring, and truncation
• Models for duration
• Hurdle models
• Case-control designs
• Model dependence
• Matching as nonparametric preprocessing
• Rare events
• Neural network models
• An overview of MCMC methods
• Compositional data
• Missing data (item and unit nonresponse) problems
• Ecological inference (avoiding aggregation bias)
• Models for reciprocal causation and endogenity
• Empirical and hierarchical Bayesian analysis
• Time series cross-sectional data
• Models for interpersonal incomparability in surveys
• Text Analysis