How to Use This Document

Below, I’ve included some categories of concepts that I expect statistically literate graduate students to be able to talk about intelligently.

If I’m serving on your committee, I may refer you to several of these categories

This document is incomplete and always under construction!

General Statistical/Quantitative Knowledge

I expect all graduate students to be familiar with these concepts.

If I’m on your committee, I’m likely to ask you about any or all of these concepts.

Readings

  • Any good general intro to stats or biostatistics book will cover all or most of these topics.
  • Bolker 2008 covers many of these in chapters 1 - 4
  • Kevin McGarigal’s old slides for ECO602 are a fantastic resource.

General Concepts

  • Deterministic functions
  • Stochastic models
  • Uncertainty: in general and how it applies to your research
  • Common descriptive sample statistics
  • Correlation coefficients
  • The sampling distribution
  • Confidence intervals
  • p-values, type 1 errors
  • Statistical power, type 2 errors
  • Row data paradigm
  • Parametric and nonparametric tests

Probability Theory and Distribution Basics

  • Sample spaces and events
  • Independent events
  • Law of total probability
  • Conditional probability
  • Counting and factorials
  • Discrete and continuous distributions
  • Distribution functions
    • Probability density and mass functions
    • Cumulative probability functions
    • Quantile functions
  • Likelihood and maximum likelihood

Specific Distributions

For each of the following distributions, you should be able to articulate:

  1. The parameter or parameters that characterize the distribution.
  2. Key properties of the distribution:
    • Sample space, when is it useful, etc.
  3. How is it relevant to your work or interests?
  4. What are its useful properties?
  5. What kinds of phenomena does the distribution model?
  6. Under what scenarios or tests does the distribution arise?

Distribution List

  • Normal
  • Poisson
  • Bernoulli and binomial
  • Beta
  • t
  • F

Statistical Models 1

Readings

  • Bolker 2008 and Zuur 2007 are classic, if slightly difficult, texts.
  • Weisberg 2014 is a great text on applied aspects of linear modeling.
  • Kevin McGarigal’s old slides for ECO602 are a fantastic resource.

Models, tests, and other concepts

  • What is the Frequentist paradigm?
  • What is a dual model?
  • Types of predictors are response variables
  • t-tests
  • Analysis of Variance: 1-way and multi-way
  • Simple and multiple linear regression
  • Analysis of Covariance
  • Model coefficient tables and the ANOVA table
    • Interpreting model table coefficients
    • Understanding the regression equation
    • Interaction terms
    • Base cases
    • Complementary information from the two tables
  • Key model assumptions
  • Model diagnostics
  • Model comparison
  • Limits of General Linear Models
  • Linearity in the parameters
  • (Multi) collinearity

Statistical Models 2: Generalized Linear Models

Readings

  • Bolker 2008 and Zuur 2007 are classic, if slightly difficult, texts
  • McCullagh is a good resource

Concepts and Models

  • Types of response variables
  • Overdispersion and zero-inflation
  • When to use a GLM
  • Logistic regression
  • Poisson regression

Statistical Models 3: Mixed Modeling

Readings

  • Zuur 2009 is a classic with lots of cased study examples

Concepts and Models

  • Fixed and random effects

Statistical Models 4: Machine Learning and Other Techniques

Readings and Other Resources

Concepts and Models

  • Support Vector Machines
  • Decision Trees and Random Forests

Spatial Stuff

Readings

  • Fletcher and Fortin 2018
  • Illian 2008

Agent-Based Modeling

Bibliography

  • Bivand, Roger, Edzer J. Pebesma, and Virgilio Gómez-Rubio. Applied Spatial Data Analysis with R. [Electronic Resource]. Second edition. Use R! Springer, 2013.

  • Bolker, Benjamin M. Ecological Models and Data in R. Princeton University Press, 2008.

  • Dunn, Peter K., and Gordon K. Smyth. Generalized Linear Models With Examples in R. Springer Texts in Statistics. Springer New York, 2018.

  • Fletcher, Robert, and Marie-Josée Fortin. Spatial Ecology and Conservation Modeling: Applications with R. Springer International Publishing, 2018.

  • Hosmer, David W., Stanley Lemeshow, and Rodney X. Sturdivant. Applied Logistic Regression. Third edition / David W. Hosmer, Jr., PhD, Stanley Lemeshow, PhD, Rodney X. Sturdivant, PhD. Wiley, 2013.

  • Illian, Janine, Antti Penttinen, Helga Stoyan, and Dietrich Stoyan. Statistical Analysis and Modelling of Spatial Point Patterns. Vol. 70. John Wiley & Sons, 2008.

  • McCullagh, P. Generalized Linear Models. Routledge, 2018.

  • Weisberg, Sanford. Applied Linear Regression. Wiley Series in Probability and Statistics. Wiley, 2014.

  • Zuur, Alain F. Analysing Ecological Data. Statistics for Biology and Health. New York.; London: Springer, 2007.

  • Zuur, Alain, Elena N. Ieno, Neil Walker, Anatoly A. Saveliev, and Graham M. Smith. Mixed Effects Models and Extensions in Ecology with R. Statistics for Biology and Health. New York, NY, USA: Springer Science & Business Media, 2009. https://doi.org/10.1007/978-0-387-87458-6.