Review and Looking Forward 2026

FW8051 Statistics for Ecologists

Todos

  • HW06: Generalized Linear Models (due Monday)
  • Read about models for zero-inflated data (Ch 17)
  • Tip of the day??

Monday 3/30/2026

  • Comparing models using likelihood ratio tests
  • Count models in JAGS (negative binomial, Poisson-Normal mixture)
  • Offsets for modeling survey effort
  • Introduction to logistic regression

Today

  • Logistic regression
    • Goodness-of-fit
    • Pearson residuals
    • Effect plots
    • Fitting models in JAGS

Monday 3/30/2026

Todos

  • HW06: Generalized Linear Models (due next Monday)
  • Read about logistic regression (Ch 16)
  • Tip of the day??

Wednesday 3/25/2026

  • Negative binomial regression model
  • Fitting models in JAGS

Today

  • Count models in JAGS
  • Offsets for modeling survey effort
  • Introduction to logistic regression

Wednesday 3/25/2026

Todos

  • HW05: Introduction to Bayesian Analysis (feedback due tonight)
  • Quiz: Bayesian Statistics (due tonight)
  • Get started on HW06: Generalized Linear Models
  • Read Regression models for count data (Ch 15)
  • Tip of the day??

Monday 3/23/2026

  • Introduction to generalized linear models
  • Regression models for count data (Poisson)
    • Model equations
    • Parameter interpretation (exp(\(\beta\)) = mutiplicate effect, while holding other predictors constant)
    • Pearson residuals versus linear predictor
    • Goodness-of-fit test

Today

  • Negative binomial regression model
  • Fitting models in JAGS
  • Offsets for modeling survey effort

Monday 3/23/2026

Todos

  • HW05: Introduction to Bayesian Analysis (due tonight, feedback due Wednesday)
  • Quiz: Bayesian Statistics (due Wednesday)
  • Read Regression models for count data (Ch 15)
  • Tip of the day??

Wednesday 3/18/2026

  • Implementing linear regression model in JAGS
  • Bayesian goodness-of-fit testing
  • Confidence and predictions intervals using JAGS

Today

  • Introduction to generalized linear models
  • Regression models for count data

Wednesday 2/18/2026

Todos

  • HW04: Probability, Maximum Likelihood (feedback due tonight/Wed)
  • HW05: Introduction to Bayesian Analysis (due on Monday)
  • Quiz: Bayesian Statistics (due next Wednesday)
  • Read Bayesian Linear Models (Ch 13), Introduction to GLMS (Ch 14)
  • Tip of the day??

Monday 3/16/2026

  • Introduction to MCMC for estimating parameters in Bayesian models
  • Fit our first model using JAGS

Today

  • Implementing linear regression model in JAGS
  • Bayesian goodness-of-fit testing

Monday 3/16/2026

Todos

  • HW04: Probability, Maximum Likelihood (due tonight, feedback on Wed)
  • Read Introduction to Bayesian Statistics (Ch 11), MCMC Sampling (Ch 12)
  • Tip of the day??

Wednesday 3/4/2026

  • Went over exam
  • Likelihood ratio tests and profile-likelihood confidence intervals
  • Introduction to Bayesian inference

Today

  • Introduction to MCMC for estimating parameters in Bayesian models
  • Fit your first(?) model using JAGS

Wednesday 3/4/2026

Todos

  • HW04: Probability, Maximum Likelihood (due Monday after spring break)
  • Read Introduction to Bayesian Statistics (Ch 11), MCMC Sampling (Ch 12)
  • Tip of the day??

Monday 3/2/2026

  • Properties of maximum likelihood estimators
  • Variance of functions of parameters

Today

  • Likelihood ratio tests and confidence intervals
  • Introduction to Bayesian inference

Monday 3/2/2026

Todos

  • Mid-term Exam (due tonight)
  • HW04: Probability, Maximum Likelihood (due Monday after spring break)
  • Read Introduction to Bayesian Statistics (Ch 11), MCMC Sampling (Ch 12)
  • Tip of the day??

Wednesday 2/25/2026

Estimating parameters using Maximum Likelihood

  • using calculus, optim, and glm

Today

  • Properties of maximum likelihood estimators
  • Variance of functions of parameters
  • Likelihood ratio tests and confidence intervals

Intro to Bayesian

Wednesday 2/25/2026

Todos

  • Mid-term Exam = 2 questions from the exercise book (due March 2)
  • Read Maximum Likelihood (Ch 10)

Monday 2/23/2026

  • Working with distributions in R
  • Introduction to Maximum Likelihood

Today

Estimating parameters using Maximum Likelihood

Monday 2/23/2026

Todos

  • Mid-term Exam = 2 questions from the exercise book (due March 2)
  • Probability Quiz (due tonight)
  • Read Maximum Likelihood (Ch 10)

Wednesday 2/18/2026

  • Probability rules
  • Probability distributions
    • Probability mass/density function
    • Expected value, variance
    • Working with distributions in R

Today

  • Learn about some other important probability distributions
  • Continue to get familiar with R’s capabilities for working with distributions (Exercise 9.2)
  • Introduction to Maximum Likelihood

Wednesday 2/18/2026

Todos

  • HW03: Non-linear relationships and GLS models (feedback due tonight)
  • Mid-term Exam = 2 questions from the exercise book (due March 2)
  • Probability Quiz (due Monday 2/23)

Monday 2/16/2026

  • Causal Inference versus stepwise selection

Today

  • Probability, probability distributions

Monday 2/16/2026

Todos

  • HW03: Non-linear relationships and GLS models (due tonight)
  • Read Ch 9.1-9.9 in book (Probability)
  • I will release the Mid-term Exam on Wednesday (due March 2)

Wednesday 2/11/2026

  • Multicollinearity, Causal Inference

Today

  • Causal Inference (continued)
  • Modeling Strategies

Wednesday 2/11/2026

Todos

  • Quiz: Non-linear relationships and GLS models (due tonight)
  • HW02: Multiple Regression feedback due tonight (Wednesday)
  • HW03: Non-linear relationships and GLS models (due next Monday)
  • Read Ch 8.1-8.5 in book (Modeling Strategies)

Monday 2/9/2026

  • Visualizing Regression Models using ggeffects package
  • Generalized least squares (relaxing the constant variance assumption)

Today

  • Multicollinearity, Causal Inference, Modeling Strategies

Monday 2/9/2026

Todos

  • HW02: Multiple Regression due tonight (Monday)
  • Read Ch 6.1-6.5, Ch 7 (Multicollinearity/Causal Inference) in the book.

Wednesday 2/4/2026

  • Visualizing Regression Models
  • Modeling non-linear relationships

Today

  • Relaxing the constant variance assumption

Wednesday 2/4/2026

Todos

  • HW01: Linear regression feedback due tonight (Wednesday)
  • HW02: Multiple Regression due on Monday
  • Read Chapter 5 (Generalized Least Squares) in the book.

Monday 2/2/2026

  • Multiple regression
    • Parameter interpretation
    • Design matrices
    • Categorical variables (reference and means coding)
  • Interactions
  • Visualizing Regression Models

Today

  • Modeling non-linear relationships

Monday 2/2/2026

Todos

  • HW01: Linear regression due tonight (feedback due on Wednesday)
  • Read Chapter 4 in the book.
  • Multiple Regression Quiz (moved back a day - due tomorrow tonight)

Wednesday 1/28/2026

  • Bootstrapping
  • Multiple regression (more than 1 predictor variable)
    • Parameter interpretation
    • Design matrices
    • Categorical variables (reference and means coding)

Today

  • Categorical variables and design matrices
  • Interactions
  • Visualizing regression models
  • Intro to Non-linear models

Wednesday 1/28/2026

Todos

  • HW00_Reproducible Research (provide feedback in using Feedback Fruits on Canvas) by end of day today
  • Linear Models Quiz due today
  • Review prediction and confidence intervals slides
  • Read start of Chapter 3 in the book.
  • HW01: Linear regression due on Monday 2/2

Monday 1/21/2026

Review of statistical concepts in context of linear regression:

If all assumptions hold:

\[\frac{\hat{\beta}_1-\beta_1}{\hat{SE}(\beta_1)} \sim t_{n-2}\]

\(\Rightarrow\) when \(H_0: \beta_1 = 0\) is true, \(\frac{\hat{\beta}_1-0}{\hat{SE}(\beta_1)} \sim t_{n-2}\)

So, we can use the \(t_{n-2}\) distribution for testing the null hypothesis.

Other topics

  • How to check assumptions
  • Confidence intervals and their interpretation

Today

  • Bootstrapping
  • Multiple regression (more than 1 predictor variable)
    • Parameter interpretation
    • Design matrices
    • Categorical variables (reference and means coding)
    • Interactions

Monday 1/26/2026

Todos

  • Reproducible Research (provide feedback in using Feedback Fruits on Canvas) by Wednesday
  • Linear Models Quiz due Wed
  • Review prediction and confidence intervals slides
  • Read Chapter 1 and Chapter 2 in the book.
  • HW01: Linear regression due on Monday 2/2

Wednesday 1/21/2026

Review of statistical concepts in context of linear regression

  • Sampling distributions
  • SE (sd of a sampling distribution)

Coding:

  • For loop in R to create a sampling distribution

Today

More review of linear regression

  • Assumptions and how to check them
  • t-distribution for regression coefficients
  • hypothesis tests
  • confidence intervals
  • \(R^2\) interpretation

Bootstrapping

Wednesday 1/21/2026

Todos

  • Complete course survey (if you have not yet)
  • Reproducible Research (turn in using Feedback Fruits on Canvas)

Last time

Usually, I would post a few bullet points to remind ourselves of what we covered during the previous class

Today Wednesday 1/21/2026

Review of statistical concepts in context of linear regression

  • Sampling distributions
  • SE (sd of a sampling distribution)
  • Assumptions of linear regression

Coding:

  • For loop in R to create a sampling distribution