On this page you will find the topics for each day’s class, along with the pre-class reading/video assignment, and the in-class activity.
Course Logistics
Statistical Models
Introduction to Statistical Inference
Note that the listed reading assignments should be completed prior to class
Read Section 7.1 in Probability and Statistics (DeGroot and Schervish)
Lecture Notes (These notes represent a summary of Wednesday’s class discussion)
Prior and Posterior Distributions
The Likelihood Function
Core definitions for statistical inference:
Note that the listed reading assignments should be completed prior to class
Prior and Posterior Distributions
The Likelihood Function
Note that the listed reading assignments should be completed prior to class
Lecture Notes (Same notes as Friday)
Computing posterior distributions
The likelihood function
Note that the listed reading assignments should be completed prior to class
The Likelihood Function
Conjugate Prior Distributions
Conjugate Prior Distributions
Beta and Binomial Connection
Poisson and Gamma Connections
Normal and Normal Connections
Note that the listed reading assignments should be completed prior to class
Bayes Estimators
Loss Functions
Properties of the Bayes estimator
Note that the listed reading assignments should be completed prior to class
Maximum Likelihood Estimator
Example MLEs:
Normal, known variance, unknown mean
Bernoulli
Gamma
Limitations of MLEs
Note that the listed reading assignments should be completed prior to class
Properties of Estimators
Invariance of MLE
Consistency
Bias, Variance, Mean Squared Error
Note that the listed reading assignments should be completed prior to class
The Method of Moments
Comparing Estimators
Properties of Estimators
Consistency
Bias, Variance, Mean Squared Error
Note that the listed reading assignments should be completed prior to class
Using R to Compute and Visualize Statistics
The ggplot2package
The Method of Moments
Comparing Estimators
Note that the listed reading assignments should be completed prior to class
Here is the whiteboard used during class today
Here is a link to the recorded lecture video (Grinnell Webex login required)
The Method of Moments
Comparing Estimators
Note that the listed reading assignments should be completed prior to class
The Sampling Distribution of an Estimator
The ggplot2package
Comparing Estimators
The Chi-Squared Distribution
The joint distribution of the sample mean and sample variance
Note that the listed reading assignments should be completed prior to class
Note that the listed reading assignments should be completed prior to class
The \(t\) distribution
Note that the listed reading assignments should be completed prior to class
Creating data visualizations using ggplot2
Vectors and Data Frames in R
Note that the listed reading assignments should be completed prior to class
None;
ggplot2 R
package, or if you’d like more practice, complete this tutorial
before class.Note that the listed reading assignments should be completed prior to class
Examples of General Confidence Intervals
The Sample Distribution Function
Bootstrapping
Note that the listed reading assignments should be completed prior to class
Note that the listed reading assignments should be completed prior to class
Note that the listed reading assignments should be completed prior to class
No DA needs to be submitted for Friday;
3/18 - 4/2
Bayesian Analysis of samples from a Normal distribution
Bayesian Credible Intervals
More about Bayesian Interval Estimates
Examples of Credible Intervals
Note that the listed reading assignments should be completed prior to class
Introduction to Hypothesis Tests
Significance Level
Power
Significance Level
Power
\(p\)-values
Note that the listed reading assignments should be completed prior to class
Significance Level
\(p\)-values
Note that the listed reading assignments should be completed prior to class
Equivalence of Confidence Sets and Hypothesis Tests
The likelihood ratio test
Note that the listed reading assignments should be completed prior to class
Confidence Intervals and Hypothesis Tests
The \(t\)-test
Note that the listed reading assignments should be completed prior to class
Note that the listed reading assignments should be completed prior to class
The two sample \(t\)-test
The \(F\)-distribution
The \(F\)-test for variances of Normal distributions
Note that the listed reading assignments should be completed prior to class
Review for Midterm 2
The F-Test
Note that the listed reading assignments should be completed prior to class
No assigned reading, but please complete this following DA indicating topics you’d like to review during class:
No class; Working differently day.
Note that the listed reading assignments should be completed prior to class
Linear Regression
Distribution of Least Squares Estimators
Inference for Simple Linear Regression
The joint distribution of \(\hat \beta_0, \hat \beta_1, \hat \sigma^2\)
Hypothesis Tests for Regression Coefficients
Note that the listed reading assignments should be completed prior to class
Inference for Simple Linear Regression
Hypothesis Tests for Regression Coefficients
Confidence Intervals for Regression Coefficients
Analysis of Residuals
Note that the listed reading assignments should be completed prior to class
Inference for Simple Linear Regression
Confidence Intervals for Regression Coefficients
Analysis of Residuals
Note that the listed reading assignments should be completed prior to class
Note that the listed reading assignments should be completed prior to class
Note that the listed reading assignments should be completed prior to class