Schedule

Set Theory Basics and Probability

1. Cover syllabus
2. Abstract the idea of an experiment
3. Develop basic set theory to be used in the development of probability
4. Start discussing probability

Introduction to Probability

1. Define probability calculus
2. Basic axioms of probability
3. Define random variables
4. Define density and mass functions
5. Define cumulative distribution functions and survivor
6. Define quantiles, percentiles, and medians

Expected Values

1. Define expected values
2. Properties of expected values
3. Unbiasedness of the sample mean
4. Define variances
5. Define the standard deviation
6. Calculate Bernoulli variance

Random Vectors, Independence

1. Define random vectors
2. Independent events and variables
3. IID random variables
4. Covariance and correlation
5. Standard error of the mean
6. Unbiasedness of the sample variance

Conditional Probabilities, Baye's Rule

1. Define conditional probabilites
2. Define conditional mass functions and densities
3.Motivate the conditional density
4. Baye's rule
5. Applications of Baye's rule to diagnostic testing

Likelihood

1. Define likelihood
2. Interpretations of likelihoods
3. Likelihood plots
4.Maximum likelihood
5. Likelihood ratio benchmarks

Distributions

1. Define the Bernoulli distrubtion
2. Define Bernoulli likelihoods
3. Define the Binomial distribution
4. Define Binomial likelihoods
5. Define the normal distribution
6. Define normal likelihoods

Asymptotics

1. Define convergent series
2. Definte the Law of Large Numbers
3. Define the Central Limit Theorem
4. Create Wald confidence intervals using the CLT

Confidence Intervals

1. Define the Chi-squared and t distributions
2. Derive confidence intervals for the variance
3. Illustrate the likelihood for the variance
4. Derive t confidence intervals for the mean
5. Derive the likelihood for the effect size

Confidence Intervals

1. Introduce independent group t confidence intervals
2. Define the pooled variance estimate
3. Derive the distribution for the independent group,
common variance, statistic
4. Cover likelihood methods for the change in the group
means per standard deviation
5. Discuss remedies for unequal variances

Presentation of Data

1. Histograms
2. Stem-and-leaf plots
3. Dot charts and dot plots
4. Boxplots
5. Kernel density estimates
6. QQ-plots

Bootstrapping

1. Introduce the bootstrap principle
2. Outline the bootstrap algorithm
3. Example bootstrap calculations

Confidence Intervals for Binomial Proportions

1. Confidence intervals for binomial proportions
2. Discuss problems with the Wald interval
3. Introduce Bayesian analysis
4. HPD intervals
5. Confidence interval interpretation

Logs and Geometric Means

1. Review about logs
2. Introduce the geometric mean
3. Interpretations of the geometric mean
4. Confidence intervals for the geometric mean
5. Log-normal distribution
6. Log-normal based intervals