Bios 6311 Syllabus 2018
Mini Calendar
- Aug 23 (First day of class: 23)
- Aug 28 & 30
- Sep 4 & 6
- Sep 11 & 13
- Sep 18 & 20 -- 1st Exam
- Sep 25 & 27
- Oct 2 & 4
- Oct 9 & 11
- Oct 16 (Fall Break: 18-19)
- Oct 23 & 25 -- 2nd Exam
- Oct 30 & Nov 1
- Nov 6 & 8
- Nov 13 & 15
- Nov (T-Giving Break: 17-25)
- Nov 27 & 29
- Dec 4 & 6 (Last day of class: 6) -- Final Exam
- Dec (Reading days and exams 7-15)
Topics Covered
Week 1 (Aug 23)
Review of Probability.
- Random Variables: Z
- Sample Space: S = {a, b, c, d}
- Events: a, b, c, d
- Probability of Events: P[Z=a]
Craps
- Basic rules for the pass the line bet
Big Picture
- Statistics is about estimation
- ... and checking your methods
Week 2 (Aug 28 & 30)
Intro to coding in R.
Detecting a weighted die.
- Using R to perform theoretical experiments.
- The Exact (1-α) level confidence interval for a proportion
- The probability statements that define the method
- Calculating the bounds "by hand", i.e. solving using trial and error in R
Week 3 (Sept 4 & 6)
How good is the exact interval?
- Developing theoretical experiments to test operating characteristics of methods
At least three (1-α) level confidence intervals for a proportion
- Exact interval
- Asymptotic Normal interval (Wald interval)
- Wilson interval
- Add 2 successes and 2 failures interval
P[LB < θ < UB] < 1-α
Central Limit Theorem.
Normal approximation for the Binomial.
Week 4 (Sept 11 & 13)
What makes x/n a "good" estimator for θ?
Unbiasedness - definition, proof for x/n.
Likelihood function L[θ].
Maximum likelihood estimator (MLE).
Values that are well supported by the data.
Likelihood Support interval for a proportion.
Big Picture - when examining a statistical method:
- Understand the philosophical justification
- Understand the mathematical justification
- Understand the performance in various simulated settings
Week 5 (Sept 18 & 20)
Sensitivity, Specificity, Positive Predictive Value, Negative Predictive Value.
Bayes theorem
Prior probability distribution and posterior probability distribution.
Bayesian Credible interval for a proportion.
Week 6 (Sept 25 & 27)
Interval methods for the population mean.
Wald interval (Z interval) with variance known.
Z interval with variance unknown.
t interval with variance unknown.
Likelihood support interval using Normal distribution.
Week 7 (Oct 2 & 4)
Bayesian credible interval using Normal distribution.
Estimating Power by hand.
Interval methods for the difference of two population means.
- Wald interval (Z interval) with variance known.
- Z interval with variance unknown.
- t interval with variance unknown.
- Likelihood support interval using Normal distribution.
Estimating sample size needed to achieve a given level of precision, e.g. SE < 0.001.
Interval methods for the difference of two population means.
- When X and Y are dependent,
- When X and Y are independent, i.e. Cov(X,Y) = 0.
- When N is large (Frequentist, Likelihoodist, Bayesian).
- When N isn't large but X is Normal-ish.
Week 8 (Oct 9 & 11)
Interval methods for the difference of two population proportions (RD).
Intervals for other measures comparing population proportions (RR, OR).
Graphical assessments of Normality: Quantile-Quantile (QQ) Plots
Week 9 (Oct 16)
Intervals for other measures comparing population proportions (RR, OR).
- Delta method
- Numerical approximation of a posterior distribution (ratio of two independent Beta distributions)
Week 10 (Oct 23 & 25)
2nd Exam
Week 11 (Oct 30 & Nov 1)
Inference.
- Hypothesis testing vs a point null
Power curves
- Type I and Type II errors
- Pre-specifying a Type I error rate (α)
Week 12 (Nov 6 & 8)
Randomization Inference
- Permuting treatment assignment to generate a null distribution
Nonparametric tests
- Wilcoxon-Mann-Whitney test (wilcox.test)
When the null shapes the variance
- one-sample proportions test
- equality of two proportions test (as Z and as Chi-squared)
Week 13 (Nov 13 & 15)
Omnibus Tests
Multiple comparisons
- Familywise Error Rate
- Bonferroni procedure
- False Discovery Rate
- Benjamini Hochberg procedure
- Controlling pre-experimental probabilities like Type I error, FWER, and FDR
Week 14 (T-Giving Break: 17-25)
Week 15 (Nov 27 & 29)
Statistical vs Clinical Significance
- Second generation p-values
- Indirect control of Type I error
Estimating post-experimental probabilities
- P[Ho true | rejected Ho] as opposed to P[reject Ho | Ho true]
Week 16 (Dec 4 & 6)
Final Exam