Do not worry about your difficulties in mathematics; I can assure
you that mine are still greater. -Albert Einstein (1879-1955)
- R download
- See Chapter 1 Notes, pages 3-6 for install and data-entering tutorial.
- Springer textbooks for using R on-line (can only use from campus connections)
- Applets advocated by your textbook.
- DUE 5/1 at 4pm. Turn in a typed report which includes all R code and a spreadsheet of the data you use. Organization is key. Pose a question of interest to you and perform the scientific method to help answer the question. Provide backgroun info in your report. Of course, you will need to collect data yourself or gather some existing data set - either way, indicate clearly where the data are from, and provide any necessary citations. Apply some of the techniques we have learned in class to that data set to answer the scientific question of interest. For example, calculate point or interval estimates using frequentist or Bayesian techniques. And/or perform a hypothesis test using frequentist or Bayesian techniques. You will be graded based on how much you do. For example, be clear regarding why you use the point estimator that you do - is it sufficient, consistent, asymptotically efficient, or asymptotically normal? Explain. If you perform a hypothesis test, is the test you use uniformally most powerful? Explain. Derivations of non-standard estimators and tests are encouraged but not necessary. For example, in class when we assumed that the data were exponential, we easily derived the most powerful test (which uses a test statistic with a Gamma distribution).
- 5/1, Tuesday, Final Exam, 4pm - 6pm, cumulative. List of topics. Closed book. You may use a single one-sided 8"x11" sheet of notes. You will be given a sheet of common distributions (like in the back cover of your text), and this sheet of formulas
- 4/4, Wednesday, Exam 2 on chapters 7, 8, 9, 10, 16. List of topics. Closed book, no notes. You
will be given a sheet of common distributions (like in the back cover of
your text), and this sheet of formulas (which now includes the Cramer Rao lower bound as well as some other additions).
Here's some suggested practice problems:
- Chapter 10 (hypothesis testing): 1, 3, 17, 21-27 odd, 33, 35, 43, 51, 55, 57, 61-77 odd.
- Chapter 16 (Bayesian estimation): 1, 2, 7, 9b (you already did 9a in #2 HW6), 13(a-c, h) (This problem is like #4-5 in HW6 - use R for the calculations).
- 2/17 Exam 1 on chapters 7, 8 and 9, here's a list of topics. Closed book, no notes. You will be given a sheet of common distributions (like in the back cover of your text), and this list of formulas.
- DUE: 4/25 Project 8 on Chapter 10. Solutions: pdf, docx
- DUE 4/20 Project 7 on Chapter 10. Mountain biking article. Please reserve your questions on this HW until I return on 4/16. We can not expect the guest speaker in class 4/11 and 4/13 to be prepared to answer HW questions. Solutions: pdf, docx
- DUE 3/30 Project 6 on Chapter 16. Solutions: #1-4: pdf, docx; #5-10: pdf
- DUE 3/9 Project 5 on Chapter 9. Solutions: pdf, docx
- DUE: 2/15 Project 4 on Chapter 9. Solutions: pdf, docx
- DUE: 2/10 Project 3 on Chapter 8. Solutions: pdf, docx
- DUE: 2/3 Project 2 on Chapters 7 and 8. Solutions: pdf, docx
- DUE: 1/27 Project 1 on Chapter 7. Solutions: pdf, docx
- 5/1 4pm-6pm Final Exam
- 4/27 Course Review
- 4/25 Equivalence tests (see paper from Quality Engineering, this link will work from MSU's campus - otherwise: pdf), Bonferroni multiple testing procedure (see Example 13.9 in your textbook).
- 4/23 §10.9, 16.4 Hypothesis tests of two population variances,
example using the deer data,
Bayesian tests of hypotheses
- 4/20 §10.10-11 Likelihood Ratio Tests, asymptotic chi-square LRT statistic, LRT for exponential data
- 4/18 §10.10 The most powerful test for the mean of an exponential distribution
- 4/16 §10.9 The most powerful test for the variance from a
single population
- 4/13 §10.10 Powerful tests and the Neyman Pearson Lemma: hand out
- 4/11 §10.8 Hypothesis testing for 2 sample means: hand out
- 4/9 §10.4,10.6 Sample Size calculations, hypothesis testing with
CIs
- UNIVERSITY DAY - No class
- Exam 2
- Review
- 3/30 §10.2 Hypothesis testing with rejection regions
- 3/28 §10.3, 10.8 Hypothesis testing with asymptotically normal estimators, one-sample t-test
- 3/26 §10.2,10.4,10.7 Type I and Type II errors
- 3/23 §10.6 Hypothesis testing with p-values, one-sample test of proportions
- 3/21 §16.5; 10.1-2 Posteriors vs likelihoods; Hypothesis Testing and the Scientific method
- 3/19 §16.2-3 Bayesian posteriors for a normal mean and variance
- 3/9 §16.2-3 Bayesian posteriors for a normal mean
- 3/7 §16.2-3 Bayesian point and interval estimators
- 3/5 §16.2 How to choose a prior. And who needs marginals
anyways? Chapter 16 notes
- 3/2 §9.7, 16.1 When calculus doesn't find the MLE, Bayes rule, posterior and prior information
- 2/29 §9.8 Asymptotic efficiency of MLEs, Cramer-Rao lower bound for MLE variance, CLT for MLEs
- 2/27 §9.7 Invariance property of MLEs
- 2/24 §9.7 MLE examples: Poisson and normal. Three beautiful MLE properties: sufficiency, MVUE, consistency
- 2/22 §9.6-7 Method of moments, method of maximum likelihood
- 2/17 Exam 1
- 2/15 Review
- 2/13 §9.5 Rao-Blackwell Theorem,
MVUE examples: binomial proportion, normal
mean, normal variance
- 2/10 §9.4 Sufficiency, Factorization Theorem, likelihood function
- 2/8 §9.3 Common consistent point estimators for the population mean, variance and standard devation; Stutsky's Theorem.
- 2/6 §9.3 Consistency, General Weak Law of Large Numbers
- 2/3 §8.9 Two-sample CI for a difference in means assuming equal variances, CI for a population variance, Calculating CI's in R: Alligator means, Biofilm repeatability.
- 2/1 §8.7-8 Sample size calculations, CIs for parameters whose estimators are (asymptotically) normal and the variance is UNknown, two-sample CI for difference in means
- 1/30 §8.6 CIs for parameters whose estimators are
(asymptotically) normal and the variance is known
- 1/27 §8.5 Pivotal method
- 1/25 §8.5 Confidence intervals
- 1/23 §8.1-8.4 point and interval estimators, bias, MSE, MVUEs.
- 1/20 §7.4 F distribution
- 1/18 §7.2,7.4 Sampling distributions: N(0,1), chi-square, t
- 1/13 §7.5 Normal approximation of the binomial
- 1/11 §7.1-7.3 Sampling Distributions and
the Central Limit Theorem, Chapter 7 notes.
- Montana State University
- Department of Mathematical Sciences
- Registrar: