MTH 412/512 Intro To Statistical Inference Spring 2021 .
MTH 412/512 Intro to Statistical InferenceInstructor: Brian Spenceremail: spencerb@buffalo.eduSpring 2021TA: Raymond Hutchingsemail: rhhutchi@buffalo.eduLectures: Tue/Thu 11:10-12:25 online lectures and discussion using Zoom (see UBLearns foraccess info).Recitation: Recitation for MTH 412 students meets Tue 5:30-6:20 with our TA to go overexercises and answer questions about homework from the previous week. MTH 512 studentsare also welcome to attend. See UBLearns for Zoom access.Virtual Office Hours: on Zoom for talk/screenshare/whiteboard (see UBLearns for schedule).Course InformationStatistics for advanced undergraduate / beginning graduate students in mathematics, scienceand engineering who have had a one-semester course in probability. The course emphasizesdevelopment of rigorous proofs of statistical results, understanding of the limitations ofstatistical analysis, usage of statistical packages written in the language R, and analysis of realworld data from case studies.Prerequisite: MTH 411/511Dual-listed course: MTH 412 students take the course for 4 credits and have a one-hourrecitation each week. MTH 512 students take the course for 3 credits and do not haverecitation. MTH 412 and MTH 512 students will have separate grading scales.Course Description: Rigorous derivation of statistical results, clarification of limitations ofstatistical analysis, extensive use of computational software, application of statistical methodsto case studies. Topics include: Graphical and numerical techniques for exploring data. Use andaccuracy of population samples using parametric and nonparametric methods. Determinationof probability distributions from statistical data. Use of computational methods based onresampling of data to determine reliability of statistical information. Classical statisticalinference methods: probability distribution estimation, confidence intervals for statisticalresults, hypothesis testing for statistical significance. Fitting of data using linear regression anddetermining the accuracy of fit. Bayesian methods for estimating probability distributions usingprior information.revised 1/30/20211
Syllabus of Topics: [0.5 wk] Data and Case Studies (Ch 1) – introduction to data and statistical questions usingcase studies [1 wk] Exploratory Data Analysis (Ch 2) – techniques for analyzing data using graphicalrepresentations (histograms, boxplots, quantile plots, cumulative distributions, scatterplots) and numerical measures (mean, median, trimmed mean, quartiles, standarddeviation, skewness, kurtosis) [1wk] Hypothesis Testing (Ch 3) – using hypothesis testing to evaluate statisticalsignificance: null hypothesis, alternative hypothesis, test statistic, p-value, one-sided vs twosided tests, permutation tests (in general and via resampling) [1 wk] Sampling Distributions (Ch 4) – sampling and sampling distributions, central limittheorem as applied to sampling statistics for continuous and discrete data [1 wk] The Bootstrap (Ch 5) – bootstrap method, plug-in principle, estimation of populationparameters, accuracy, bias, Monte Carlo sampling [1 wk] Parameter Estimation (Ch 6) – maximum likelihood estimation of distributionparameters, method of moments, unbiasedness, efficiency, mean square error, consistency,transformation invariance [1.5 wks] Classical Inference: Confidence Intervals (Ch 7) - confidence intervals for meansand difference of means, t-statistic, other applications of confidence intervals, usingbootstrap method to determine confidence intervals [1.5 wks] Classical Inference: Hypothesis Testing (Ch 8) – hypothesis tests for means andproportions, type I and type II errors, significance level, power of a test, statisticalsignificance vs practical importance, adjustments for multiple testing, likelihood ratio tests,Neyman-Pearson Lemma [1wk] Regression (Ch 9) – covariance, correlation, least-squares regression, residualanalysis, simple linear models and confidence intervals, resampling methods, logisticregression [1 wk] Categorical Data (Ch 10) - contingency tables, chi-square statistics, testing forindependence, homogeneity, goodness of fit [1.5 wks] Bayesian Methods (Ch 11) – Bayes' theorem (prior, likelihood, posteriordistributions), implementation and computational issues, Bayesian analysis of binomial datafor discrete and continuous prior distributions, Bayesian analysis of continuous data,Bayesian method for sequential dataLearning Outcomes: Upon successful completion of this course students will be able to: describe data sets using statistics and represent data graphically (Ch 1-2 HW, Exam 1) use statistics to determine if data supports a theory or not (Ch 3 - 11 HW, Exam 1,2,3) determine the reliability of statistical information using probability-based or computationalbased tests (Ch 4,5,7,8,10 HW, Exam 2,3) find correlations in data and quantify the variability in the correlations (Ch 9 HW, Exam 3) use prior information about a system in a statistical analysis of data (Ch 11 HW, Test #3) use R programming language for statistical analyses (Ch 2-11 HW)These student learning outcomes incorporate the learning objectives of the undergraduatemathematics program as described here: ograms.html2
Course MaterialsText: Mathematical Statistics with Resampling and R, by Laura Chihara andTim Hesterberg (2nd edition, Wiley, 2018) ISBN: 978-1119416548[*do not get 1st edition*].UBLearns: UBLearns is the central online component for the course. It contains the syllabus,instructions, course notes, R programs, homework assignments, homework solutions, links toclass recordings, important announcements. Updated each class. Urgent announcements willbe sent by email through UBLearns.Zoom: I will use Zoom for live class sessions and office hours (video, talk, text, screen sharing,whiteboard, etc). Guidelines for in-class Zoom usage are posted on UBLearns.In-class Materials: I post course materials (notes, example codes, other handouts) on UBLearnsin advance of class and give a presentation based on these materials during class time. Atypical class involves going through ideas/theory/examples from the notes, combined with lineby-line discussion of calculations/examples using R programs and figures.Computational Software: The programming language R will be used to illustrate computationbased methods from class. The programs will be written and executed within a JupyterNotebook environment in which the code, text descriptions and output appear in a singledocument. Students will be required to use R for some assignments. Example code forcalculations will be presented in lecture, with a copy of the program available for download viaUBLearns. Instructions for installing the necessary (free) software Anaconda3 / JupyterNotebook and setting it up to run programs in R will be posted on UBLearns during the firstweek of class. Prior experience with R is not necessary.Gradescope: Homework and exams are submitted through gradescope.com. Instructions forsetting up an account and submitting work to gradescope are posted on UBLearns.Panopto: Video streaming service licensed by UB to providing access the lecture recordings.There will be a link to Panopto on UBLearns.Course Workflow: The course materials for each class posted will be posted on UBLearns by 5pm the daybefore class (it not, I will notify you by email about the delay). Have the notes/code examples in front of you before class (either printouts or online) sothat you can make your own annotations. Attend class virtually: either live via Zoom or by watching the video of the Zoom classposted on UBLearns. I strongly suggest rewriting the course notes yourself after class, before attempting thehomework, to help reinforce understanding of the material. This process is as important asdoing the homework. After reviewing the notes, read the assigned sections of the textbook, then work on theexercises/homework. If you have questions or need help, ask for help from the instructor3
or TA by email or during office hours (it is most efficient if you can send/screenshare a scanof your work).Recitation section meets Tue 5:30-6:20 to go over exercises and answer questions abouthomework from the previous week.Homework from the previous week will be Wednesday at 11pm; plan ahead!CourseworkAttendance Policy: You are expected to attend every class virtually, either live (on Zoom) orasynchronously (by watching the class video).Exercises: These are questions/problems for you to do on your own to reinforce learning ofmaterial from class. "Exercises" are not submitted for grading; answers for checking your workwill either be given in the back of the book or posted on UBLearns.Homework Assignments: Almost every class there will be a homework assignment "HW"posted on UBLearns: Written step-by-step solutions to the homework assignments are to be submitted togradescope by the due date specified on UBLearns. Generally, problems for a givenweek will be due Tuesday 11:00pm of the following week. Format for Homework Set Problems:o Homework solutions should be written in pen or dark pencil so that the writing is legiblewhen scanned/photographed. Solutions produced by word processing software LaTeX,Word, OpenOffice etc are also acceptable.o Use a separate page for each problem.o Scan your completed homework to a pdf file (see instructions on ublearns "gradescope"for instructions on making a pdf if you do not have a scanner).o Upload your homework to your account on gradescope.com (see ublearns forinstructions) then associate which pages of your work go with which question.o Homework must be submitted by deadline for full credit. Homework problems are graded using the rubric below and the homework grade isdetermined by adding the total points of all assignments and using a grading scalesimilar to the rubric below.Late homework policy: Homework is due on gradescope by 11:00pm on the due date.Late homework is accepted with the following penalties:o turned in by 11:59pm on due date: -10%o turned in by 11:59pm day after due date: -20%o 20% penalty per day for each day thereafter.Exams are taken during the scheduled exam times while on Zoom. The exam questions will beonline and administered through the UB Math Department using 2-device proctoring describedhere: https://exams.ubmath.info/index.html. More detailed instruction be given in advance ofthe exam. The exam dates are Exam #1 in lecture on Thu Mar 4 Exam #2 in lecture Thu Apr 1 Exam #3 (during finals week) Tue May 11 from 11:45am-2:45pm4
GradesCourse Grades are determined by averaging the grades with the following weightings:Exam #120%Exam #220%Exam #325%Homework 35%Grading Rubric: Points for homework and exam questions are allocated using the followingguidelines (assuming 10-point question):10/10 - Correct method, clearly presented, correct answer. No significant mistakes(grade A work).8/10 - Correctly captures the essential method or idea in the solution of the problem, isclearly presented, but has one or more minor errors (grade B work).6/10 - Displays some understanding of the underlying concepts and ideas but thesolution contains significant errors in execution of the details (grade C work).4/10 - Questionable understanding of the underlying concepts and ideas and/or majorerrors (grade D work).2/10 - Minimal progress, but some parts of the solution are not totally incorrect (gradeF work).0/10 - The solution has no redeeming features (grade F).Point scores are scaled proportionally for problems of 5 points, 15 points, etc.Each exam grade and the overall homework grade will be determined by the point score using agrading scale similar to the rubric above.5-point grading scale: For calculating course grades on exams and homework a 5-point scale isused:A 4.66-5.00A 4.33-4.66A- 4.00-4.33B 3.66-4.00B 3.33-3.66B- 3.00-3.33C 2.66-3.00C 2.33-2.66C- 2.00-2.33D 1.66-2.00D 1.33-1.66D- 1.00-1.33F 0 - 1.00 /- grades will be used in assigning course grades. Note: the university does not permit A orD- grades (A is submitted as A, D- as D).5
Other Administrative DetailsUB Statement on Academic Integrity: Academic integrity is critical to the learning process. It isyour responsibility as a student to complete your work in an honest fashion, upholding theexpectations your individual instructors have for you in this regard. The ultimate goal is toensure that you learn the content in your courses in accordance with UB’s academic integrityprinciples, regardless of whether instruction is in-person or remote. Thank you for upholdingyour own personal integrity and ensuring UB’s tradition of academic excellence.Instructor Expectations Academic Integrity: Students must obey the university policy onacademic integrity in all their coursework including homework, computer programs and examsadministered online. Cheating, plagiarism, or representing the work of others as your own willbe formally reported following the university policies on Academic Integrity as outlined hp.Technology Recommendations: To effectively participate in this course, regardless of mode ofinstruction, the university recommends you have access to a Windows or Mac computer withwebcam and broadband. Your best opportunity for success in the blended UB course deliveryenvironment (in-person, hybrid and remote) will require these minimum capabilities.Make-up Exams: If, due to severe circumstances beyond your control (car accident, illness,death in the family, etc), you will not be able to take an exam, please contact me immediately(before the exam) and let me know your situation. If you have a valid reason and can presentadequate documentation we can make arrangements for a make-up exam to be taken at theend of the semester.Incompletes: Incompletes will be given only under extraordinary circumstances (like surgeryduring the last week of class). Per university rules a student must have a passing grade topetition for an incomplete.Accessibility Resources: If you have any disability which requires reasonable accommodationsto enable you to participate in this course, please contact the Office of Accessibility Resourcesin 60 Capen Hall, 716-645-2608 and also the instructor of this course during the first week ofclass. The office will provide you with information and review appropriate arrangements forreasonable accommodations, which can be found on the web epartments/accessibility.html.Important Dates:Mon Feb 8 - Last day to drop the course - no record appears on transcript.Fri Apr 16 - Last day to resign from the course - an 'R' appears on transcript.6
Lecture Scheduletue feb 2 - syllabus, review of probabilitythu feb 4 - Data and Case Studies (Ch 1)tue feb 9 - Exploratory Data Analysis (Ch 2) [Part 1 of 2]thu feb 11 - Exploratory Data Analysis (Ch 2) [Part 2 of 2]tue feb 16 - Hypothesis Testing (Ch 3) [Part 1 of 2]thu feb 18 - Hypothesis Testing (Ch 3) [Part 2 of 2]tue feb 23 - Sampling Distributions (Ch 4) [Part 1 of 2]thu feb 25 - Sampling Distributions (Ch 4) [Part 2 of 2]tue mar 2 - review for Exam #1thu mar 4 - Exam #1tue mar 9 - The Bootstrap (Ch 5) [Part 1 of 2]thu mar 11 - The Bootstrap (Ch 5) [Part 2 of 2]tue mar 16 - Parameter Estimation (Ch 6) [Part 1 of 2]thu mar 18 - Parameter Estimation (Ch 6) [Part 2 of 2]tue mar 23 - Classical Inference: Confidence Intervals (Ch 7) [Part 1 of 3]thu mar 25 - Classical Inference: Confidence Intervals (Ch 7) [Part 2 of 3]tue mar 30 - Classical Inference: Confidence Intervals (Ch 7) [Part 3 of 3] / review for Exam #2thu apr 1 - Exam #2tue apr 6 - Classical Inference: Hypothesis Testing (Ch 8) [Part 1 of 3]thu apr 8 - Classical Inference: Hypothesis Testing (Ch 8) [Part 2 of 3]tue apr 13 - Classical Inference: Hypothesis Testing (Ch 8) [Part 3 of 3]thu apr 15 - Regression (Ch 9) [Part 1 of 2]tue apr 20 - Regression (Ch 9) [Part 2 of 2]thu apr 22 - Categorical Data (Ch 10) [Part 1 of 2]tue apr 27 - Categorical Data (Ch 10) [Part 2 of 2]thu apr 29 - Bayesian Methods (Ch 11) [Part 1 of 2]tue may 4 - Bayesian Methods (Ch 11) [Part 2 of 2]thu may 6 - review for Exam #3finals week - Exam #3 [tue may 11, 11:45am-2:45pm]revised 1/30/20217
development of rigorous proofs of statistical results, understanding of the limitations of statistical analysis, usage of statistical packages written in the language R, and analysis of real-world data from case studies. Prerequisite: MTH 411/511 Dual-listed course: MTH 412 students take the course for 4 credits and have a one-hour
Current Eligibility Placement Chart Course GPA Additional Course ENG 111-College Composition 3.0 None MTH 154-Quantitave Reasoning 3.0 None MTH 155-Statistics 3.0 None MTH 161-PreCalculus I 3.0 HS Algebra 2 MTH 167Combined PreCalculus I/II 3.0 HS Algebra 2 MTH 162-PreCalculus II 3.2 Math Analysis MTH 245-University Statistics 3.2 Math Analysis or Statistics MTH 261-Applied Calculus 3.2 Math .
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Contest Rules of the University Interscholastic League 2017-2018 Telephone: 512-471-5883 Theatre Only: 512-471-9996 P.O. Box 8028 Austin, Texas 78713 Fax: Administration - 512-471-5908 Fax: Academics - 512-232-7311 Fax: Athletics - 512-471-6589 Fax: Theatre - 512-471-7388 Fax: Order Department - 512-232-6471 E-mail Addresses:
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