AdvancedDataAnalysis - News · AdvancedDataAnalysis Lecture:Mon,Wed,Fri ... Measuresofpositionofnibofapenwriting"fda". 20replications, ... packagesinR,Matlab Goals: ...

Advanced Data Analysis

Lecture: Mon,Wed,Fri12:30 - 1:30 PMWSC 248

Lecturer: Jiguo Cao

Office Hours: Friday1:30-2:30pm WSC278

http://www.stats.uwo.ca/faculty/cao/Teaching/FDA/

What is Functional Data?

What are the most obvious features of these data?

I quantityI frequency (resolution)I similar trends



I quantity

I frequency (resolution)I similar trends



I quantityI frequency (resolution)

I similar trends



I quantityI frequency (resolution)I similar trends


Most important: smoothness

These data describe (nearly) aprocess that changes smoothing,and continuously over time.Functional Data Analysis =Analysis of data that arefunctions.Domain is usually time, but canbe anything: space, energy ...



These data describe (nearly) aprocess that changes smoothing,and continuously over time.

Functional Data Analysis =Analysis of data that arefunctions.Domain is usually time, but canbe anything: space, energy ...



These data describe (nearly) aprocess that changes smoothing,and continuously over time.Functional Data Analysis =Analysis of data that arefunctions.

Domain is usually time, but canbe anything: space, energy ...



These data describe (nearly) aprocess that changes smoothing,and continuously over time.Functional Data Analysis =Analysis of data that arefunctions.Domain is usually time, but canbe anything: space, energy ...


20 replications

Functional data analysis involves repeated measures of the sameprocess.


20 replications, 1401 observations within replications

Functional data is oftencomplicated:

I not easily described bymathematical formulae

I variation betweenreplications even harder todescribe


20 replications, 1401 observations within replications, 2 dimensions

Functional data is oftencomplex:

I often a large number ofrelated quantities

I viewing each replication asa single observation canmake the data easier tothink about (once we havethe right machinery)

I What are these data, anyway?I What if I plot one component against another?
























I What are these data, anyway?

I What if I plot one component against another?







Classical Functional DataMeasures of position of nib of a pen writing "fda". 20 replications,measurements taken at 200 hertz.

Characteristics

I Data are measurements of smooth processes over timeI We usually do not want to make parametric assumptions

about those processes.I Often have multiple measurements of the same processI We are interested in describing the variation of processes.I Frequently, collected data have high resolution and low noise.I Can be applied to any estimate of a smooth process.

About Functional Data Analysis

1. FDA is NewI First named in Dalzell & Ramsay, 1991I Relatively little penetration into applied fields (= easy

publication)I Several competing methodologies (we focus on one)I Limited public software/resourcesI data analysis rather than inference

2. Functional Data is ComplexI Requires more thought/judgement than a t-testI data needs pre-processingI parametric inference is rarely available/appropriate

What will this course offer?

Audience: application areas with functional dataFocus: I What can Functional Data Analysis do?

I How do I make it happen?Software: packages in R, Matlab

Goals: Enabling you toI Understand and interpret the result of FDA

applied to real dataI Use existing FDA libraries to analyze functional

dataI Evaluate its usefulness/correctnessI Extend the methods in existing software if you

need toNot Covered: reproducing-kernel Hilbert spaces, asymptotics,

theorems...

Pre-requisites and Recommendations

Pre-requisites: multiple linear regressionUseful: Life will be easier if you do not need to learn some of

the following:

I R/Matlab or other programming experienceI CalculusI Matrix algebraI Multivariate statisticsI Computational statistics

Any necessary material will be covered in class, butwill be out of context.

Resources

Textbook: Ramsay and Silverman, 2005, Functional DataAnalysis, Springer.

Books: I Ramsay and Silverman, 2002, Applied FunctionalData Analysis, Springer.

I Ramsay, Hooker and Graves, 2009, FunctionalData Analysis with R and MATLAB, Springer

Online: I http://www.functionaldata.org for FDAI http://www.r-project.org a general site for RI

http://www.stats.uwo.ca/faculty/cao/Teaching/FDA/All class notes, exercises etc will be posted here.

I Class materials will also be posted to Blackboard;a general discussion board has also been set up.

Assessment

3 Assignments (10% each) I Using the FDA libraries to analyzedata

I Interpreting results of this analysisI Some simulation studies

Class Project (70%) I Analysis of real-world dataI End of semester presentationI Written report.I Paper publishing.

Example: C. X. Feng, J. Cao, and L.Bendell-Young (2011) “Exploring Spatial andTemporal Variations of Cadmium Concentrationsin Pacific Oysters from British Columbia".Biometrics 67, 1142-1152.

Policies

I Never miss any classes, because classes are importantI Questions are always very welcomed. No questions are naÃŕve.

You are helping other students by asking questions.I Except asking questions loudly, never talk with your neighbors.

Please share your questions with all of us. Respect otherstudents.

I Turn off your cellphone.I Try to talk with me after class or in my office hours. Try not

to send me emails. I may read emails, but almost never answeremails.

Policies

I Turn in your assignments before the deadline. No lateassignments will be accepted for any reason. If you do not turnin your assignment on time, the percentage of the assignmentmark will be added to the percentage of the final exam.

I you are welcome to discuss homework, but you should do andwrite it individually

I project will be done individually

AdvancedDataAnalysis - News · AdvancedDataAnalysis Lecture:Mon,Wed,Fri ... Measuresofpositionofnibofapenwriting"fda". 20replications, ... packagesinR,Matlab Goals: ...

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