Smoothing with P-splines (Using R)

taught by Brian Marx
and Paul Eilers

Brief Description:

Splines are combinations of different functions that are used to describe and model data differentially in a smooth fashion over different ranges.  In this course, you will learn how to use R software to develop splines for data smoothing.

Instructor(s):
Level: ADVANCED / INTERMEDIATE - see prerequisites

Who Should Take This Course:

Medical and social science researchers, data miners, environmental analysts;  any researcher who must develop statistical models with "messy" data.

Dates:
June 22, 2012 to July 20, 2012December 07, 2012 to January 11, 2013
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Registration:
Please read the syllabus tab, noting the prerequisites, text and software requirements.

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Register Online -$399 (you must be affiliated with a college, university or high school)

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Smoothing with P-splines (Using R)

taught by Brian Marx
and Paul Eilers

Aim of Course:

The linear model is ubiquitous in classical statistics, yet real-life data rarely follow a purely linear pattern.  In fact, real-life data often do not follow a pattern that is well-described by a single simple function of any sort.  Splines are combinations of different functions that are used to describe and model data differentially in a smooth fashion over different ranges.

P-splines are especially popular (over 500 citations for the instructors' original article in Statistical Science introducing P-splines) because they are widely applicable and effective. In this course, you will learn how to use R software for data smoothing via P-splines - a combination of regression on a B-spline basis (basis splines) and difference penalties (on the B-spline coefficients).

Smoothing is presented as an everyday tool for data analysis and statistics.  The course starts with univariate P-splines smoothing using B-splines and penalties, then extend such tools into the generalized linear model framework, specifically through Poisson and binomial smoothing. This leads to a natural development in density estimation. The optimal amount of smoothness, via the choice of a positive tuning parameter, is suggested through both cross-validation and AIC.  We further extend P-spline modeling, demonstrating its adaptive ability to accommodate rich data structure, including: varying coefficient models, generalized additive models, and full two-dimensional smoothing using tensor product P-splines. We close with some extensions to high dimensional regression, where the regressors are in the form of signals or curves.

You will learn how to balance the competing demands of fidelity to the data and smoothness, and how to optimize the smoothing.  The final session of the course covers multidimensional smoothing.

This course is a core requirement or elective in the following Program(s) in Analytics and Statistical Studies (PASS):

• Using R

Prerequisite(s):

• Introduction to R - Data Handling
• Introduction to R - Statistical Analysis

Recommended:

• Generalized Linear Models (GLM)
• Modeling Count Data

Course Program:

SESSION 1:  Smoothing via Regression - Local vs Global Bases

• Global bases can be ineffective
• Local bases are attractive
• B-splines
• Difference penalties

 

SESSION 2: Introducing P-splines

• Dealing with non-normal data
• Moving from GLM to P-spline
• Density estimation
• Variance smoothing

 

SESSION 3: Optimizing the Smoothing

• Fidelity to the data vs smooth curve
• Cross-validation, AIC
• Error bands

 

SESSION 4: Multidimensional Smoothing

• Generalized Addition Models
• Varying coefficient models
• Tensor products

HOMEWORK:

Homework in this course consists of guided data analysis problems using software and guided data modeling problems using software.

Organization of the Course:

This course takes place over the internet at the Institute for 4 weeks. During each course week, you participate at times of your own choosing - there are no set times when you must be online. Course participants will be given access to a private discussion board. In class discussions led by the instructor, you can post questions, seek clarification, and interact with your fellow students and the instructor.

The course typically requires 15 hours per week. At the beginning of each week, you receive the relevant material, in addition to answers to exercises from the previous session. During the week, you are expected to go over the course materials, work through exercises, and submit answers. Discussion among participants is encouraged. The instructor will provide answers and comments, and at the end of the week, you will receive individual feedback on your homework answers.

Credit:
Students come to the Institute for a variety of reasons. As you begin the course, you will be asked to specify your category:

1. You may be interested only in learning the material presented, and not be concerned with grades or a record of completion.
2. You may be enrolled in PASS (Programs in Analytics and Statistical Studies) that requires demonstration of proficiency in the subject, in which case your work will be assessed for a grade.
3. You may require a "Record of Course Completion," along with professional development credit in the form of Continuing Education Units (CEU's).  For those successfully completing the course, 5.0 CEU's and a record of course completion will be issued by The Institute, upon request.

Course Text:

The text will be provided.

Software:

We emphasize the use of modern softwar and we provide functions for R/S-Plus.  The text and R-code will be provided.  You must have a copy of R for the course. Click Here for information on obtaining a free copy.

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Smoothing with P-splines (Using R)

taught by Brian Marx
and Paul Eilers

Instructor(s):
Dates:
June 22, 2012 to July 20, 2012December 07, 2012 to January 11, 2013
Course Fee: $499
Academic Rate: $399

Before registering, please read the syllabus tab, noting the prerequisites, text and software requirements. When you click the register button, you will be taken to our secure transaction page.

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