Computational Statistics and Optimization Theory at UCLA

By Lange, Kenneth | The American Statistician, February 2004 | Go to article overview

Computational Statistics and Optimization Theory at UCLA


Lange, Kenneth, The American Statistician


Computational statistics is both growing in importance and evolving in nature. Graduate courses in computational statistics need to incorporate recent advances in high-dimensional optimization and integration. These advances are being driven by applications in data mining, bioinformatics, and imaging. Modern algorithms for optimization and integration can only be fully understand and extended by statisticians with considerable mathematical sophistication. Thus, graduate courses in computational statistics should stress those principles of mathematical and numerical analysis most pertinent to algorithm design and evaluation.

KEY WORDS: Algorithms; Graduate curricula; Numerical analysis.

1. INTRODUCTION

Everyone would agree that computational statistics is in flux. The last 50 years have brought enormous strides in hardware, software, modeling, inference, and numerical methods. We are both blessed and confused by these advances. Trying to guess where the field is headed is important because such prognostication will drive the education of the next generation of statisticians. Unfortunately, most of our crystal balls resemble the glass snow domes that I used to see in my youth. The discipline has been tipped upside down, and the obscuring snowflakes are descending quickly.

The two mathematical pillars upon which computational statistics rests are optimization and integration. Optimization propels maximum likelihood and least squares, the primary tools of frequentist inference. Markov chain Monte Carlo (MCMC) propels the sampling of posterior distributions, the staple diet of Bayesian inference. Our ability to optimize and integrate in high-dimensional spaces is what distinguishes the modern era. Despite the myriad directions statistics is taking, it is doubtful that either optimization or integration will be dislodged from their positions of primacy. The real issue is the right combination of theory and practice we should impart to students. My own bias is that we spend too much time on specific numerical techniques and too little time on general principles.

The ability to write computer code implementing statistical algorithms stands somewhere between practice and theory. Widely applied algorithms are available in commercial software. Research-level algorithms are not. Most students in the statistical sciences master SAS, S-Plus, or R. Despite their overall comfort with computers, surprisingly few students are facile in a lower-level language. Such ignorance is blissful until advanced students undertake time-consuming simulation studies in support of their doctoral dissertations. At this point, many students are forced to learn a lower-level language such as C or Fortran for the first time. Perhaps, waiting this long is just as well. The learning curve always seems less steep with proper motivation. While no one would argue that learning to program is wasted effort, most departments in the statistical sciences do little to foster programming directly. We all await the day when higher level systems such as MATLAB achieve speeds comparable to compiled languages.

2. THE UCLA COMPUTATIONAL STATISTICS COURSE

The flux in computational statistics is certainly reflected in the curriculum at UCLA, my own institution. The Departments of Biomathematics, Biostatistics, and Statistics have introduced a raft of courses that would have been unrecognizable 20 years ago. At the same time, these departments have maintained a traditional graduate course on computational statistics. This course was first taught by Robert Jennrich, one of the pioneers of the subject, and is now taught by Yingnian Wu, one of its current stars. Under Jennrich, the course revolved around regression analysis and variance component models. Roughly two thirds of the course still stresses these topics. The biggest change has been the introduction of MCMC methods.

None of the departments crosslisting the course require it in their doctoral programs. …

The rest of this article is only available to active members of Questia

Sign up now for a free, 1-day trial and receive full access to:

  • Questia's entire collection
  • Automatic bibliography creation
  • More helpful research tools like notes, citations, and highlights
  • Ad-free environment

Already a member? Log in now.

Notes for this article

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items

Items saved from this article

This article has been saved
Highlights (0)
Some of your highlights are legacy items.

Highlights saved before July 30, 2012 will not be displayed on their respective source pages.

You can easily re-create the highlights by opening the book page or article, selecting the text, and clicking “Highlight.”

Citations (0)
Some of your citations are legacy items.

Any citation created before July 30, 2012 will labeled as a “Cited page.” New citations will be saved as cited passages, pages or articles.

We also added the ability to view new citations from your projects or the book or article where you created them.

Notes (0)
Bookmarks (0)

You have no saved items from this article

Project items include:
  • Saved book/article
  • Highlights
  • Quotes/citations
  • Notes
  • Bookmarks
Notes
Cite this article

Cited article

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited article

Computational Statistics and Optimization Theory at UCLA
Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this article

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Full screen

matching results for page

Cited passage

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited passage

Welcome to the new Questia Reader

The Questia Reader has been updated to provide you with an even better online reading experience.  It is now 100% Responsive, which means you can read our books and articles on any sized device you wish.  All of your favorite tools like notes, highlights, and citations are still here, but the way you select text has been updated to be easier to use, especially on touchscreen devices.  Here's how:

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select.

OK, got it!

Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.

For full access in an ad-free environment, sign up now for a FREE, 1-day trial.

Already a member? Log in now.