For those who may be interested in learning about current mathematical techniques applied to brain images for measuring, mapping, and modeling brain structure and function, the Institute of Pure & Applied Mathematics at UCLA will be holding a two-week workshop July 14-25. Topics will include Bayesian methods in fMRI, random field methods, multivariate methods, and connectivity models.
Description
This two-week intensive workshop will focus on mathematical techniques applied to brain images to measure, map and model brain structure and function. Topics will range from modeling anatomical structures in MRI scans, and mapping connectivity in diffusion tensor images, to statistical analysis of functional brain images from fMRI and other imaging modalities. Current applications in radiology and neuroscience will be highlighted, as will new directions in the mathematics of structural and functional image analysis. In the second week on Functional Brain Mapping, a series of lectures on diffusion tensor imaging will discuss mathematics and tools for registration, segmentation, fiber tracking and connectivity modeling in tensor and “beyond-tensor” (high-angular resolution) diffusion images, using metrics on Riemannian manifolds. Software implementing a wide range of algorithms will be demonstrated; tutorial notes will be provided. Talks will interest newcomers as well as experts in the field. Morning lectures on the principles behind the methods; afternoon lectures will go in-depth into applications.
Organizing Committee
Michael Miller (Johns Hopkins University, Center for Imaging Science)
Thomas Nichols (University of Oxford, GlaxoSmithKline Clinical Imaging Centre )
Russell Poldrack (University of California, Los Angeles (UCLA), Psychology)
Jonathan Taylor (Stanford University, Statistics)
Paul Thompson (University of California, Los Angeles (UCLA), Laboratory of NeuroImaging)
Keith Worsley (McGill University, Department of Mathematics and Statistics)
Website: http://www.ipam.ucla.edu/programs/mbi2008/
Schedule: https://www.ipam.ucla.edu/schedule.aspx?pc=mbi2008
David Liu comments in regards to "Robustness of Causal Claims" :
It was said in the paper that: "if the two estimates of b happen to disagree in a specific study, we can conclude that the disagreement must originates with violation of those extra assumptions that are needed for the second, and we can safely discard the second in favor of the first." But, if the first (minimal assumptions set) is false, then the two estimates of b may disagree too. So we can only conclude that the first or the second is false.
Clark Glymour writes:
Nancy Cartwright devotes half of her new book, Hunting Causes and Using Them, to criticizing "Bayes Net Methods"–as she calls them–and what she takes to be their assumptions. All of her critical claims are false or at best fractionally true. This paper reviews the literature she addresses but appears not to have met. Please click here to read further.
For related discussion, please see a previous post by Judea Pearl.
For those who have shown interest in obtaining slides from Judea Pearl's talk at JSM 2007 in Salt Lake City, UT entitled "The Mathematics of Causal Inference in Statistics", you may do so by visiting the following address: http://bayes.cs.ucla.edu/jsm07-final.pps
Also, we would like to invite others to share slides from their talks or provide commentary about related topics covered during the conference. Please send us your thoughts using the post submission page.
David Judkins writes:
I just saw Dylan Small give a very interesting talk in Salt Lake City on mediation analysis using random assignment interacted with baseline covariates as instrumental variables. He mentioned that Albert (2007) just established a formal definition for mediated effects with Neyman-Rubin causal language. Anyone know which Albert? Is it James Albert at Bowling Green? Any rival formal definitions for mediated effects? Page 165 of Pearl's 2000 text has a definition of indirect effects, but I didn't find it quite as satisfying as the version that Small put on the screen last week.
David Liu writes:
In Statistics and Causal Inference: A Review (Pearl 2003), it was said 'the bulk of SEM methodology was developed for linear analysis, and until recently, no comparable methodology has been devised to extend its capabilities to models involving dichotomous variables or nonlinear dependencies.' Is it true by now?
Judea Pearl writes:
A new book on causality came out last month, Hunting Causes and Using Them by Nancy Cartwright (Cambridge University Press, 2007.) Cartwright is a renown philosopher of science who has given much thought to the methodology of econometrics, and I was keenly curious to read her take on the current state of causality in economics.
Cartwright summarizes what economists such as Heckman, Hoover, Leroy and Hendry said and wrote about causal analysis in economics, she occasionally criticizes their ideas, and further discusses related works by philosophers such as Hausman and Woodward, but what I found surprising is that she rarely tells us how WE OUGHT to think about causes and effects in economic models. Given that economists admit to the chaotic state of affairs in their court, the role of philosophy should be, in my opinion, to instill clarity and provide coherent unification of the field. This I could not find in the book.
Additionally, and this naturally is my main concern, Cartwright rejects the surgery method as the basis of counterfactual and causal analysis and, in so doing, unveils and reinforces some of the most serious misconceptions that have hindered causal analysis in the past half century (see my earlier posting on Heckman's articles.)
I will focus on the latter point, for this will illuminate others.
(more…)
Judea Pearl writes:
My previous posting in this forum raised questions regarding Jim Heckman's analysis of causal effects, as described in his article, "The Scientific Model of Causality" (Sociological Methodology, Vol. 35 (1) page 40.)
To help answer these questions, Professor Heckman was kind enough to send me a more recent paper entitled: "Econometric Evaluation of Social Programs," by Heckman and Vytlacil (Draft of Dec. 12, 2006. Prepared for The Handbook of Econometrics, Vol. VI, ed by J. Heckman and E. Leamer, North Holland, 2006.)
This paper indeed clarifies some of my questions, yet raises others. I will share with readers my current thoughts on Heckman's approach to causality and on where causality is heading in econometrics.
(Post edited 5/4: revisions in red, thanks to feedback from David Pattison)
(Post edited 5/17: correction and new comments by LeRoy and Pearl)
(more…)
In reference to his previous post , Thomas Colignatus writes:
There is a first draft of the first chapter of my intended book "Elementary statistics and causality" available at http://www.dataweb.nl/~cool/Papers/ESAC/Index.html
The question on the search co-authors might have been formulated a bit strict. I would welcome comments and questions a lot. Obviously, many authors have written on causality a lot, and it is kind of silly to put things in my very own words just to prevent issues on copyrights. On the other hand I am hesitant on full collaboration since the book would be programmed in Mathematica and I know that this is a kind of skill that is not available abundantly. Permissions to quote freely, with proper reference, would be ideal, and in the end you might simply appear to be a co-author. So, take a look at this first chapter and see if your work links up to it. The next chapter is to start with notions of conditional independence.
Thomas updates (5/30):
There is now a discussion "The 2 × 2 × 2 case in causality, of an effect, a cause and a confounder. A cross-over’s guide to the 2 × 2 × 2 contingency table" available at http://mpra.ub.uni-muenchen.de/3351/.
Thomas Colignatus writes:
I plan to write a book with the working title "Basics of causality, correlation, economics and epidemiology, using graphical models. Applications of Mathematica". This book would use Mathematica (www.wri.com) as an environment, so that the reader/user can directly experiment and simulate.
It would be handy to be in contact with other users of Mathematica and to have critical proof-readers in the process, to reduce confusion and increase user friendliness. If interested, send me an email at cool@dataweb.nl. If the input is important we might turn this into a collaboration.
I am currently following a course in graphical models, given by Richard Gill in Leiden, http://www.math.leidenuniv.nl/~gill/teaching/graphical/index.html, which together with Judea Pearl's "Causality" would give a good starting point.
(more…)