212 karma · joined August 30, 2009
For instance, Yahoo Mail puts my IP address in a line like this
Received: from [xxx.xxx.xxx.xxx]
For model year 2009, Volkswagen had 11.5 complaints per 100k vehicles, whereas Toyota had 7.5 and BMW 5.8
Two experimenters contrast treatments A and B. They both have A preferred to B in first 5 patients, and B preferred in the 6th. First experimenter planned to run 6 experiments and count the number of successes, so they get P-value 0.11 for the hypothesis that A is better. The second experimenter planned to run comparisons until B is preferred, up to 6, and got P-value of 0.03. (see Appendix A of http://www.annals.org/content/130/12/995.full.pdf+html)
A realistic example of this issue coming up http://www.jstor.org/pss/2336980
Another example is choosing between one-tailed and two-tailed t-test. When you ask for the probability of effect being as extreme as observed x under null hypothesis, should you ask for probability of effect>x or |effect|>|x|?
Eliezer Yudkowsky goes into some discussion on this http://lesswrong.com/lw/1gc/frequentist_statistics_are_frequ...
The most illustrative example of subjectivity of hypothesis testing is probably the issue of testing strings for randomness. There are many tests for testing whether a particular string of bits is generated by a Bernoulli process, with not one having a legitimate claim to being "the right one"
One way to remove the bias is three-way triple-blind testing, ie to measure effects of existing, new, and placebo treatments, have statistician analyze datasets while blinded to their true labels.
L1 minimization here refers to trying to represent the image as a linear combination of basis functions a1 f1+a2 f2+ ... by minimizing objective function fit(a1,a2,...)+sum_i |a_i| where "fit" represents how closely the reconstruction fits the image (for instance, squared distance). The second term in the sum is the L1 norm of the parameter vector, and it has a special property of being non-differentiable at 0, and often causing individual components a_i to become exactly 0 during minimization, hence resulting in "sparse" solution vector.
Compressed sensing refers to the idea that when the image is sparse in the chosen basis {fi}, it's sufficient to take a small number of random measurements of the image. We can then compute "fit" approximately which gives us a different objective function that we minimize. The result will be close to what we'd get if we used the original (full) "fit" function
http://www.niehs.nih.gov/news/events/pastmtg/2007/cehr/docs/...
Funny enough, I have the same issue with my old student ID -- it works to get access to those databases long after I graduated
"Digital Image Processing Using MATLAB" ended up the most useful, along with some basic Matlab tutorials
here's what I ended up with http://yaroslavvb.blogspot.com/2009/08/robust-ocr-in-video.h...
This is a bit of an anathema to purist Bayesians like Radford Neal who say that Jaynes Maximum Entropy method is not consistent with Bayesian methods and that it "doesn't make any sense"
http://groups.google.com/group/sci.stat.consult/msg/2cf57ceb...
Now comes the cuasality connection -- if the best model is P(A)P(B)P(C|A,B) you read it as A->C<-B. If best model is P(A)P(B|A)P(C|B), you read it as A->B->C. (ie, A causes B, B causes C)
I think causality connection is questionable because the model that corresponds to A->B->C will have the same fit as model for A<-B<-C or A<-B->C. In fact, you could take any causal network without loops and "unshielded colliders" (connections of the form A->B<-C), pick any node as a root, and re-order the arrows to face away from the root to get a model with a different semantic causal structure, but the same mathematical structure, meaning it'll give identical fit to data.
What would be really interesting is if someone deduced causality using Pearl's approach, then verified it using a direct experiment