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What is a polytope sampler? Link to work?
It's just a vanilla (MH) MCMC sampler for (some convenient family of) distributions on polytopes; hopefully like this: http://cran.r-project.org/web/packages/limSolve/vignettes/xsample.pdf , but faster. It's motivated by a model for inferring network link traffic flows from counts of in- and out-bound traffic at each node; the solution space is a polytope, and we want to take advantage of previous observations to form a better prior. But for the approach to be feasible we first need to sample.
But this is not a long-term project, I think.
It seems like you might want to check this guy's work out.
Looks like good stuff ... thanks for the tip.
I am curious: what do you plan to work on in stats?
I personally think more people should be working on efficient general sampling methods for Bayesian stats, for reasons I have written about here: http://goodmorningeconomics.wordpress.com/2010/11/16/the-promise-of-bayesian-statistics-pt-2/ .
Programming skills are very useful there. I am a programmer and one of my hobbies is implementing bayes stats algorithms in the literature. Do let me know if you come up with anything revolutionary.
Currently I'm taking classes and working on a polytope sampler. I tend to be excited about Bayesian nonparametrics and consistent families of arbitrary-dimensional priors. I'm also excited about general-purpose MCMC-like approaches, but so far I haven't thought very hard about them.
In response to
What Else Would I Do To Make a Living?
In undergrad I feared a feeling of locked-in-ness, and ditched my intention to do a PhD in math (which I think I could have done well in) partly for this reason, though it was also easier for me because I hadn't established close ties to a particular line of research, and because I had programming background. I worked a couple of years in programming, and now I'm back in school doing a PhD in stats, because I like probability spaces and because I wanted to do something more mathematical than (most) programming. I guess I picked stats over applied math partly out of the same worry about overspecialization; I think stats has a bigger wealth of better-integrated more widely applicable concepts/insights.
In response to
Open Thread: Mathematics
What should you use for the "ignorance prior" for the value of a continuous random variable whose underlying distribution is unknown? (For a random variable that is both discrete and finite, you can always use the uniform distribution as your prior, but that doesn't work when the variable can take an infinite number of values.) And you can't always use an improper prior, either...
Would you be surprised if the absolute value was bigger than 3^^^3? I'm guessing yes, very much so. So that's a reason not to use an improper prior.
If there's no better information about the problem, I sortof like using crazy things like Normal(0,1)*exp(Cauchy); that way you usually get reasonable smallish numbers, but you don't become shocked by huge or tiny numbers either. And it's proper.
My point is that 1 and 2 above don't seem to differ fundamentally in either of the two descriptors you used.
Conversations about definitions of words are not useful, but definitions of concepts are necessary. I'm pointing at the fuzziness because it indicates to me that the supposed distinction is not being made based on any principle, but simply to rationalize a preexisting bias.
I wasn't trying to present a principled distinction, or trying to avoid bias. What I was saying isn't something I'm going to defend. The only reason I responded to your criticism of it was that I was annoyed by the nature of your objection. However, since now I know you thought I was trying to say more than I actually was, I will freely ignore your objection.
- A person doesn't want to have a baby, so she has an abortion to stop the fetus from developing into one.
- A person doesn't want to have a fetus, so she uses contraception to stop the ovum and sperm from developing into one.
If 1 is reactive, then so is 2.
For a given fetus, there is a finite possibility space of all the persons into which it could develop, taking into account different values of unknown future parameters. The same can be said of any combination of sperm and ova; it's just that the possibility space is larger. How would one derive a concept of "specific" that discriminates between the fetus space and the sperm/ova space without drawing an arbitrary line based on the size of the space?
Do you have an instance of "I proactively do X" where you do not class it as reactive? Do you have an instance of "I wish to avoid Y" where you do not class it as specific? I don't like conversations about definitions. I was using these words to describe a hypothetical inner experience; I don't claim that they aren't fuzzy. You seem to be pointing at the fuzziness and saying that they're meaningless; I don't see why you'd want to do that.
Every time contraception is used, it prevents a specific multitude of "potential humans" from existing. Sure, most of them would have been prevented from existing by other factors, but contraception still actively contributes to that. It's also done reactively, in that it's a reaction to someone's desire to have sex with a lower risk of pregnancy. It may not feel the same way as abortion, but that's just because it's easier for humans to value fetuses than sperm and egg cells. Both abortion and contraception have specific and reactive components, in principle.
It seems to me that we mean different things by the words "reactive" (as opposed to proactive) and "specific". A weak attempt at a reductio: I proactively do X to avoid facing Y; I am thus reacting to my desire to avoid facing Y. And is Y general or specific? Y is the specific Y that I do X to avoid facing.
abortion is more evil than contraception is because it's an error of commission rather than omission.
I think taking birth control precautions is pretty comission-y. Abstinence would be the omission version of not having babies.
Ah, yes indeedy true. I guess I was thinking of abstinence. So wrong distinction. More likely, then: abortion is done to a specific embryo who is thereby prevented from being, and it's done reactively; there's no question that when you have an abortion it's about deciding to kill this particular embryo. Contraceptive use on the other hand is nonspecific and proactive; it doesn't feel like "I discard these reproductive cells which would have become a person!", it feels like exerting prudent control over your life.
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I might just be being stupid, but how was this figure derived at all? I understand that the point of the article is that statistics can be presented in non-intuitive and confusing ways, but whenever I've seen such examples in the past there has always been some justification, however shaky.
Did the media just outright lie this time, or am I missing something?
Nope: the odds ratio was (.847/(1-.847))/(.906/(1-.906)), which is indeed 57.5%, which could be rounded to 60%. If the starting probability was, say, 1%, rather than 90.6%, then translating the odds ratio statement to "60% as likely" would be legitimate, and approximately correct; probably the journalist learned to interpret odds ratios via examples like that. But when the probabilities are close to 1, it's more correct to say that the women/blacks were 60% more likely to not be referred.