gusl

Bickel, Klaassen, Ritov, Wellner
* p. 227, Re: estimating cell probabilities in a two-way contingency table with known marginals.  "Iterative Proportional Fitting converges to the minimum Kullback divergence estimator"

Casella & Berger (2nd Edition) says nothing

Gelman, Carlin, Stern, Rubin (2nd Edition)
* p.107, asymptotics of estimation under mis-specified model.
* p.586-588, details about this.

Hastie, Tibshirani, Friedman (2nd Edition)
* p. 561, KL "distance".  Used in definition of mutual information, on a section about ICA.

Hogg, McKean, Craig (6th edition) says nothing

Ferguson
* p.113-114, "Kullback-Leibler information number", on chapter titled "Strong Consistency of Maximum-Likelihood Estimates"

Keener
* p.59: proof question: show that KL > 0 unless the two distributions are equal.
* p.156: consistency of MLE.
* p.466: solution to the proof question.

Lehmann & Romano
* p. 432: optimal test rejects for large values of T_n, and T_n converges to -K(P0, P1).
* p. 672: in non-parametric test for the mean, KL is used to define the most favorable distribution in H0.

van der Vaart
* p. 56: asymptotics of estimation under mis-specified model.
* p. 62: viewing MLE as an M-estimator.

Wasserman
* p. 125: consistency of MLE. "By LLN, M_n converges to -D(θ*, θ)"

Supply charges

Manhattan: 8.3333c/kWh
Brooklyn: 15.8377c/kWh


Delivery charges

Manhattan: 10.1321c/kWh
Brooklyn: 10.1789c/KWh


SBC/RPS charges

Manhattan: 0.3082c/kWh
Brooklyn: 0.3911c/KWh


This means that in Manhattan I used to pay 18.7736c/kWh, whereas in Brooklyn I'm paying 26.4077c/kWh.

On top of that, in Manhattan, my two-person household was spending 5.12 kWh per day; in Brooklyn, my 3-person household has been spending 9.87 KWh per day.

On the positive side, Con Edison has adjusted their ridiculous "estimated" charges, and the adjusted bill looks almost reasonable.

I'm going to Rio for WWW2013 next week. Exciting!

I went to AirBnb look for rooms near Barra. I found a studio here, for $150/night, "Enjoy Nature Studio in Lagoon RIO!":



The conference is near the Sheraton, which is a 20-minute walk from the center of the pink circle, and I'm otherwise not very picky, so I didn't mind the Strict cancellation policy. I accept the charge of $750 for 5 nights + $82 in AirBnb fees.

Once I book, I get the address: Av. Armando Lombardi 370. I tell my friend in Rio, who walks by and tells me that address given is a gas station! I call the host, and her daughter explains to me that the studio is on an island: Ilha Primeira, which falls completely outside of the pink circle (the triangular island just North of the pink circle), and that this address is where the boat picks you up. I understand why they did this: AirBnb requires a street address, and Ilha Primeira doesn't have streets.

The place sounds very beautiful, but it would be extremely inconvenient to have to depend on boats all the time. After I make a few inquiries about the boat service, the host advises me to cancel. I agree, pending her reassurance that she will give me a full refund. I call AirBnb twice, and learn that their resolution procedure is essentially: "you guys find an agreement", and they tell me that I'm going to lose the fees ($82) regardless. They heard my complaint about the misleading address, and seemed to agree with me, but didn't want to take any action on it.

Anyway, I accept losing the $82, so just before midnight, I cancel... Today I spoke to the host again, and she told me that she will refund me all the money they give her, but that this is only $727. So it sounds like AirBnb is charging her $23, on top of the $82 from me! Unfortunately, this means that my total loss would be $105... which crosses the threshold for picking a fight with me. Maybe this means that I need to call AirBnb again and threaten them with reversing charges. I have a debit card, but my bank reassured me that they will give me the benefit of the doubt in such a dispute... but first I have to wait until the transaction posts.

For the future, I should probably use credit cards more often: my understanding is that they are better when it comes to dispute resolution.

I do worry about burning my bridges with AirBnb, but this is a matter of principle. Hopefully they wouldn't do anything to my San Francisco booking if I reverse charges on the Rio booking.

I'm subletting my apartment. It's a great deal. You will not find this much space in such a nice area for $900/month. See here.

A lot of people in the Data Science world seem to be on Twitter. And I think it's true of techy people in general, at least the sort of techy people who are into Free Culture type things.

Of course, I much prefer having a real blog, with space to develop my thoughts and a permanent record. But there is something to be said for Twitter, which is hard to put my finger on. Twitter gives a feeling of immediacy, that you're speaking to the whole world. Although real blogs are just as public and just as immediate as Twitter, (a) blog interaction suffers from interoperability issues, especially commenting: there are many competing standards, and unfortunately OpenID didn't take off (though maybe Facebook Connect will), whereas Twitter is unified and simple; and (b) the set of people who read you somehow on real blogs feels more limited^*. This may be because Twitter users often browse by hashtags (#), rather than users (@).

I have a little problem now: I have "followed" way too many people on Twitter, so I need to split my friends into groups, i.e. reading lists.

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^{* - I, however, have had the opposite experience, which is part of why I abandoned Twitter the first time.}

Perhaps one of the defining traits of "nerds" is a low level of body awareness, which comes with "spending too much time in the head". This may explain why yoga has been so revealing for me. I have been learning which sensations correspond to stretch, strain, and pain; and how to move muscles independently of other muscles (often my brain used to think of them as just one thing). Sometimes I need visual feedback to learn to control my muscles. I am lucky to have a teacher who understands how unintuitive this is for me.

I wish we had a standard language for naming specific sensations. I would like to convey precisely the twinge on my lower back, which might be a pinched nerve, but might just be soreness. If my teacher could feel what I feel, he would know what it was, but instead his judgement has to rely on my imperfect attempts at describing it.

When it comes to bodily sensations, we don't know how much subjectivity there is. Psychologists (psychophysicists) can often quantify the subjectivity of senses (say color), because even when words fail, they can do experiments to test whether subjects are able to detect tiny differences in stimuli (perhaps defining a metric on perceptual space, or more!), and then quantify how much people differ in this ability, in different regions of stimulus space. But when it comes to your body, it is much harder to stimulate a sensation to a precision worthy of being called "reproducible". And then there's habituation (which is also a problem for scientists trying to study smell).

Right now you could start a philosophical food fight by bringing up the label-switching problem (namely that, just because you and your teacher are in verbal agreement doesn't mean that your experiences agree), but I just want to be practical here: how can we develop a shared vocabulary that would allow me to better convey my sensation to my teacher, so that he may make a better guess about what is wrong with my back? Are there existing human cultures in which people can easily convey their bodily sensations to each other?

I think that the biggest obstacle here is establishing joint attention. It is easy to teach the names of visual stimuli to a seeing person. But when it comes to coining words to describe types of pain in the back, this becomes like two blind people trying to come up with words for categorizing shapes (they can experience shapes by touch, but without joint attention, i.e. let's say they are not allowed to pass shapes to each other).

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Why are "the arts" traditionally visual and/or auditory? Because out of all our senses, vision and hearing are the only senses whose stimulus-response mapping is reliable enough. With the other senses, there is too much variation within and across people to have any control over their experience (which also explains why we have so few olfactory words/concepts). Smell and taste have very little spatiotemporal resolution. Touch may actually be a good candidate.

Tyler Cowen's 8 insights on how human-computer collaboration in the context of chess
Insight #1, as one might imagine, is that human creativity is now worth more than it used to be, since most of the analysis is now automated.

Skeptical friends: some people say that when remembering things, your eyes move in a certain direction; when inventing things, they move in a different direction. The source of these ideas seems to be a pseudo-scientific field known as "Neuro-Linguistic Programming" (NLP). Is there any empirical basis for this claim?

See here
.

Although I love graphical models, I suspect that the "potential outcomes approach" is a more proper treatment of causal inference. See new book by Hernan and Robbins (h/t Michael Sobel).

Key concepts:
* counterfactuals: should be well-defined, but often aren't in the social science literature (e.g. to answer "what is the effect of marriage on health?", we'd have to imagine interventions that cause or prevent people from getting married; there are many non-equivalent ways to do this)
* potential outcomes: formalism in which all subjects are considered to have missing data for all but one experimental condition (i.e. the one that they were assigned to). This provides a direct way of thinking about token causation (a.k.a. causes-of-effects).
* ignorability: an important assumption that makes causal inference possible, similar to a missing-at-random assumption.
* propensity score matching: a way of coping when ignorability fails. (See also: Inverse probability weighting)

Directed graphical models perhaps provide something like a more concrete mechanism, allowing us to simulate the effects of interventions and propagate them downstream. But as far as real applications are concerned, papers in this tradition tend to make assumptions less explicit, and tend to mislead practitioners into thinking that the required assumptions are satisfied. (See Dawid - "Beware of the DAG")

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UPDATE: Cosma Shalizi writes:

<< You've read Pearl's Statistics Surveys paper, right? I think the critique of the potential outcomes framework there, in section 4, is very strong. (Look at the stuff on ignorability, especially.) As for propensity matching, when the set of covariates you're using to calculate propensities doesn't meet the back door criterion, well, you get results like this. >>

5 days to the big exam! We get to use 10 pages of notes, double-sided. It's way too much for my taste, but it's an interesting exercise, since it encourages you to think about relations between topics.

Asymptotics of Estimators (asymptotic consistency, normality)
* MLE: for regular parameter, asymptotically normal, with rate 1/sqrt(n).
* MLE: for truncation parameter, asymptotically exponential, with rate 1/n or worse.
* If family has both types of parameters, we cannot(?) use the Fisher Information to find the asymptotic variance of the regular one. But can't we plug in the true value of the truncation one, and use the asymptotics of the regular subfamily?
* Consistency is guaranteed if n/p -> infinity, plus a few other conditions ("for all theta, the density is bounded" should suffice)
* UMVUE: when is it asymptotically equivalent to the MLE?
* Sample quantiles
* Estimating Equations, a.k.a. no closed form for the MLE (e.g. Beta, Gamma, GLMs). Van der Vaart proves consistency (5.10), normality (5.19).

Fisher Information
* Why the two formulas are equivalent.
* Delta Method (for Rˆn -> Rˆm functions, we can easily generalize it using Jacobians!)
* Why knowing the nuisance parameter decreases the asymptotic variance of the parameter of interest
* Why location-scale families of *symmetric* distrs have a diagonal information matrix.
* Cramér-Rao Inequality, about *unbiased* estimators, comes from Cauchy-Schwarz. Not asymptotic: holds for every n! Equality is attained when we have "linear dependence". In other words, I think this means that an unbiased estimator U will be efficient iff can be written as: U = a*MLE + c.
* Compare: variance bounds for unbiased estimators vs other estimators.
* What if calculating the Fisher information is intractable?
* ATTENTION: is this for a single observation or for the whole sample?

Taylor Expansions
* How the asymptotic normality comes from one-step Newton-Raphson.
* Why asymptotics of likelihood ratio is Chi-Square.
* Delta Method, and how if the first derivative is zero, we get slower convergence to a Chi-Squared.
* Edgeworth Expansions

Testing
* Simple vs Simple: Neyman-Pearson.
* Simple vs Composite: compute MLE of the alternative.
* Composite vs Composite: MLE of the null (a.k.a. least favorable distribution)
* UMP: Monotone Likelihood Ratio on the *sufficient* statistic implies that I{T>c} is UMP.
* UMPU: Power function has slope 0. Is it a mixture of two UMPs?
* LMP: maximize the derivative of the power function at the boundary.
* Asymptotic power under contiguous alternatives: projections, non-Central Chi-Squared (I might need more practice with basic power calculations first!)

UMVUE
* Do there exist simple conditions for existence or non-existence?? For location families, UMVUEs for the location parameter should always exist: U = MLE + constant.
* If U is unbiased for 0 and T is UMVUE, then Cov(U,T) = 0.

Confidence Intervals
* Studentized Intervals
* Bootstrap intervals
* Many options for the Fisher information: Fisher Information at MLE, observed Fisher Information, etc. The observed Fisher Information may be biased. If the bias is positive, the resulting coverage probability will be below 1-alpha (but maybe the coverage probability converges to 1-alpha). If the bias is negative, the intervals will be conservative.
* Variance-stabilizing transformations. Do we get better intervals this way? These intervals will be asymmetrical.
* What if the first derivative of g is near zero at the MLE?


Linear Models
* Is S^2 always independent of beta-hat? Why?
* Why is the F-test equivalent to the T-test, and to the Likelihood Ratio Test?
* Review matrix calculus
* Simultaneous Confidence Intervals (studentized maximum modulus, studentized range distributions)

Non-parametrics
* Complete sufficient statistics for non-parametric families (e.g. all distrs, symmetric distrs, mean-zero distrs, etc)
* Kernel Regression
* Kernel Density Estimation (work out the bias!)
* U-statistics, and using projections to obtain asymptotic normality

Bayesian
* Review exam problem on Metropolis-Hastings
* Bayes Risk: may be minimized by posterior mean, median, mode, depending on the loss function

Probability Facts
* Distributions: pdfs, cdfs, means, variances
* Relations between distributions: conjugacy, convolutions, scaling
* Law of Total Covariance
* Joint distribution between minimum and maximum order statistics.
* Inequalities: Markov, Chebyshev, Jensen
* Dominated Convergence / Monotone Convergence: swap limit and integral.


Calculus facts
* (1 + x/n)^n -> e^x
* \sum_k x^k / k! = e^x
* \sum_{k=0}^n p^k = (1 - (p^n+1)) / (1 - p)
* \sum_{k=0}^n k p^k =