Small Area Estimation is a field of statistics that seeks to improve the precision of your estimates when standard methods are not enough.

Say your organization has taken a large national survey of people’s income, and you are happy with the precision of the national estimate: The estimated national average income has a tight confidence interval around it. But then you try to use this data to estimate regional (state, county, province, etc.) average incomes, and some of the estimates are not as precise as you’d like: their standard errors are too high and the confidence intervals are too wide to be useful.

Unlike usual survey-sampling methods that treat each region’s data independently, a Small Area Estimation model makes some assumptions that let areas “borrow strength” from each other. This can lead to more precise and more stable estimates for the various regions (if the assumptions are reasonable).

Also note that it is sometimes called Small Domain Estimation because the “areas” do not have to be geographic: they can be other sub-domains of the data, such as finely cross-classified demographic categories of race by age by sex.

If you are interested in learning about the statistical techniques involved in Small Area Estimation, it can be difficult to get started. This field does not have as many textbooks yet as many other statistical topics do, and there are a few competing philosophies whose proponents do not cross-pollinate so much. (For example, the U.S. Census Bureau and the World Bank both use model-based small area estimation but in quite different ways.)

Recently I gave a couple of short tutorials on getting started with SAE, and I’m polishing those slides into something stand-alone I can post. [Edit: I still haven’t polished them, but I’ve posted my old slides and code.] Meanwhile, below is a list of resources I recommend if you would like to be more knowledgeable about this field. Continue reading “Small Area Estimation resources” →

Would there be any demand for a statistics class taught by M from the James Bond films?

M: You don’t like me, Bond. You don’t like my methods. You think I’m an accountant, a bean counter, more interested in my numbers than your instincts.
JB: The thought had occurred to me.
[…]
M: I’ve no compunction about sending you to your death, but I won’t do it on a whim.

Continue reading “Evil Queen of Numbers” →

Partly continuing on from my previous post…

So I think we’d all agree that applied mathematics is a venerable field of its own. But are you tired of hearing statistics distinguished from “data science“? Trying to figure out the boundaries between data science, statistics, and machine learning? What skills are needed by the people in this field (these fields?), do they also need domain expertise, and are there too many posers?

Or are you now confused about what is statistics in the first place? (Excellent article by Brown and Kass, with excellent discussion and rejoinder — deserving of its own blog post soon!)

Or perhaps you are psyched for the growth of even more of these similar-sounding fields? I’ve recently started hearing people proclaim themselves experts in info-metrics and uncertainty quantification. [Edit: here’s yet another one: cognitive informatics.]

Is there a benefit to having so many names and traditions for what should, essentially, be the same thing, if it hadn’t been historically rediscovered independently in different fields? Is it just a matter of branding, or do you think all of these really are distinct specialties?

Given the position in my last post, I might argue that you should complete Chemistry Cat’s sentence with “…and those who can quantify their uncertainty about those extrapolations.” And maybe some fields have more sophisticated traditions for tackling the first part, but statisticians are especially focused on the second.

In other words, much of a statistician’s special unique contribution (what we think about more than might an applied mathematician, data scientist, haruspicer, etc.) is our focus on the uncertainty-related properties of our estimators. We are the first to ask: what’s your estimator’s bias and variance? Is it robust to data that doesn’t meet your assumptions? If your data were sampled again from scratch, or if you ran your experiment again, what’s the range of answers you’d expect to see? These questions are front and center in statistical training, whereas in, say, the Stanford machine learning class handouts, they often come in at the end as an afterthought.

So my impression is that other fields are at higher risk of modeling just the mean and stopping there (not also telling you what range of data you may see outside the mean), or overfitting to the training data and stopping there (not telling you how much your mean-predictions rely on what you saw in this particular dataset). On the other hand, perhaps traditional stats models for the mean/average/typical trend are less sophisticated than those in other communities. When statisticians limit our education to the kind of models where it’s easy to derive MSEs and compare them analytically, we miss out on the chance to contribute to the development & improvement of many other interesting approaches.

So: if you call yourself a statistician, don’t hesitate to talk with people who have a different title on their business cards, and see if your special view on the world can contribute to their work. And if you’re one of these others, don’t forget to put on your statistician hat once in a while and think deeply about the variability in the data or in your methods’ performance.

PS — I don’t mean to be adversarial here. Of course a good statistician, a good applied mathematician, a good data scientist, and presumably even a good infometrician(?) ought to have much of the same skillset and worldview. But given that people can be trained in different departments, I’m just hoping to articulate what might be gained or lost by studying Statistics rather than the other fields.

I’ll admit it: before grad school I wasn’t fully clear on the distinction between statistics and applied mathematics. In fact — gasp! — I may have thought statistics was a branch of mathematics, rather than its own discipline. (On the contrary: see Cobb & Moore (1997) on “Mathematics, Statistics, and Teaching”; William Briggs’s blog; and many others.)

Of course the two fields overlap considerably; but clearly a degree in one area will not emphasize exactly the same concepts as a degree in the other. One such difference I’ve seen is that statisticians have a greater focus on variability. That includes not just quantifying the usual uncertainty in your estimates, but also modeling the variability in the underlying population.

In many introductory applied-math courses and textbooks I’ve seen, the goal of modeling is usually to get the equivalent of a point estimate: the system’s behavior after converging to a steady state, the maximum or minimum necessary amount of something, etc. You may eventually get around to modeling the variability in the system too, but it’s not hammered into you from the start like it is in a statistics class.

For example, I was struck by some comments on John Cook’s post about (intellectual) traffic jams. Skipping the “intellectual” part for now, here’s what Cook said: Continue reading “One difference between Statistics vs. Applied Math” →