Statistics Is Like Medicine, Not Software

Stats questions--even when they're pure cut-and-dried homework--require dialog. Medicine might be a better analogy than software: what competent doctor will prescribe a remedy immediately after hearing the patient's complaint? One of our problems is that the [Stack Exchange] mechanism is not ideally suited to the preliminary dialog that needs to go on.

That's from the ever erudite William Huber, in this chat about why the statistics Q&A site has problems that the software Q&A site does not. Some users argue that a high proportion of questions on the stats site should not be answered unless they are disambiguated further.

You might assume that "more answers are better," but answering an ill-posed question adds more noise to the internet. When searching to clarify an ambiguous term, somebody might find that question, read the answer, and end up even more confused. Recall that this is a field already stricken by diametric ideology and short-term incentives.

Here is my previous post on the wisdom of Huber. 

The Psychosocial Costs Of Ambition

If I had accepted that leadership role, there would have been a lot of pressure on me to do something really exciting. I can sometimes do exciting things, but I can't do them on demand. My energy level waxes and wanes. My creativity is irregular. When I do have an idea, sometimes it catches on and other times people just stare at me and think "What's wrong with him?" 

To be ambitious is a commitment. It's saying "Take a chance on me, and I will continue being creative and exciting and dependable for the foreseeable future." It's promising people that you're never going to let them down. If you act ambitious, and then when push comes to shove you say "Nah, I don't need the aggravation", then you don't look ambitious and high-status, you look like a flake.

Scott's lucid explanation of the costs to ambition is a great example of hot and cold decision-making. We tend to overestimate the stability of our beliefs, so when we feel ambitious and full of energy (like, at the start of a project) we assume that this feeling will continue indefinitely.

Of course, this is unlikely. Most of us have daily circadian rhythms, some less-well understood medium-term fluctuations, and gradual decays in interest.

So, as Scott learned early in life, it is prudent to anticipate and explicitly correct for your likely decline in motivation towards a topic when you present yourself to the world. The insidious part of this is that if you want to obtain resources you need to actually complete a task (e.g., a job, a grant, collaborators), you will have to sell yourself. This is why trade-offs aren't fun; they're just real.

Is *Any* Human Activity Long-Run Sustainable?

Intensive rice agriculture began in the Yangtze basin about 8,000 years BP, a sustainable model for agriculture by any reasonable standard. The extensive water infrastructure network around Chengdu, China, has diverted part of the Min River through the Dujiangyan for both flood control and irrigation without restricting fish connectivity since 256 BC, while some forests in India have been actively managed by surrounding communities for even longer periods.

That's from a guardedly optimistic article by Matthews and Boltz. It's academic but contains most of the good aspects of scholarly writing (copious references, measured tone), without most of the others (argument to authority, unwillingness to point out the obvious). There are 2650 words so you should expect to read it in about 12 minutes. Assuming you are an average blog reader (well, above average if you're reading this one), I recommend it, unless you haven't stared at the Vostok ice core data recently, in which case you should do that for 15 seconds first. 

The Meaning Of The Mean

Bob Carpenter has a few enlightening thoughts on the distinctions between 1) the sample mean, 2) the expected value of a random variable, and 3) the mean of a distribution. I've long been confused by the difference between the mean and expected value, and his trichotomy helps alleviate my confusion. With that in mind, I changed the intro of the article mean, which had remained static since the dawn of time (2001, when the page was created).

Of the major subjects on Wikipedia, statistics seems to be the most convoluted. My two explanations for this are that 1) there are so many schools that disagree on fundamental interpretations (likelihood, non-parametric, empirical Bayesian, objective Bayesian, etc), and 2) many practitioners are so busy with applications that they don't have time to reconcile their disagreements.

When You Should Be Most Skeptical

One of the hardest things we can do as readers is disagree with the methods of authors we agree with ideologically. It makes us feel good to find authors who agree with us, but this is when we should be at our most skeptical. Searching the world for self-justification is not a worthwhile goal, it simply turns you into another short-sighted, argumentative know-it-all.

That's from Keely's scathing, analytical review of The Giver. I like the idea that we should be especially skeptical of the arguments of those we agree with, to counteract out natural tendency to the contrary.

When More Data Trumps Logic

A difficulty with the “more data is better” point of view is that it’s not clear how to determine what the tradeoffs are in practice: is the slope of the curve very shallow (more data helps more than better algorithms), or very steep (better algorithms help more than more data). To put it another way, it’s not obvious whether to focus on acquiring more data, or on improving your algorithms. Perhaps the correct moral to draw is that this is a key tradeoff to think about when deciding how to allocate effort. At least in the case of the AskMSR system, taking the more data idea seriously enabled the team to very quickly build a system that was competitive with other systems which had taken much longer to develop.

That's Michael Nielsen in an interesting post describing how machine learning question-and-answer systems work. I completely agree that identifying trade-offs is one of the most useful ways to decide how to proceed on a problem. That's why I think the general study of trade-offs, across fields, is underrated. 

GATCACA

In many American states it is legal to screen and select on the basis of sex, for non-medical reasons. In fact, a 2006 study (see below) found that 9% of [preimplanation genetic diagnosis] procedures carried out in [in-vitro fertilization] clinics in the U.S. were performed for this reason. Other reasons include screening for an embryo with the same immune type (“HLA type”) as a current child who is ill and requires a transplant of some sort. Screening for these “savior siblings” was done in 1% of PGD procedures. And 3% used it for a reason I personally find jarring – to specifically select embryos with a mutation causing a genetic condition. This is usually in cases where both parents have either deafness or dwarfism and they want their child to be similarly affected. This gets into the political movement objecting to society labelling conditions as “disabilities”. I can sympathise with that to some degree – more for some conditions than others – but I think, if it were my child, I would still rather he or she could hear.

That's Kevin Mitchell, discussing GATTACA, an entertaining sci-fi movie with a respectable 7.8 imdb rating. Spoiler alert, the premise of the movie is that at some point in the future there will be strong stratification of people into two classes, the "valids" and the "invalids", based on whether they had healthy traits selected for via preimplanation genetic diagnosis.

It seems to me highly unlikely (<0.01%) that a nightmare scenario of this sort would actually occur. One of the main reasons is because of the large plurality of values among parents, as seen above. A prevailing reason people have kids is to propagate a form of themselves into the future, and in many ways it defeats the purpose when you select against certain traits or even perform some sort of genetic engineering.

The other reason is something we know now better than we did 15 years ago, when GATTACA was released. And that is that DNA doesn't actually explain all that much of physiology and behavior--there are also strong epigenetic effects as well as stochastic effects of gene expression. 

No Darkness But Ignorance

Here's Nancy Kanwisher's suggestion on how to improve the field of neuroimaging:

NIH sets up a web lottery, for real money, in which neuroscientists place bets on the replicability of any published neuroimaging paper. NIH further assembles a consortium of respected neuroimagers to attempt to replicate either a random subset of published studies, or perhaps any studies that a lot of people are betting on. Importantly, the purchased bets are made public immediately (the amount and number of bets, not the name of the bettors), so you get to see the whole neuroimaging community’s collective bet on which results are replicable and which are not. Now of course most studies will never be subjected to the NIH replication test. But because they MIGHT be, the votes of the community are real.... 

First and foremost, it would serve as a deterrent against publishing nonreplicable crap: If your colleagues may vote publicly against the replicability of your results, you might think twice before you publish them. Second, because the bets are public, you can get an immediate read of the opinion of the field on whether a given paper will replicate or not.

This is very similar to Robin Hanson's suggestion, and since I assume she came up with the idea independently, it bodes well for its success. Both Hanson and Kanwisher are motivated to promote an honest consensus on scientific questions.

When John Ioannidis came to give a talk at the NIH (which was interesting), I asked him (skip to 101:30) for his thoughts on this idea. He laughed and said that he has proposed something similar.

Could this actually happen? Over the next ten years, I'd guess almost certainly not in this precise form; first, gambling is illegal in the US, and second, the markets seem unlikely to scale all that well.

However, the randomized replication portion of the idea seems doable in the near term. This is actually now being done for psychology, which is a laudable effort. It seems to me that randomized replications are likely precursors to any prediction markets, so this is what interested parties should be pushing now.

One objection is that these systems might encourage scientists to undertake more iterative research, as opposed to game-changing research. I have two responses. First, given the current incentives in science (i.e., the primacy of sexy publications), this might actually be a useful countervailing force.

Second, it seems possible (and useful) to set up long-standing prediction markets for a field, such as, "will the FDA approve an anti-amyloid antibody drug to treat Alzheimer's disease in the next ten years?". This would allow scientists to point to the impact that their work had on major questions, quantified by (log) changes in the time series of that market after a publication. 

Evaluating The Regret Heuristic, Part II

In a comment to my post on how our regrets change over time, Eric Schwitzgebel asks, 

But why adopt regret minimization as a goal at all? Regret seems distorted by hindsight bias, status quo bias, and sunk cost bias, at least.

I've written before that projecting your future views about your present actions can be a good way to make decisions. So, Eric's prompting is a good occasion to re-evaluate that.

Given perfect information, the theoretically best way to make decisions is to 1) calculate the costs and benefits of each possible outcome, 2) estimate how your choice affects the relative probability of those outcomes, 3) use the costs and benefits as inputs to some sort of valuation function, and 4) make the decision with the highest probabilistic value. 

Cost-benefit analysis is a common way to implement this, with, say, QALYs as the value measure. If you have perfect information, this is just math. 

But as Ben Casnocha says, if you don't have enough information, that framework can break down. In particular, even when #2 is pretty straightforward, #1 can still be very tricky. For example, although studying for the LSAT makes it much more likely that I will earn a JD, it's still hard to quantify the precise costs and benefits of entering that earning that degree. 

Here is where the regret heuristic can be useful. Instead of explicitly tallying each cost and benefit, it asks: in total, which would you regret more: studying or not studying? 

This is in fact a simplifying measure, but there remains oodles of freedom in how you perform the regret estimation. For example, you can:

• use as reference classes your current regrets about your previous, similar actions and/or the regrets of other people who have made similar decisions, or just make it up; 
• integrate your regret over all of your possible future states (e.g., ages) weighted by their probability of occurring, or just choose one arbitrary time point; 
• extend the regret over broad classes of choices you could make, or keep it local;
• apply systematic techniques to adjust for various biases (e.g., impact, confirmation, status quo, hindsight, planning, sunk cost), or not.

Ultimately, I still think that the regret heuristic can be a useful one. But tread carefully, as there are many crucial micro-decisions to make; it's not magic. 

Age's Stealing Steps

Michael Wolff has written a gripping but narrative-heavy article about the troubles he has experienced in addressing his mother's worsening dementia. It is hard not to feel for him and his family. Still, I think there are two perspectives which his piece underemphasized:

1) Many debilitated but cognitively intact individuals do have a good quality of life. For example, in a recent survey of 62 seniors with an average of 2.4 daily living dependencies and fairly good cognitive well-being (≥ 17/30 on the MMSE), 87% reported that they had a quality of life somewhere in the fair to very good range. I consider this to be a testimony to the resiliency of the human psyche. Also, it makes me worry that people will read the article and think that LTC insurance is only useful for those with dementia, which Wolff implies, when that is far from the case.

2) Why is it that many of the doctors depicted his story seem so unhelpful? There's little doubt that fear of litigation plays a role. For example, in a Mar '12 study, over half of the 600+ palliative care physicians surveyed reported being accused of euthanasia or murder within the past five years. In many respects this is a legislative issue, and I wish his article had discussed that angle more.

Many pointers in this post go to the excellent blog GeriPal. 

Should Revenge Have Bounds?

I recently finished Steven Pinker's book attempting to explain the decline of human-on-human violence over the last twenty thousand years. All in all, I recommend it. It has noteworthy psychology nuggets on nearly every page, explained with good data and lucid metaphors. I especially enjoyed how he built up many cute explanations of various phenomena--like the Freakonomics-popularized abortion theory of the crime rate decrease in the 1990s--only to soundly and evenly debunk them. My two major points of disagreement:

1) As Tyler Cowen argues, it is possible that although the mean number of causalities from interstate conflicts has been falling, the variance has been increasing. Aside from WWII, we can't easily observe this variance, though we can see signs of it in events like the Cuban Missile Crisis. Pinker employs per-capita log-scales for many of his charts and on these WWII does not seem quite as bad, but still it sticks out indelibly.

Wisely, Pinker does not project the decrease in violence indefinitely into the future, rather seeking to explain what we have observed so far, so his thesis is technically immune to this critique. Still, I imagine that there have been some not-easily observed historical aberrations which, if they had gone differently, would have meant that this book would never had been written. The winner's curse comes to mind.

2) As one reads about the incredible violence that occurs in US prisons, it is difficult not to wonder whether the benefits to decreasing violence always outweigh the costs. I have previously written about the protection vs freedom trade-off. The laudable decrease in person-to-person violence comes at the cost of constraining the actions of individuals by probabilistically putting them in prison. This is an imperfect process and has negative externalities in that it further exacerbates the burden of those locked up for non-violent crimes.

So, I would have liked to see more discussion about the violence in modern-day prisons and whether it is more apt to say that violence has been displaced rather than decreased. In a provocative article, Christopher Glazek argues that the US should be more like the UK and have slightly looser violent crime convictions which would make the conditions in prison slightly less awful. In most cases I would probably come down in favor of protecting innocent bystanders, but it is a conversation that needs to happen and that I wish Pinker had addressed. 

A Brief History Of Bioinformatics, 1996-2011

That's from an interesting article by Christos Ouzounis. Here he discusses the "adolescence" period:

One factor in policymakers' high expectations might have been a certain lack of milestones: due to the field's dual nature, that of science and engineering, computational biology rarely has the “eureka” moment of a scientist's discovery and is grounded in the laborious yet inspired process of an engineer's invention. 

And there's this bit, too:

The notion of computing in biology, virtually a religious argument just 10 years ago, is now enthroned as the pillar of new biology.

So why has "bioinformatics" become less discussed? In part, because it has been so successful. 

Schelling Points And Bioinformatics

A lot of what think about when I do bioinformatics is how to set parameters non-arbitrarily. Basically I am looking for Schelling points: round, clear numbers that are easy to justify. The classic case is setting a p-value threshold to 0.05, which has been around for over eighty years and is still going strong, despite the haters. Other examples are setting e-value thresholds to 0.01 and setting Bayes factor thresholds of 10 as the first to indicate "strong" evidence. Like any threshold, these are arbitrary, but following the paradigm of statistics as rhetoric, their staying power make sense insofar as scientists need to be able to resort to standard procedures to settle debates. Anyway, I have no profound point here, I just think it's cool that a seemingly esoteric topic affects what I actually do on a day-to-day basis.

Is It Possible, In Principle, To Do Methodologically Sound Research?

In a paper published 31 years ago, Joseph McGrath argues (html, pdf) that the answer is no. Specifically, he claims that any research design faces two trade-offs: 1) being obtrusive vs unobstrusive (which maps to my terminology as acquiring info vs altering subject), and 2) being generalizable vs context-cognizant (which maps to my terminology as precision vs simplicity).

In his terminology, these trade-offs allow for the optimization of three distinct values (generalizability of samples to populations; precision in measuring variables; and context realism for the participants). Initially, I disagreed with this. To me, intuition suggests that there should be four points which maximize certain qualities when you are considering the intersection of two-trade offs: one in each corner of the 2-d space.

One way to get around this is if you claim that, in the context of this decision (study design), the trade-offs are not independent. For example, it might be very difficult for a design to be both highly generalizable and highly obstrusive.

Below I've drawn an example. Think of the dots as realizations of actually feasible study designs sampled from someone's mental generation process; i.e., they are probably not at the absolute extremes of the theoretical distribution, but with enough realizations, would come close.

I'm not sure that I agree with this exact distribution, and it would need some justification, but it seems like the only way to justify his three-pronged rather than four-pronged set-up.