On Priors, Bayesians and Frequentists

A dialog between a bunny and a philospher in which questions of current concern are asked or not asked, and answered or not.  The philosopher will, until the philosopher wishes be anonymous or not.

[Eli]  So every once and then, Eli gets serious, and asks some questions.  In this case about Bayesian statistics.  Andrew Gelman pointed out that

[Andrew Gelman] Twenty-five years ago or so, when I got into this biz, there were some serious anti-Bayesian attitudes floating around in mainstream statistics. Discussions in the journals sometimes devolved into debates of the form, “Bayesians: knaves or fools?”.

[Eli]  Eli thought the proper designation of Bayesians was the batshit crazy, but no never mind.  The questions revolve around something lower down in that post, and frankly, in a vague attempt not to out his bunnyship as an idiot, Socrates, Eli thought you might be a reasonable spirit to ask.   

[Socrates] Shoot.

[Eli] So here’s Andrew Gelman on Noah Smith:

[Andrew] Smith does get one thing wrong. He writes:

[Noah] When you have a bit of data, but not much, the Frequentist – at least, the classical type of hypothesis testing – basically just throws up its hands and says

[Frequentist] We don’t know.

[Noah] It provides no guidance one way or another as to how to proceed.

[Andrew] If only that were the case! Instead, hypothesis testing typically means that you do what’s necessary to get statistical significance, then you make a very strong claim that might make no sense at all. Statistically significant but stupid. Or, conversely, you slice the data up into little pieces so that no single piece is statistically significant, and then act as if the effect you’re studying is zero.

[Eli] Andy underlines another mistake by Noah, this time when he says:

[Noah] If I have a strong prior, and crappy data, in Bayesian I know exactly what to do; I stick with my priors. In Frequentist, nobody tells me what to do, but what I’ll probably do is weaken my prior based on the fact that I couldn’t find strong support for it.

[Andrew]  This isn’t quite right, for three reasons.

First, a Bayesian doesn’t need to stick with his or her priors, any more than any scientist needs to stick with his or her model. It’s fine—indeed, recommended—to abandon or alter a model that produces implications that don’t make sense (see my paper with Shalizi for a wordy discussion of this point).

Second, the parallelism between “prior” and “data” isn’t quite appropriate. You need a model to link your data to your parameters of interest. It’s a common (and unfortunate) practice in statistics to forget about this model, but of course it could be wrong too. Economists know about this, they do lots of specification checks.

Third, if you have weak data and your prior is informative, this does not imply that your prior should be weakened!

[Eli] Eli's take on all this is that starting with priors (from models/theories/other data sets) which are close to the data set under analysis will result in improved statistical estimates.  The (very old language here) surprisal, the difference between the prior and the posterior, will be small and one may be able to used it to extract meaningful dynamics from under the statistical noise.

[Ms. Rabett, looking into Eli’s eyes] Very meaningful dynamics indeed.

[Eli, keeping his cool] However, if the prior is awful, the result may actually diverge from the underlying statistical information in the data set, so with Bayes, you have to know the answer, or a good approximation to it to make progress, or, as Gelman points out

[Eli, using Andrew’s voice] If the prior is derived from previous work, the data set may be crap, in which case the use of the Bayesian statistics is to identify crap data.

[Eli] So how good is Eli's prior?

[Ms. Rabett]  And posterior, which I admire on occasion.

[Socrates] Gelman's post is brilliant.  I like his blog.  I also like Mayo's.  And not to mention yours.  What's your priors, again?

[Eli] Eli has been brought up on charges by many.  More or less something we used a lot of years ago, taking the prior from theory and applying it to measured data, to see what the theory missed.   Still like that approach.

[Socrates]  Oh, that.  Well, yeah.  Some call this post hoc data mining.  Some call it experimentation. I never understood the concept of post hoc.  Can we really check if econometrists are not peeking at their data before designing their models?

Perhaps Solomon would pronounce my judgement better than me:

[Solomon] Make sure your statistical inference is minimal and all will be well.

[Eli] Not if the theory is done before the experiment.

[Socrates] Hmmm. Some say that if you choose your model after you analyze your data, quite nasty things will happen to the data and you must throw it out. Replace data with brains and you get zombie stories:

[Zombified econometrist]  Must... get.. more... data.

[Eli]  Real science is messy, this is arguing for only doing things when you know the answer before you start.  Is statistics a tool or a means in itself, if it is a tool, why let it run your life?

[Socrates]  Because auditors request it, perhaps.  

[Eli]  They seriously lack rhythm and sound like Hell’s version of karaoke.  All noise, no music.

[Socrates]  Pithy.  Let’s envision this myth of an Hell like Dante’s, but with four circles of accusations, which I’m tempted to characterize via D&D allegiances:

[The Neutral] You're picking cherries with your post hoc method.

[The Chaotic] Your data is just a bunch of cherries anyway!

[The Lawful] You're not following a standard based on any official (e.g. statistical) authority.

[Socrates’ Avatar] You're not following your own standards.

[Socrates]  This sums up most of econometrical concerns, as far as I can see.  When valid, the last argument may be tough to dodge. Since this is my avatar talking through econometrists, I might be biased.

[Eli]  Well ok, you analyze the old data for your prior and then get new data.

The anti-Bayesian about that is that if your new data is wildly different from your old you got a load of splainin to do cause either the prior or the later data is screwed up.

Or you could split the fifty co authors into two groups, one who does the prior and the other who does the data gathering.

The equivalent would be to take the FAR as the prior for the SAR, etc.

[Socrates]  That could be a start, but how exactly do you find new very old proxies, Eli?  Historical data can be scarce.

[Eli]  The journals are full of them, it is an industry, with lots of folks out there digging up old logs, drilling new ones, inventing new tools of analysis and more.

Good solutions to these problems depend on using the right prior distribution, one that properly represents the uncertainty that you probably have about which inputs are relevant, how smooth the function is, how much noise there is in the observations, etc.  In other words you pretty much know the answer.

[Socrates] Easier said than done.  Let’s leave this aside. Since the last time Plato channeled me, Aristotle proved that providing evidence was more substantial.  I rather like this statement by Radford Neal in this presentation:

[Radford] The Bayesian approach takes modeling seriously. A Bayesian model includes a suitable prior distribution for model parameters. If the model/prior are chosen without regard for the actual situation, there is no justification for believing the results of Bayesian inference.

[Socrates] Just under it, there's also a note about the pragmatic compromises.  It's a rather neat intro, which even me can almost understand.  For better sound bites, there’s Cromwell’s rule:

[Dennis Lindsay] Leave a little probability for the moon being made of green cheese; it can be as small as 1 in a million, but have it there since otherwise an army of astronauts returning with samples of the said cheese will leave you unmoved.

[Eli]  Eli will give the points on that one.  No one ever got poor betting with cranks against green cheese or the ether.

[Socrates] The name was inspired by Oliver Cromwell’s address to the Church of Scotland:

[Oliver Cromwell] I beseech you, in the bowels of Christ, think it possible that you may be mistaken.

[Socrates] According to this rule, only logical impossibilities should have zero prior.  I believe this rule is in the spirit of your remark about proxies.

[Eli]  I think my point is that Bayesian statistics only works if you have an intelligent prior.  If the prior work is of Dunning Kruegar quality you are screwed.  You will know less after the analysis than before you started it.

[Socrates] More than that: you become affected by DK yourself, and you start to use the theorem to prove the existence of God.

I'll read Gelman's paper.  I feel I already did.  Oh, I just had this reminescence of asking a non-Bayesian philosopher king why he was not Bayesian, and he said:

[Philosopher King]  Beats me.  I just ain’t.  Methinks this is like sexuality.  I liked the first three pages of Gelman.  I agree with his claim about philosophical bayesianism being crap. 

[Socrates]  I'm paraphrasing, even if it looks like Philosopher King’s talking.  Socratic dialogs are a rhetorical trick to have multiple lines of argument.

While I was making you believe that Philosopher King was talking, I searched the Internet (which Plato anticipated in his Phaedo) and found this video lecture, by Michael... Jordan.  Clicking on the titles of the slides makes them appear.

It’s a slam dunk.

[Eli] In other words, if you have a good idea of the answer they can help you, but if not you need physics or biology or chemistry or meteorology.

[Socrates] You always do, but as soon as you put any of that into the prior you have to face the Erinyes.

[Eli] You’ve not told me much, Socrates.  What’s your final answer?

[Socrates] Do I look like a truth machine to you?  Please confer to Yoda:

[Yoda] The Proper Statistics you must use, Eli.  Within it everything is.

[Eli] Eli is but an humble bunny, oh Yoda, how shall he know what to do if Socrates does not tell him.

[Socrates] Us oracles consult for carrots, silly Rabett.

The Dagger

It was pretty obvious there was one, and here it is out in plain view (well buried in a footnote, which is plain view in science speak) in Recursive fury: Conspiracist ideation in the blogosphere in response to research on conspiracist ideation Stephan Lewandowsky, John Cook, Klaus Oberauer and Michael Hubble-Marriott

5.   The authors subsequently obtained a control sample via a professional survey  rm
in the U.S: This representative sample of 1,000 respondents replicated the results
involving conspiracist ideation reported by LOG12 (Lewandowsky et al., 2013).

Lewandowsky, S., Gignac, G. E., & Oberauer, K. (2013). The role of conspiracist ideation and worldviews in predicting rejection of science. Manuscript submitted for
publication.

Considerable Controversy

Bunnies may recall the controversy stirred by Lewandowsky , Oberauer and Gignac, NASA faked the moon landing therefore (climate) science is a hoax: An Anatomy of the Motivated Rejection of Science.  Readers of Rabett Run and the Weasel may have noticed that this was no joke, for example, Gerhard Wisnewski featured by Willis Eschenbach on Willard Tony's blog of no repute, believes the moon landing was faked, climate science is a hoax and much much more, even worse, he has a publisher who has doubts that the moon is not made of green cheese (slight, very slight exaggeration).

At the time, several of the more suspicious amongst us, including Eli and John Mashey warned (using Silvia Tognetti's term) the cranks to be careful.  Their response was simply fodder for the social scientists.  Indeed just last week Eli cautioned "Herr Prof. Dr.  Lewandowsky is warming up his grist mill" and, indeed it has ground exceedingly fine, with a new paper, accepted for publication

In the case of the response to our earlier paper, we were struck by the way in which some of the accusations leveled against our paper were, well, somewhat conspiratorial in nature. We therefore decided to analyze the public response to our first paper with the hypothesis in mind that this response might also involve conspiracist ideation. We systematically collected utterances by bloggers and commenters, and we sought to classify them into various hypotheses leveled against our earlier paper. For each hypothesis, we then compared the public statements against a list of criteria for conspiracist ideation that was taken from the previous literature.

This follow-up paper was accepted a few days ago by Frontiers in Psychology, and a preliminary version of the paper is already available, for open access, here.

Exploding heads will notice that John Cook is one of the authors.  The abstract, which may be discussed holds forth

Conspiracist ideation has been repeatedly implicated in the rejection of scientific propositions, although empirical evidence to date has been sparse. A recent study involving visitors to climate blogs found that conspiracist ideation was associated with the rejection of climate science and the rejection of other scientific propositions such as the link between lung cancer and smoking, and between HIV and AIDS (Lewandowsky, Oberauer, & Gignac, in press; LOG12 from here on). This article analyzes the response of the climate blogosphere to the publication of LOG12. We identify and trace the hypotheses that emerged in response to LOG12 and that questioned the validity of the paper's conclusions. Using established criteria to identify conspiracist ideation, we show that many of the hypotheses exhibited conspiratorial content and counterfactual thinking. For example, whereas hypotheses were initially narrowly focused on LOG12, some ultimately grew in scope to include actors beyond the authors of LOG12, such as university executives, a media organization, and the Australian government. The overall pattern of the blogosphere's response to LOG12 illustrates the possible role of conspiracist ideation in the rejection of science, although alternative scholarly interpretations may be advanced in the future.

Eli cautions the cranks that there is almost certainly more to come.  When you are in a hole, stop digging.

MT and Willard Discuss JC

A long time ago, Eli played around with XTRANORMAL (like in 2010) using an exchange between Michael Tobis and Willard on Judith Curry. Willard posted it on Neverending, but Eli never did.  James Annan reminded Eli about this today or at least pointed the bunny close enough to it, and, to be honest things have not really changed. Consider this the first of the Rabett Dialogs.

Why the Poor Fail

Eli, industrious bunny that his is was following some chicken tracks today when he wandered across Tim Worstall's blog.  Tim is one of those Galt in their own mind types and his boyz are of the same ilk. The topic was income inequality and Tim is for it.  From his point of view he earned his.  Fair enough, but there is an important subtext which is captured in two of the comments

• Dennis The Peasant // Feb 3, 2013 at 5:39 pm
  What people like Reich fail to see is this:
  Much inequality results not because of the violence inhernet in the system, but because people make extremely poor life choices.
  And that ain’t our problem.
• Martin Davies // Feb 3, 2013 at 9:45 pm
  If you chucked money at people making poor life choices, they’d still make poor life choices.Lost count of the number of times I’ve been told so and so has had a hard life. So for some reason they decided not to make a change then?
  Put a free opportunity in front of a hundred people and you won’t have all of them choosing to use it.

The question, of course, is why do the poor make bad choices, and Eli's visceral point of view was set by where he grew up but intellectually it was captured by George Orwell in the Road to Wigan Pier

Now compare this list with the unemployed miner’s budget that I gave earlier. The miner’s family spend only tenpence a week on green vegetables and tenpence half-penny on milk (remember that one of them is a child less than three years old), and nothing on fruit; but they spend one and nine on sugar (about eight pounds of sugar, that is) and a shilling on tea. The half-crown spent on meat might represent a small joint and the materials for a stew; probably as often as not it would represent four or five tins of bully beef. The basis of their diet, therefore, is white bread and margarine, corned beef, sugared tea, and potatoes–an appalling diet. Would it not be better if they spent more money on wholesome things like oranges and wholemeal bread or if they even, like the writer of the letter to the New Statesman, saved on fuel and ate their carrots raw? Yes, it would, but the point is that no ordinary human being is ever going to do such a thing. The ordinary human being would sooner starve than live on brown bread and raw carrots. And the peculiar evil is this, that the less money you have, the less inclined you feel to spend it on wholesome food  A millionairemay enjoy breakfasting off orange juice and Ryvita biscuits; an unemployed man doesn’t. Here the tendency of which I spoke at the end of the last chapter comes into play. When you are unemployed, which is to say when you are underfed, harassed, bored, and miserable , you don’t want to eat dull wholesome food. You want something a little bit ‘tasty’. There is always some cheaply pleasant thing to tempt you. Let’s have three pennorthof chips! Run out and buy us a twopenny ice-cream! Put the kettle on and we’ll all have a nice cup of tea! That is how your mind works when you are at the P.A.C. level. White bread-and-marg and sugared tea don’t nourish you to any extent, but they are nicer (at least most people think so) than brown bread-and-dripping and cold water. Unemployment is an endless misery that has got to be constantly palliated, and especially with tea, the English-man’s opium. A cup of tea or even an aspirin is much better as a temporary stimulant than a crust of brown bread.

There is much truth in this but it turns out that it is a middle class simplification of something much deeper rooted.  Anuj K. Shah, Sendhil Mullainathan, and  Eldar Shafir from the Booth School of Business at the University of Chicago published the results of a series of experiments in Science last November, investigating "Some Consequences of Having Too Little."  What are they.  We know what the problem is

The poor often behave in ways that reinforce poverty. For instance, low-income individuals often play lotteries, fail to enroll in assistance programs, save too little, and borrow too much. 

There are two general frames for this behavior, the first we could call progressive and Robert Reich almost certainly signs onto that

The first focuses on the circumstances of poverty, such as education (6), health (7), living conditions (8), political representation (9), and numerous demographic and geographic variables (10, 11). Put simply, the poor live in environments (for sociological, political, economic, or other reasons) that promote these behaviors.

Basically it is all of our faults and as Orwell points out being poor sucks so let's have a sweet.  The second is that of Tim Worstall and Dennis the Phesant and Martin Davis, it is the fault of the poor for making bad choices and their poverty is their own choice.

Shah and colleagues have a different point of view

When money is abundant, basic expenses (e.g., groceries, rent) are handled easily as they arise. These expenses come and go, rarely requiring attention and hardly lingering on the mind. But when money is scarce, expenses are not easily met. Instead of appearing mundane, they feel urgent. The very lack of available resources makes each expense more insistent and more pressing. A trip to the grocery store looms larger, and this month’s rent constantly seizes our attention. Because these problems feel bigger and capture our attention, we engage more deeply in solving them. This is our theory’s core mechanism: Having less elicits greater focus.

This is actually a general principal that applies not only to the poor, but to those for whom any resource, for example time, is scarce

And this hypothesis is about scarcity more generally, not just poverty. Indeed, just as expenses capture the attention of the poor, researchers have found that people who are hungry and thirsty focus more on food- and drink-related cues Likewise, the busy (facing time scarcity) respond to deadlines with greater focus on the task at hand.  Across many contexts, we see a similar psychology. People focus on problems where scarcity is most salient.

The pressing need to get through today leads to the neglect of tomorrow and the disasters that follow.

Because scarcity elicits greater engagement in some problems, it leads to neglect of others. While focusing on the groceries from week to week,we might neglect next month’s rent.While consumed with meeting tomorrow’s manuscript deadline, we might fail to prepare next week’s lecture. Attentional neglect appears in many domains. Low-income homeowners often do not attend to regular home maintenance while they focus on more pressing expenses. Neglected, these small repairs become major projects. 

This hypothesis provides a simple explanation of why the poor fall into the toils of the pay day lenders

Attentional neglect can explain another particularly striking behavior: why low-income individuals take short-term, high-interest loans, with interest rates that can approach 800%. These loans make it easier to meet today’s needs, but the loans’ deferred costs make it difficult to meet future expenses. If scarcity creates a focus on pressing expenses today, then attention will go to a loan’s benefits but not its costs. This suggests a clear prediction: Scarcity, of any kind, will create a tendency to borrow, with insufficient  attention to whether the benefits outweigh the costs.

 But cast in that frame we see ourselves

Consistent with this prediction, the busy also borrow. Facing tight budgets (i.e., deadlines), they borrow time by taking extensions. Like the poor, the busy often take extensions because they focus on urgent tasks, but neglect important tasks that seem less pressing. We suggest that both forms of borrowing stem from how scarcity shifts attention.

So if the poor are not morally deficient, the question remains what to do to help them.  Shah, et al.,  think that pointing out to people what their future needs are will help.  They are at the business school at the University of Chicago after all.  Eli demurs, remember that colleague who recommended you start working on that paper, grant recommendation, etc a few months ago.  You know she was right, you also know that you ignored her.  A straightforward reading of Shah, et al., is that the most effective method of dealing with poverty is to give the poor money.  This will break the heads of Dennis Martin and Tim, but, at least on the first level it is the answer that science provides.  Giving people a job without removing the stresses associated with poverty will not work because they will neglect their work under the pressure of their other problems.  One needs to provide the poor the space they need to devote the necessary energy to their work and lives.

Shah et al imply that the US welfare reforms of the 1990s were doomed.

UPDATE:  The Orwellian 1996 Personal Responsibility and Work Opportunity Reconciliation Act has had little effect on poverty in the US, which continues to scale with the economy.  What has happened is that other mechanisms (e.g. food stamps and unemployment) have taken the place of cash payments.

The OEM Version

The Bitch Always Gets Her Money Back

Hoisted from the comments, Bernard J muses

There's an ecological principle that about 10% of photosynthetically-captured energy passes from one trophic level to the next hight one. So of a million joules of shiney sunshine captured by lettuce, ~ a hundred thousand will fuel caterpillars, ten thousand will fuel chickens, and one thousand will fuel humans... with any degree of sustainability. Of course it's more complicated than that (including the presence of more trophic levels than I describe) but you get the general idea.

Consider that humans are currently sucking about 550 exajoules per annum:

and that annual photosynthetic energy capture is apparently around ten times this value:

For a species that exists at the apex of the trophic pyramid to co-opt such a disproportionate amount of energy is simply thermodynamically unstable. This is not to say that the energy must comes from the biosphere, now or in the future (obviously we're sucking moat of it from the last three hundred millions years or so of photosynthetic banking), but its expenditure during human activity is inextricably linked to the overall entropic state of the biosphere.

And as I said recently on another Rabbet Run thread, thermodynamics is a bitch. There's simply no way that a huge proportion of the sand in the sandpit can be stacked grain upon grain upon grain in one corner. Other civilisations found this out in the past: our turn is coming, with much of the thermodynamic debt to be paid by the agency of extinction - if not of our species, then by many others, both floral and faunal.

Thermodynamics/entropy imply an asymptote that defines maximum sustainable human energy use, no matter the source of the energy. Overdraw, and the excess will be paid with high interest.

And the bitch always gets her money back.

It's a lesson that too few understand, even amongst the scientific fraternity.

Scheduled For Release Friday, 5 PM

One of the first lessons you learn in DC is to be prepared to head for the bar at 5 PM on Friday cause that is when all the bad news that makes your head want to explode appears.  A couple of weeks ago Eli reported that DSCOVR (aka Triana, aka Goresat) was being readied for launch, with a new primary space weather mission required by NOAA, but carrying the Earth Observation instrumentation,  Some of the bunnies were a mite cynical

Hank Roberts said... So it's got to be up to politicians -- today's politicians -- to decide if there's funding for a camera at L1, eh, not to mention the Dark Side Climatesat also needed.

Damn.

You want to grab a politician by the scruff of the neck and drag him a quarter of a million miles out and say, “Look at that, you son of a bitch!”
— Edgar Mitchell, Apollo 14 astronaut, People magazine, 8 April 1974.

Anonymous said... The earth observation suite will almost certainly not fly.

NASA can't spend money on the earth observation suite. NOAA most likely won't spend money on the earth observation suite (they have bigger problems right now).

-HAUS.MAUS

Now Eli never answers questions when he can ask people who actually know the answers, so he wrote a brief note to Alexander Marshak who is the Goddard SFC person leading the Earth Observation System part of the DSCOVR program

Greetings,

Could you point me to an INTERNET resource or send me files about the current status of the Earth observation instruments on DSCOVR and plans for their operation.

and received this curious reply

Dear Eli,

Thank you for your interest in the DSCOVR Earth science instruments.  I was instructed by the project that all questions related to the status the Earth observation instruments on DSCOVR should be addressed to Mike Simpson who is the NOAA contact at GSFC.
Regards, A. Marshak

Well, like Eli said, Eli asks, so Eli wrote to Mike Simpson

Greetings,

Could you provide any information about the current status of the Earth observation instruments on DSCOVR and plans for their operation. URLs or informational files would be a great help

and, after a prod, received this reply

Dr, Rabett:

Thanks for your email regarding the status of DSCOVR. At this time, NOAA is not able to  answer your questions, pending the outcome of the ongoing Congressional budget process. Once those issues have been resolved, we'll be in a better position to discussthe way forward on DSCOVR.

Regards, Michael Simpson
DSCOVR Program Manager

The list of copy to's on the Email included

NESDIS OSDactions: The Office of Systems Development (OSD) conducts requirements definition studies; provides overall systems planning; performs conceptual and detailed engineering; arranges the development and manages the acquisition of major system elements (spacecraft, instruments, launch services, and ground systems); and coordinates the integration, installation, and acceptance of NOAA civil operational environmental satellite systems and several of the higher ups in the OSD  and people in NOAA public affairs.

This is a NASA built satellite, but NOAA is the mission lead and responsible for operation.  There appears to be a concern at NOAA about committing to the Earth Observation part of the mission and its costs. 

The Rabett has been known to kick over a few hornet's nests, and this may be one.  It is obviously a decision that NOAA and NASA want to keep in house.   Shall we help them?

Explain the Universe. Give Two Examples

was one of the questions Eli and the bunnies wrestled with as a possible stumper on our comprehensive exams.  AGU has another:  Define the Anthropocene

But it has to be done in terms of what the cyanobacteria, or whatever succeeds humans, will be able to spot in 100K years or more.  Paul Crutzen introduced the term to describe an epoch in which humans dominate changes to the Earth, but for the geologists (and they have the last word in naming epochs) it has to be done in terms of traces in the solid Earth at the stratigraphic level.

There is a working group and there was a symposium on this issue at the 2012 AGU and an article in EOS Jan 22.  Anthony Barnosky from UC Berkeley pointed to

some applicable biostratigraphic evidence for the placement of the Anthropocene boundary could include biostratographic zones for taxa lineage, assemblage, and abundance. He also noted that the road system could be a useful boundary layer. Barnosky said that roads, which often include several layers of geologically resistant human-derived strata, “are probably going to be a more significant boundary layer in the long run than the K-T boundary clay.” Defining the Anthropocene as a formal epoch “clearly is already supportable by paleontological principles you would apply for other epochs,” and biostratigraphy argues for a Holocene-
Anthropocene boundary near 1950, he noted.

IEHO, some of the folks are too hung up on assigning an exact date.  You can't do that for other Epochs.

What say thee.  The Subcommission of Quaternary Stratigraphy is interested in hearing.