Kingsley and Darwin. From Wikipedia, I learn that Charles Kingsley, a well-known Victorian evangelical pastor, was an enthusiast for Darwin's theory of evolution--- at at least in Darwin's first book. The Origin of Species. (Click here to read more.)

He was sympathetic to the idea of evolution, and was one of the first to praise Darwin's book. He had been sent an advance review copy and in his response of 18 November 1859 (four days before the book went on sale) stated that he had "long since, from watching the crossing of domesticated animals and plants, learnt to disbelieve the dogma of the permanence of species."[2]. Darwin added an edited version of Kingsley's closing remarks to the next edition of his book, stating that "A celebrated author and divine has written to me that 'he has gradually learnt to see that it is just as noble a conception of the Deity to believe that He created a few original forms capable of self-development into other and needful forms, as to believe that He required a fresh act of creation to supply the voids caused by the action of His laws '." [3]

I just realized that the title of Darwin's book is about the weakest part of his theory. He explains the spread of species, and the adaptation of species by natural selection, but the "origin of species"? At a minimum, that needs the idea of mutations introduced later, and even that does not work very well, it seems.

Hard Hat Area. (click to enlarge)

Price Discrimination Terminology. Last week at the I.O. workshop someone had a good idea for replacing the old 1st, 2nd, 3rd degree price discrimination terminology. Exogenous-feature price discrimination is based on things the buyer can't change that the seller observes, such as his age. Endogenous-feature price discrimination is based on things the buyer can change, such as the quantity he buys or the quality he buys.

The Uses of Suffering. Not all suffering can be explained as useful, but some can, as Paul does in Romans 5:3-5: (Click here to read more.)

More than that, we rejoice in our sufferings, knowing that suffering produces endurance, and endurance produces character, and character produces hope, and hope does not disappoint us, because God's love has been poured into our hearts through the Holy Spirit which has been given to us.

The sermon at St. Ebbe's today was on that passage, and I tried applying it to my own sleepiness at the time. Hardly suffering, but one of those little annoyances that we ought to try to turn to our advantage. Maybe I'll get a little endurance out of it.

The progression is interesting in the passage. Really, I'd have to learn about the Greek to understand it. The King James Version uses quite different words in the middle-- Patience and Experience.

And not only [so], but we glory in tribulations also: knowing that tribulation worketh patience; And patience, experience; and experience, hope: And hope maketh not ashamed; because the love of God is shed abroad in our hearts by the Holy Ghost which is given unto us.

At any rate, the point is that tribulation is, for the faithful, a cause of hope, not of despair, but not directly. God wants us to develop character through our life on earth, and that seems to require suffering. Why, we must leave as a mystery perhaps, but it does not seem unreasonable that God's aim is to create a certain sort of being that requires memories of mild suffering. This is not as hard as the Problem of Evil; this passage does not seem directed towards that.

HTML-Expanding Thumbnail Images. Highslide is javascript for putting a thumbnail image to show up in your HMTL page and for another, larger, file, to appear if it's clicked upon. (Click here to read more.)

It's freeware for noncommercial use. The instructions are not very clear, but I got it to work without too much trouble. Here are my instructions:

1. Download the zip file.

2. Unzip it.

3. Upload the "highfile" directory to the top directory of your weblog. In my case, with Blogger, this is the same directory where I have blogger.html and index.html, and it is not the root directory for my server.

4. Save one version of your graphic file with full quality (say, 1012kb) and another with lower quality but faster to load for the thumbnail which shows up first (say, 24kb).

5. Don't put the entire code into your weblog entry. Blogger objects to having things like html, head, body, there. Instead, put in something like my example: http://rasmusen.org/t/images-2007/highfile.example.txt. What it looks like as a blog entry is here.

6. Or, change your Blogger template, which as the css style file as part of its file, by inserting http://rasmusen.org/t/images-2007/highfile.example3.txt in the style section of it. Then you can leave the style parts out of each blog entry, just using a blog entry like http://rasmusen.org/t/images-2007/highfile.example2.txt.

I've also done this for Wordpress. There, the css file in step 6 is inserted in the Style Sheet. The highfile directory in step 3 is loaded up to some wordpress directory. I put up duplicates to make sure, to the top directory and to the wp-content one where the index.htm file is.

I changed the code slightly. I deleted the height parameter, because if you have both a height and a width parameter the image is fit into that thumbnail space and distorted. Some people might want that, though.

Longevity. Ian Ayres, author of Supercrunchers (which sounds good though I've only read the first chapter as yet) told me of Northwestern Mutual's "The Longevity Game" website, which lets you estimate how long you will live. If I remember rightly, I came out to live to 87.

Jimmy Carter. David Frum lists a couple of sleazy things about Jimmy Carter. I ought to link to a cite that collects items about the old pharisee, but this will do for now. (Click here to read more.)

In his book, Palestine: Peace Not Apartheid, Carter plagiarized maps drawn by former Middle East envoy Dennis Ross for Ross's own books, and then presented the work as Carter's own.

While the IPCC has tried to spread awareness of genuine risks, Gore brings to his work all the objectivity and balance of a Hollywood screenwriter.

Worse, Carter systematically misrepresented conversations with Syrian president Hafez Assad, to create a false impression that Assad was more conciliatory than he really was. The note-taker at Carter's meetings with Assad, Kenneth Stein, resigned in protest from his post at the Carter Center after the publication of Peace Not Apartheid.

Colorful Blurs From Christchurch's hall.

Playing at Christianity. The Baylyblog has this excellent quote from Kierkegaard. I really should read more of him.

We all know what it is to play warfare in mock battle, that it means to imitate everything just as it is in war. The troops are drawn up, they march into the field, seriousness is evident in every eye, but also courage and enthusiasm, the orderlies rush back and forth intrepidly, the commander’s voice is heard, the signals, the battle cry, the volley of musketry, the thunder of cannon—everything exactly as it is in war, lacking only one thing...the danger.

So also it is with playing Christianity, that is, imitating Christian preaching in such a way that everything, absolutely everything is included in as deceptive a form as possible—only one thing is lacking...the danger. (Kierkegaard, Attack upon Christendom)

This should link to my post on Alistair McGrath. A theologian should put himself on the line, rather than just describing what other people believe.

An economist, too?

Written Pornograph: A Recent Case. Via Baylyblog, the New York Times, we learn that the Clinton Administration quit doing obscenity prosecutions. Bush has resumed, but only now has brought one for anything other than images. What the liberals courts will do with it is uncertain. (Click here to read more.)

In an era when pornography has exploded on the Web almost beyond measure, Ms. Fletcher is one of only a handful of people to have been singled out for prosecution on obscenity charges by the Bush administration. She faces six felony counts for operating a Web site called Red Rose, which featured detailed fictional accounts of the molesting, torture and sometimes gruesome murders of children under the age of 10, mostly girls....

The Fletcher case has been brought by Mary Beth Buchanan, the United States attorney for Western Pennsylvania, who is regarded by many people in the pornography industry and by outside analysts as the government’s most aggressive opponent of the spread of pornography in the nation....

Although a narrowly divided Supreme Court said in 1973 that images were not necessary to label a work obscene, there has not been a successful obscenity prosecution in the country that did not involve drawings or photographs since then.

Courts have overturned or blocked convictions connected to other nonillustrated books, including the well-known “Fanny Hill: Memoirs of a Woman of Pleasure,” on the basis that sexual images have a fundamentally different impact than words alone. ...

About the same time the Fletcher case goes to trial, Ms. Buchanan will be prosecuting a second obscenity trial in the same courthouse involving a large-scale producer of pornographic films called Extreme Associates, based in California. The company’s films depicted women being gang-raped and defecated on.

In addition to those cases, Ms. Buchanan said in the interview that she had several more in the pipeline.

Todd Lochner, an assistant professor at Lewis & Clark College in Portland, Ore., who has written about prosecutorial decision-making in obscenity cases, said that Ms. Buchanan had established herself as the nation’s foremost obscenity prosecutor. “I can’t think of anybody who is as aggressive as she is,” Professor Lochner said.

Ms. Buchanan said she selected cases that she hoped would have deterrent effects on other pornographers.

“We want producers to know that these things are not tolerated,” she said. Ms. Buchanan said that the rarity of obscenity prosecutions during the eight years of the Clinton administration meant that the pornography industry had come to believe that law enforcement had tacitly “agreed to an anything-goes approach.” ...

While pornography by itself is not illegal, it can be prosecuted as obscenity if it fits the definition laid out by the Supreme Court more than 30 years ago. Under that ruling, Miller v. California, a work may be deemed obscene if, taken as a whole, it lacks artistic, literary or scientific merit, depicts certain conduct in a patently offensive manner, and violates contemporary community standards.

Despite stirring anti-pornography speeches by both heads of the Justice Department during the Bush administration — John Ashcroft and, more recently, Alberto R. Gonzales — there have been fewer than two dozen federal obscenity prosecutions that did not also involve charges of child pornography. The making and possession of child pornography, a separate category, has, however, been prosecuted widely. (Ms. Fletcher is not being prosecuted for any violations of the child pornography laws.)...

The indictment, which has the potential for a long prison term, charges Ms. Fletcher with commercial involvement with obscenity because she charged people $10 to join her group. Jerome Mooney, another of her lawyers, argued in court that the fee barely covered her expenses and was imposed only because she believed using a credit card requirement would prevent minors from signing into the site. In the end, only 29 people subscribed, at least one of whom is likely to have been a police informant.

 

Writing Numerical Examples. I was just reading Frank Buckley's Just Exchange (what a nice title!) and he gave a numerical example using $105 and $100. That is how I would do it too. But my eye started skipping past the numbers. I wonder if it would be better to use words, and to adjust the numbers. Should he have used fifteen dollars and fourteen dolalrs instead? I'm not sure.

A Grand Stone Head. From inside Dore Abbey in Herefordshire. Click the image to enlarge it.

Antitrust Thoughts. It's the mark of a good journal article that it stimulates thought. On the strong recommendation of JV, I started reading Professor William Kovacic's "THE INTELLECTUAL DNA OF MODERN U.S. COMPETITION LAW FOR DOMINANT FIRM CONDUCT: THE CHICAGO/HARVARD DOUBLE HELIX," Columbia Business Law Review, 2007. He argues that modern antitrust law should not be viewed as Chicago School plus Post-Chicago School, but as Chicago School economics plus Harvard Law pragmatism. Areeda, Turner, and Breyer had a big impact in the way they thought about how judges can actually implement antitrust law. (Click here to read more.)

This got me to thinking about antitrust generally. First, what are the main problems with market power in the economy? We're doing a good job in developed economies with mergers, price-fixing, and unfair practices. We're doing a bad job with monopoly labor unions, monopoly government providers of services, trademark monopolies, and copyright monopolies. Marginal improvements in antitrust law are of trivial importance compared with the legal monopoly given to Microsoft Windows, either looking at the output restriction or the lost entry by more efficient competitors.

Nonetheless, antitrust policy is interesting at the margins, if not important. This week the theory workshop had a neat idea about merger policy. I won't try to trace the credit for it, but it goes like this. Suppose our aim is to maximize the sum of producer and consumer surplus. Should we make our merger rule, "The merger's OK if (PS+CS) go up"? No. If we impose that as a constraint, a company will propose the merger in that category which most increases PS, not the merger that most increases PS+CS. If, instead, we had a rule of "The merger's OK if CS goes up", then the company will still only propose efficient mergers, because we don't have to require the company to make sure PS goes up too. The only problem is that sometimes companies will not have any CS-increasing mergers to propose, and we'll lose some efficient mergers in which PS+CS would rise but CS fall.

What I really need to do, though, is figure out how to categorize monopoly as a form of market failure. Market failure taxonomy is a mess. Component problems include: real externalities, asymmetric information, rentseeking, and poor thinking. Market power is *not* directly a problem, though it is a contributor.

If there is perfect information and contract enforcement, a monopoly will use perfect price discrimination and there will be no triangle losses. It is only because a monopolist doesn't know the demand curve of each consumer or can't prevent resale that he would use simple monopoly pricing and restrict output. Otherwise, the Coase Theorem works.

The monopoly position is a contributor, though, because if sellers compete, then not knowing demand curves and not being able to enforce fancy contracts doesn't matter.

One way we might look at the monopoly problem is as a form of rentseeking. The loss is not directly from monopoly, but from inefficiencies arising in the attempt to manipulate a market. Indeed, rentseeking itself is really an informational problem. If Smith knows that Jones can spend $200 on a gun and steal Smith's car, then Jones can offer Smith $1 for the car and get it without having to buy the gun. Rentseeking losses occur only when the rentseeker and victim cannot reach an agreement.

It is useful to think of two kinds of rentseeking. One is direct taking of goods-- pickpocketing, for example. The other is attempts to manipulate prices --- monopoly output restriction. But where, then, do I put attempts to change rules?

Negative Reviews and Inframarginal Subsidies for Investment. MR emailed me recently asking me to look at part of a review by RM of his recent book. As you can see, the review says the book's theory is "remarkable", quotes at length including a diagram, and then implies that the theory is wrong, without saying why. (Click here to read more.)

MR wondered if he and his co-author had made some obvious mistake and if I'd explain it to him.

I was equally puzzled, though. Maybe they should have used a numerical example. Suppose that a Japanese company invests 10 billion yen because it has to pay a 4% interest rate to borrow the money in the private financial markets and the last yen of those 10 billion invested would have a return of 4%. If they invested another billion yen, they'd only get 3%, having to go to worse projects, so they don't. But then the Japanese government offers to lend them the 10 billion at an interest rate of 2%. They eagerly take up the offer of course. But they still don't invest more than 10 billion. If they invested another billion by borrowing at 4% from the private sector, they'd still only get a 3% return and they'd lose money. Thus, government lending meant to increase investment won't succeed unless the government lends more than a private company was originally borrowing. Put more technically, this is an example of how inframarginal price changes have zero effect on real behavior.

That idea is correct, unless I'm missing something big, and it looks to me as if the explanation above is correct too. Am I missing anything?

I think there are two morals to the story. First, simple Chicago-style price theory really is remarkable. It can surprise even an experienced, much-published economist. Second, when criticizing someone's ideas in print it's a good idea to send a copy to them to see if they have a response you hadn't thought of.

December 2: Someone suggested that even an inframarginal subsidy would increase investment via its effect on the probability of bankruptcy. A firm which has a subsidy will be more profitable, and hence less likely to go bankrupt, and hence will be able to borrow more cheaply, and hence will invest more. That sounds right. A lump sum subsidy would have the same effect.

A Model of Probabilistic Rules for Project Acceptance. This is inspired by a recent working paper by Vickers and Armstrong. Project i has payoff (Ui,Vi) to agent and principal and is feasible with probability theta_i. Both players must agree to implement a project; otherwise they get (0,0). They can agree to one project at most. Only the agent observes which projects are available. He can keep silent or he can truthfully reveal the (U,V) of a project, but he cannot lie. (Click here to read more.)

First, the principal commits to an accept/reject rule.

Second, the agent proposes a project if he wishes.

Third, if an acceptable project was proposed, it is implemented.

Project A: (9,10), probability = 1.

Project B: (7,100), probability = .7.

Rule Alpha: Accept the proposed project if V < 8.

Rule Beta (best) Accept the proposed project for sure if V < 8. Accept with probability .5 if V > 8.

Rule Gamma (worst): Accept any proposed project. There are two possible states of the world. With probability .7, both A and B are feasible; with probability .3 only A is. Under Rule Alpha, the agent will propose either B or nothing. The principal's expected payoff is .7(100) + 0 = 70. Under Rule Beta, the agent will propose B if it is feasible and A otherwise. The principal's expected payoff is .7(100) + .3(.5)(10) = 71.5. Under Rule Gamma, the agent will propose A. The principal's expected payoff is 1. What's happening is that since the principal can't use cash to reward a high-V proposal (or punish a low-V one), he commits to destroying some of the value of a low-V proposal. Could we change the example to have probability .001 of every other project on the convex set containing A and B?

Global Warming. This picture is from NASA. It shows nicely that global warming shows up as only small summer changes, with the action coming in winter-spring temperatures in the Arctic centered in Yukon and Siberia. I also came across NASA's page on how they got the 2000-2006 data wrong, with their explanation that the mistakes in their secret method weren't really important. True, but their credibility is gone now, and if they got the USA temperatures wrong in the direction they favor, how about the much harder to measure temperatures elsewhere in the world?

Global Warming: Ice Caps and the Argument from Authority. Why should we trust a PhD in climate science when he talks about ice caps any more than we trust a D.Phil. in theology when he talks about God? Both are experts, but both entered their vocations because they had policy views on their subjects. (Click here to read more.)

This makes it hard to figure out the science on global warming, of course. Here's an example. If there is global warming, will sea levels rise?

Sea levels might rise because the warmth will melt the ice near the North Pole. Also, if sea water is warmer, it will expand, even if there is no more of it.

Sea levels might fall because the warmth and the extra water in the air will increase snowfall near the South Pole, where most of the ice in the world is. Also, there will be more water in the atmosphere instead of in the ocean.

Which is the bigger effect?

Alistair McGrath. David Wegener writes this about Alistair McGrath's theologizing.(Click here to read more.)

Maybe McGrath is right about Calvinism, the first point---I don't know.

McGrath consistently speaks out against Reformed theology. In his published works dealing with Post-Reformation theology, he has championed the position that the Calvinists who followed Calvin betrayed their mentor’s theology and came up with doctrine not in line with his. Well, this is bunk, even if it was articulated by theologians like Karl Barth and a whole host of others who have tried to tell us that Calvin was not a Calvinist. Richard Muller and others have shown, time and again, that there are clear lines of continuity between Calvin and the later Calvinists and any minor changes that occurred are merely in the packaging as the Calvinists sought to pass on the faith to their children. Yet McGrath continues to maintain a perspective that has been shown to be false and one used to dismiss the relevance of Puritan and Reformed thinking for today.

5. It is surprisingly difficult to find out what McGrath actually believes. His systematic theology text is really historical theology. There is no Scripture index and very little discussion of the meaning of actual Bible verses and how they speak to the normal loci of systematic theology. Even after a long historical presentation, he rarely if ever says, “these are the range of views presented in the history of the church, but I am persuaded that the Scriptures teach this because …” So, for example, in the chapter on “The Doctrines of Human Nature, Sin and Grace,” McGrath first discusses, “The Place of Humanity within Creation.” Genesis 1:27 is quoted and its meaning is explored by quoting and summarizing from Tertulliian, Origen, Augustine, Lactantius, Athanasius, the Cappadocians, Cyril of Jerusalem, and then back to Augustine. At the end, we’re never told what McGrath believes or even how he evaluates what these theologians have taught. The questions at the end of each chapter sometimes require answers more personal than the preceding exposition of views.

6. While McGrath is identified with the evangelical movement in England, such a designation has problems. The label “evangelical” used to have meaning in the English context but it seems to me that it has less and less today. An evangelical used to refer to an orthodox Protestant who believed the gospel, aimed to share it with the whole world, and found it at the center of an inerrant and infallible Bible. Today the term is used as a self-designation by so many who believe none of this. The difference between someone who calls himself a left-wing evangelical and a liberal who reads the Bible and accepts some of what it says is non- existent. Though it is hard to tell (see above), McGrath does not hold to inerrancy (it’s a recent American innovation), and he seems open to salvation outside of explicit faith in Christ. Yet he insists on using the term “evangelical” to refer to himself, and so he is contributing to the loss of meaning for the term.

7. He is an Anglican, come what may. McGrath wrote a shameful piece just as Rowan Williams was being named the archbishop of Canterbury (and thus the head of the Anglican communion of churches). The liberal views of Williams were well known, including his approval of the ordination of homosexuals. McGrath’s piece was a “down on his knees” plea for Bible- believers not to leave the Anglican church. It calls to mind the question Lloyd-Jones put to evangelical Anglicans (and he asked it when the term still had meaning): Is there any position that, if the Anglican church took it, would cause you to leave the church? MLJ was answered with a resounding silence. There is no line in the sand and McGrath’s article helps to prove it. Nothing will cause him to do a Popeye: “that’s all I can ‘stanz,’ I can’t ‘stanz’ no more”. He is an Anglican and the phrase, “evangelical Anglican” has been voided of content.

8. His wife, Joanna Collicutt McGrath, is an ordained Anglican priestess, so we know where he stands on that one. ...

"No Good News: A reply to Alistair McGrath" by Garry Williams criticizes the McGrath piece about the new archbishop. I couldn't find the original piece.

Partial Identification and Chi-Squared Tests

I heard Adam Rosen give his paper, "Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities." It stimulated some thoughts. (Click here to read more.)

1. Suppose we wanted to estimate means of X and Y,(μ(x) μ(y)). Our theory says that they are distributed independently, bounded by [0,1]. But we only have data on X.

My maximum likelihood estimator will be a point estimate for μ(x) and an interval for μ(y). I have partial identification. If the sample mean of x were .6, my estimate would be (.6, [0,1]).

If I had a prior on μ(y), I could use that. Maximum likelihood or any kind of minimum distance-MOM estimator would leave every value in [0,1] equally good as an estimate of μ(y).

Another example would be if we wanted to estimate the mean of X+Y, μ(x+y), but only had data on x. If the sample mean of x was .6, our estimate for μ(x+y) would be the interval [,6, 1.6].

We would also have partial identification in a model in which y = αx1 + βx2 but x1 and x2 were endogenous and we had an instrument for x1 but not for x2.

2. Suppose we have partial identification, and our estimation has yielded us a best-estimate interval for the single parameter theta, which is thetahat = [5,10]. Our null hypothesis is that &theta &ge 6. Do we reject it?

We want to construct a confidence set C such that if we repeat the procedure, &alpha = 5% of the time we will wrongly reject the null when it is true:

(1) Prob(&theta -hat is in C)|&theta &ge 6) = .05

C will be a set of intervals.

But that probability in (1) is ill-defined, because C will differ depending on whether &theta =.6, 7, 9, 26, or whichever value greater than 6 we might pick. So we'll be conservative, making it hard to reject the null, and pick the value of &theta for which C is biggest. That kind of conservatism problem arises even in the simplest frequentist inequality null-- the problem is that the null is not "simple".

A nice thing about the chi-squared test is that it avoids having to define C for the &theta -hat space. Instead, we just find the scalar chibarredsquared statistic, a function of the interval, and look at the confidence interval for that test statistic. This is what chi-squared tests do in general--- they transform a multi-dimensional acceptance region into a one-dimensional acceptance interval. For example, we could use a Chi-squared test (or its close relation, an F-test), to test whether the pair of numbers (α, β) was close enough to (0,0).

Here, though, it's especially neat because we're not just doing an R-n to R mapping: we're mapping from a set in (R, intervals on R) to R. An interval on R can be reduced to its pair of endpoints, but even then our mapping wouldn't be as simple as a mapping from three real numbers to one.

King Offa's Border Policy

I was reading about the border policies of King Offa, the Anglo-Saxon king of Mercia. He made no attempt to conquer Wales. Instead, he built Offa's Dyke, a boundary-marking ridge, and every few years he raided Wales. (Click here to read more.)

That is a common imperial boundary policy. Mark the boundary, so the barbarians know how far they're permitted to loot to, and if the barbarians make trouble, launch a punitive expedition and burn down some of their houses. Don't attempt to conquer them, because it's not worth the expense of keeping a garrison in a wasteland that won't yield much taxes anyway.

That's what we should have done in Iraq and Afghanistan, with the addition of pre-emptive expeditions to stamp out any preparations for barbarian raids.

Metaphysics

What do you get if you castrate a man, feed him estrogen, and stuff him into a dress?

---A fat, castrated, man in a dress.

An Umbrella with a Drip Case

I brought this umbrella back from Taipei. It has a case to prevent dripping from the wet umbrella onto the floor when it is folded up. The case opens automatically when you open the umbrella, telescoping down into a little cap on top of the umbrella.

A Coin Flip Example for Intelligent Design

1. Suppose we come across a hundred bags of 20-chip draws from hundred different urns. Each bag contains 20 red chips. We naturally deduce that the urns contain only red chips. (Click here to read more.)

2. We realize that somebody might have come along and rigged the bags. So we decide to look at videotape of what happened.

3. On looking at the videotape, we see that someone came along and took away 95 of the bags and replaced them with new bags. We now have lost those bags' evidence of redness.

4. But what about the other 5 bags? Our videotape showed nobody replacing them. Shouldn't we be surer than at (1) that those 5 urns contain only red chips? And mightn't we deduce that the other 95 urns contain only red chips too?

Clicking to Expand Concealed Text in HTML

Arvind Satyanarayan's "Toggle Visibility - Show/Hide Anything" is worth knowing about. (Click here to read more.)

It is Javascript code for HTML files such that if you click on certain text, other text appears or disappears, toggling from its current state. As modified by Manu Agrawal in the comments and by me (he had a typo I think), what you do is put the following just after the <body> command in the HTML file (maybe anywhere after it would do)

<!-- Arvind Satyanarayan script added by John Smith on Oct XX, 20XX. -->
<script type="text/javascript">
<!--
function toggle_visibility(id) {
var e = document.getElementById(id);
if(e.style.display == 'block')
e.style.display = 'none';
else
e.style.display = 'block';
}
//-->
</script>

Then, to display "(Click here to read more.)" and have "Here is where all the rest of the post would go." display when "(Click here to read more.)" is clicked (or concealed when it is clicked again), insert

<a href="#" onclick="toggle_visibility('07oct2');">(Click here to read more.)</a>

<div id="07oct2" style='display:none'>
Here is where all the rest of the post would go.
</div>

You can insert as many of these as you like in one file, with just one insertion of the script, so long as you give distinct titles, not "07oct2" to the second and later concealed sections.

Case Control Studies and Repeated Sampling

A standard counterintuitive result in statistics is that if the true model is logit, then it is okay to use a sample selected on the Y's, which is what the "case-control method" amounts to. You may select 1000 observations with Y=1 and 1000 observations with Y=0 and do estimation of the effects of every variable but the constant in the usual way, without any sort of weighting. This was shown in Prentice & Pyke (1979). They also purport to show that the standard errors may be computed in the usual way--- that is, using the curvature (2nd derivative) of the likelihood function. (Click here for more)

This, I was skeptical of. If the constant is misestimated, how can you deduce the variance of the disturbance term, and if you can't deduce that, how can you deduce the standard error of any of the coefficients? Nowhere have I seen a clear demonstration or an intuition for the result, so I thought there might be a crucial unnoticed mistake in the math somewhere, as is not unknown in famous papers (e. g. Hotelling on location, Tullock on overdissipation, Viner on average cost curves, and Rothschild-Stiglitz on risk).

Since I did not follow all the steps of the Prentice-Pyke proof and so did not know of any error in what they did, I tried doing a Monte Carlo study which seemed to confirm my intuition.

Since then, however, I have seen where my Monte Carlo study went wrong, and now I believe Prentice and Pyke. Some details are instructive.

1. An intuition-- a bit shaky, I think, but better than nothing (let me know if it's false). Suppose that a coefficient is estimated correctly by some estimator. We want to estimate the estimator's standard error, to know how variable the estimate would be if we repeated the estimation with different disturbances. For this, we need to know how noisy the data is. We do not need to know how noisy the data in the whole population is, however, just how noisy in the kind of sample we draw. If our procedure is to draw a biased sample, then we need to know what will happen in other biased samples, not in the population. It is okay to use the sample for this purpose. In using a standard error, we are not generalizing anything to the population (not estimating goodness of fit, for example), we are just generalizing to repeated samples.

2. How to think about repeated sampling and how to do a Monte Carlow study. What I did was to construct a population of 60,000 data points, drawing X from a uniform distribution on [0,1] and a disturbance epsilon from a logit density with an α "constant" coefficient of -4 and a β X coefficient of 0. If α + epsilon < 0 then Y=0; if α + epsilon >= 0 then Y = 1. That yields 1,039 points with Y= 1, about 1.7% of them.

Our estimation procedure is to combine two random samples of 1,000 observations with Y=0 and 1,000 observations with Y=1 and do a logit estimate of alpha and beta. We would expect the estimate of alpha to be wrong-- not close to 0.017-- and the estimate of beta to be right-- close to 0.000-- since we have a large enough sample that consistent estimates ought to be close to the true parameters.

The maximum likelihood estimate would give us standard errors based on the second derivative of the likelihood function or on bootstrapping. In repeated sampling, we would expect the standard deviation of the alpha estimates not to be close to the average of the estimates of its standard error. The question to be investigated is whether the the standard deviation of the beta estimates is close to the average of the estimates of its standard error.

So far, so good. Where I made my mistake, I think, is in the definition of "repeated sampling". Ordinarily in frequentist thinking, in repeated sampling we keep the X values the same in each sample, and we draw new disturbances, which combine with the fixed X's to give new Y's. That also amounts to conditioning on the X's, though we wouldn't have had to condition the X's, since our estimator should work fine even if we changed the X's in each sample too. (If we did change the X's, though, that change the information content in each sample--- a sample in which X only varied between .3 and .4 would have less information and yield worse estimates than one with X varying widely between .02 and .94. So in small samples, especially, we'd have to make some allowance for that.)

Here, though, we can't keep the X's fixed. If we did, then although our first sample would have 1,000 observations with Y=1, our succeeding samples would have about 34. We wouldn't be using the case-control method.

So what we have to do is to think about repeated samples with 1,000 Y=0 observations and 1,000 Y=1's. Turning our usual thinking upside down, we need to keep the Y's fixed, draw new disturbances, and let the X's vary. This is especially hard to think about here, because knowing Y and epsilon does not tell us X-- remember, Y is coarse and contains less information than alpha + beta*X + epsilon,and beta is zero here too, making things even worse.

The best way to proceed is to think about repeating the entire scientific procedure, including the sampling as well as the estimation. The way I did this was to take 100 n=2000 samples from the 60,000-point population, each time combining equal-sized subsamples with Y=0 and with Y=1.

Recall, however, that there are only 1,037 Y=1 values in the entire population. Thus, my repeated sampling had to be with replacement, and was using the same Y=1 observations over and over. It is OK to use the same X values repeatedly, but these observations also had the same epsilon values each time, so the samples are not independent in the way needed for the law of large numbers to work. The standard errors computed by maximum likelihood came out wrong--- not equal to the standard deviation of the estimates, but that is to be expected when the draws are not independent.

Realizing this, I also tried doing the procedure with 100 n=200 samples instead of 100 n=2000 samples. I still used sampling with replacement, but now there was less overlap between replacements, less dependence between samples. And now the estimated standard errors were close to the standard deviations.

This, I expect is what would happen if I did the kind of repeated sampling that is our thought experiment for the kind of real studies that use the case-control method. That thought experiment is to take repeated draws of 60,000-point populations, with the same X's each time but with different epsilons and hence Y's. Each of the 100 Monte Carlo samples would be from a different population draw.

Evolution and Religion

David Sloan Wilson, author of Darwin’s Cathedral, a book about the usefulness of religion as an evolutionary adaption, harshly criticizes Richard Dawkins for sloppiness in thinking about religion and evolution. This is part of Dawkins's contempt for group selection, which is misguided. Click here to read more

It is the more sober work of Wilson that is the more serious criticism of Christianity. He says, re Dawkins:

Richard Dawkins and I share much in common. We are both biologists by training who have written widely about evolutionary theory. We share an interest in culture as an evolutionary process in its own right. We are both atheists in our personal convictions who have written books on religion. In Darwin’s Cathedral I attempted to contribute to the relatively new field of evolutionary religious studies. When Dawkins’ The God Delusion was published I naturally assumed that he was basing his critique of religion on the scientific study of religion from an evolutionary perspective. I regret to report otherwise. He has not done any original work on the subject and he has not fairly represented the work of his colleagues....

As one example reported in the July 6, 2006 issue of Nature, a group of microbiologists headed by Benjamin Kerr cultured bacteria (E. coli) and their viral predator (phage) in 96-well plates, which are commonly used for automated chemical analysis. Each well was an isolated group of predators and their prey. Within each well, natural selection favored the most rapacious viral strains, but these strains tended to drive their prey, and therefore themselves extinct. More prudent viral strains were vulnerable to replacement by the rapacious strains within each well, but as groups they persisted longer and were more likely to colonize other wells. Migration between wells was accomplished by robotically controlled pipettes. Biologically plausible migration rates enabled the prudent viral strains to persist in the total population, despite their selective disadvantage within groups.

As a second example reported in the December 8, 2006 issue of Science, economist Samuel Bowles estimated that between-group selection was strong enough to promote the genetic evolution of altruism in our own species, exactly as envisioned by Darwin. These and many other examples, summarized by Edward O. Wilson and myself in a forthcoming review article, are ignored entirely by Dawkins, who continues to recite his mantra that the selective disadvantage of altruism within groups poses an insuperable problem for between-group selection.

 

Election Fraud and Fired US Attorney John McKay

I have read people saying that election fraud has trivial importance in the United States, so the Republicans' desire for investigations and for identity to be verified for voting is unjustified. Here's clear evidence against that. Note, too, the behavior of US Attorney John McKay, who was later fired.Click here to read more

It was right to fire him for that.

But the most interesting news came out of Seattle, where on Thursday local prosecutors indicted seven workers for Acorn, a union-backed activist group that last year registered more than 540,000 low-income and minority voters nationwide and deployed more than 4,000 get-out-the- vote workers. The Acorn defendants stand accused of submitting phony forms in what Secretary of State Sam Reed says is the "worst case of voter-registration fraud in the history" of the state.

The list of "voters" registered in Washington state included former House Speaker Dennis Hastert, New York Times columnists Frank Rich and Tom Friedman, actress Katie Holmes and nonexistent people with nonsensical names such as Stormi Bays and Fruto Boy. The addresses used for the fake names were local homeless shelters. Given that the state doesn't require the showing of any identification before voting, it is entirely possible people could have illegally voted using those names.

Local officials refused to accept the registrations because they had been delivered after last year's Oct. 7 registration deadline. Initially, Acorn officials demanded the registrations be accepted and threatened to sue King County (Seattle) officials if they were tossed out. But just after four Acorn registration workers were indicted in Kansas City, Mo., on similar charges of fraud, the group reversed its position and said the registrations should be rejected. But by then, local election workers had had a reason to carefully scrutinize the forms and uncovered the fraud. Of the 1,805 names submitted by Acorn, only nine have been confirmed as valid, and another 34 are still being investigated. The rest--over 97%--were fake. ...

In Washington state, King County Prosecutor Dan Satterberg said that in lieu of charging Acorn itself as part of the registration fraud case, he had worked out an agreement by which the group will pay $25,000 to reimburse the costs of the investigation and formally agree to tighten supervision of its activities, which Mr. Satterberg said were rife with "lax oversight."...

Take Washington state, where former U.S. attorney John McKay declined to pursue allegations of voter fraud after that state's hotly contested 2004 governor's race was decided in favor of Democrat Christine Gregoire by 133 votes on a third recount. As the Seattle media widely reported, some "voters" were deceased, others were registered in storage lockers, and still others were ineligible felons. Extra ballots were "found" and declared valid 10 times during the vote count and recount. In some precincts, more votes were cast than voters showed up at the polls.

Mr. McKay insists he left "no stone unturned" in investigating allegations of fraud in the governor's race but found no evidence of a crime. But in an interview with Stefan Sharkansky of SoundPolitics.com in May, Mr. McKay admitted that he "didn't like the way the election was handled" and that it had "smelled really, really bad." His decision not to prosecute was apparently based on the threshold of evidence he insisted be met before he would even deploy FBI agents to investigate: a firsthand account of a conspiracy to alter the outcome of the election.

But Mr. McKay is incorrect in saying that he had to find a conspiracy in order to reach the federal threshold for election crimes. In Milwaukee, after the 2004 election U.S. Attorney Steve Biskupic investigated many of the same problems that were found in Seattle: felons voting, double-voting and more votes cast than voters who signed poll books. In 2005 Mr. Biskupic concluded that he had found nothing that "has shown a plot to try to tip an election," but he nonetheless prosecuted and won six convictions for felon voting and double-voting.

 

Note that the federal law apparently doesn't make it a crime to use fraud to change the result of an election---it only makes it a crime to use fraud to change the result of an election *because you want your side to win*. If you do it for money, that doesn't count. Or so the US attorneys interpret the law.

Wooden Forks

Kew Gardens had these nice wooden implements at the cafe near the Victoria Gate. Aren't they better than plastic?

Is Not Necessarily Equal To

At lunch at Nuffield I was just asking MM about some math notation I'd like: a symbol for "is not necessarily equal to". For example, and economics paper might show the following:

Proposition: Stocks with equal risks might or might not have the same returns. In the model's notation, x IS NOT NECESSARILY EQUAL TO y.

Click here to read more

I can't say x \neq y there, because maybe x=y, maybe not, depending on the parameter values.

If anybody knows of such a symbol, please let me know. In fact, just a symbol for IS NOT NECESSARILY might be useful, since we could combine it with other symbols, e.g.

x IS NOT NECESSARILY = y

Horse heights ARE NOT NECESSARILY > cow heights

The biased estimator IS NOT NECESSARILY \sim N(0,1).

OCTOBER 7. Stimulated by a comment below: The modal logic symbols might work well. Wikipedia's "Modal logic" says: "The basic modal operators are usually written (or L) for Necessarily and (or M) for Possibly."

Maybe I could say " x ≠ y" for "x is not necessarily equal to y".

How Does Christianity Affect My Life

A good question to ask oneself is: "How do I live my life differently because of my religious beliefs?" Or, put a little differently: "If I didn't believe X, how would my life change?" Personally, I don't think I'd engage in much vice, since gross sin is not advisable even if one's aim is temporal happiness. I guess I'd not be writing posts like this if I were not Christian, nor would I go to church, or teach my children about God, or find interest in reading the Bible or thinking about theology. I wouldn't pray, I suppose, though there is an earthly case to be made for prayer too. I would not give money to charity, and I would spend a lot more of my income--- that is perhaps the biggest behavioral change I would expect.

Bayesian vs. Frequentist Statistical Theory: George and Susan

Susan either likes George or dislikes him. His prior belief is that there is a 50% chance that she likes him. He also believes that if she does, there is an 80% chance she will smile at him, and if she does not, there is a 60% chance. She smiles at him. What should he think of that?

The Frequentist approach says that George should choose the answer which has the greatest likelihood given the data, and so he should believe that she likes him.Click here to read more

It warns, however, that if he follows this plan, and she really doesn't like him, then he will come to the wrong conclusion with 60% probability. Thus, he can't confidently reject the null hypothesis that she dislikes him. (Though he also could not confidently reject the null hypothesis that she likes him-- that plan would lead him to mistakenly rejecting the null 80% of the time!)

The Bayesian answer is that he should do this computation:

Prob(likes|smiles) = Prob (smiles|likes)Prob(likes)/Prob(smiles)

Prob(likes|smiles)= .8*.5/(.8*.5+.6*.5) = .4/(.4+.3) = 4/7.

If he must choose a binary action-- say, to invite her out or not-- then if the losses from each kind of mistake are symmetric, he should act as if she likes him, knowing that with probability 3/7 he will be making a mistake.

Now let's think about where prior information enters. It enters via the Prior, of course-- the 50% chance that she likes him. But it also enters via the Likelihood Function-- the 80% and 60% figures. If we ask how sure George is of his 50% prior, it is in the Likelihood Function that we need to look for the answer. Suppose we want to keep George's belief at 50% but make him very sure of 50%, as if he'd had lots of evidence on each side rather than not knowing Susan at all and guessing based on his experience with other women. How does that show up here?

It shows up as this one smiling incident having very little effect on his belief. If his prior is solid, then he thinks that the data conveys little information. Maybe she would smile with probability 80% if she likes him and 79% if she dislikes him. Moreover, the next time he meets her, her second smile or frown will convey about the same, small, amount of information.

If his prior were loose, the first incident would have a big impact and the second would have a noticeably smaller impact. Maybe she would smile with probability 80% if she likes him and 20% if she dislikes him. Moreover, the next time he meets her, her second smile or frown will convey less information-- maybe the numbers would shift to 80% and 40%.

But my last two paragraphs do not satisfy me. I must go on to other things, so I will leave this post now.

 

Civil Suits for Shoplifting

This sign at Sainsbury's grocery store says (you might have to enlarge it to get a clear view) that they not only criminally prosecute shoplifters, but use a more fearsome tactic: the civil suit. They'll go after the thief for their losses *and* their expenses in dealing with him.