** 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.)

**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.)

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

## 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.)

## 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.)

## 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.)

## Clicking to Expand Concealed Text in HTML

Arvind Satyanarayan’s “Toggle Visibility – Show/Hide Anything” is worth knowing about. (Click here to read more.)

## 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)

## 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

## 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

## 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.

## 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

## 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.

## Naturalism

I’ve started reading the just-published book, God’s Undertaker: Has Science Buried God?, of John Lennox, whom I met at St. Ebbe’s. It’s good. I think I see the essence of the philosophical position of Naturalism now,Click here to read more

## Shoulder Muscles and Handwriting

"Tips for improving your handwriting," by Dyas A. Lawson sounds worth trying.Click here to read more

## Weighted Least Squares and Why More Data is Better

<p>In doing statistics, when should we weight different observations differently?<p>

Suppose I have 10 independent observations of $x$ and I want to estimate the population mean, $\mu$. Why should I use the unweighted sample mean rather than weighting the first observation .91 and each of the rest by .01?<p>

Either way, I get an unbiased estimate, but the unweighted mean gives me lower variance of the estimator. If I use just observation 1 (a weight of 100% on it) then my estimator has the variance of the disturbance. If I use two observations, then a big positive disturbance on observation 1 might be cancelled out by a big negative on observation 2. Indeed, the worst case is that observation 2 also has a big positive disturbance, in which case I am no worse off by having it. I do not want to overweight any one observation, because I want mistakes to cancel out as evenly as possible.<p>

All this is completely free of the distribution of the disturbance term. It doesn't rely on the Central Limit Theorem, which says that as $n$ increases then the distribution of the estimator approaches the normal distribution (if I don't use too much weighting, at least!).<p>

If I knew that observation 1 had a smaller disturbance on average, then I *would* want to weight it more heavily. That's heteroskedasticity. <p>

## Who Most Wants To Be Elected Policeman?

Jerusalem Post via National Review

Two weeks after Israel’s alleged bombing raid in Syria, which some foreign reports said targeted North Korean nuclear material, the UN’s nuclear watchdog elected Syria as deputy chairman of its General Conference on Monday.

## Asymptotics

Page 96 of David Cox’s 2006 Principles of Statistical

Inference has a very nice one-sentence summary of asymptotic theory:

[A]pproximations are derived on the basis that the amount of

information is large, errors of estimation are small, nonlinear

relations are locally linear and a central limit effect operates to

induce approximate normality of log likelihood derivatives.

## Bayesian vs. Frequentist Statistical Theory

The Frequentist view of probability is that a coin with a 50% probability of heads will turn up heads 50% of the time.

The Bayesian view of probability is that a coin with a 50% probabilit of heads is one on which a knowledgeable risk-neutral observer would put a bet at even odds.

The Bayesian view is better.

When it comes to statistics, the essence of the Frequentist view is to ask whether the number of heads that shows up in one or more trials is probable given the null hypothesis that the true odds in any one toss are 50%.

When it comes to statistics, the essence of the Bayesian view is to estimate, given the number of number of heads that shows up in one or more trials and the observerâ™s prior belief about the odds, the probability that the odds are 50% versus the odds being some alternative number.

I like the frequentist view better. Itâ™s neater not to have a prior involved.

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