Comments for Radford Neal's blog

Comment on Down Syndrome and Decision Theory by Radford Neal

Radford Neal — Sat, 03 Oct 2009 22:21:37 +0000

Note that I had to resort to the "cached" version to get the PDF of the paper mentioned above. From a brief glance, it seems to be flawed. It ends up using the expected value of a utility function, since the utility function is regarded as uncertain. But the mathematical nature of a utility function makes this expectation operation meaningless. Utility functions are defined only up to an arbitrary affine transformation, which destroys the ability to take expectations. I mentioned this problem to my colleague Craig Boutilier, who has done similar things, which resulted in him writing the following paper that attempts to solve the problem:: On the foundations of expectedexpected utility. I believe that, unfortunately, this paper does not actually solve the problem, which is essentially the same as the problem of interpersonal utility comparisons.

Comment on Down Syndrome and Decision Theory by Adriana

Adriana — Wed, 30 Sep 2009 09:28:08 +0000

An interesting post!
Here is a paper related to this subject

Making Rational Decisions using Adaptive Utility Elicitation (2000)

Comment on Design Flaws in R #2 — Dropped Dimensions by Los Angeles remodeling

Los Angeles remodeling — Wed, 26 Aug 2009 14:34:44 +0000

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Comment on The Harmonic Mean of the Likelihood: Worst Monte Carlo Method Ever by Harmonic mean estimators « Xi'an's Og

Harmonic mean estimators « Xi'an's Og — Thu, 30 Jul 2009 10:09:39 +0000

[...] support is one of those regions. This cancels the infinite variance difficulty rightly stressed recently by Radford Neal. In short, the fact [...]

Comment on Inconsistent Maximum Likelihood Estimation: An “Ordinary” Example by ekzept

ekzept — Fri, 10 Jul 2009 05:32:36 +0000

Regarding “The big difference between Bayesian and non-Bayesian methods is that Bayesian methods integrate over the parameter space, and non-Bayesian methods don’t”, frequentist methods are not the only non-Bayesian method. There are also Kullback-Leibler methods, means of inference based upon divergence measures between likelihood functions. See for instance Burnham and Anderson, Wildlife Research, 2001, 28, 111–119, “KL information as a basis for strong inference in ecological studies.”

Comment on The Harmonic Mean of the Likelihood: Worst Monte Carlo Method Ever by Nicolas Lartillot

Nicolas Lartillot — Fri, 01 May 2009 14:36:59 +0000

Radford,

thanks for your response

actually, the cases I am interested in are such that the variance of the HME is not truly infinite (the likelihood does not vanish at infinity) although it is practically immensely large (~ V > 10^100). Therefore, in principle, the sample variance IS well behaved estimator of this large V, and people do expect to see the sample variance give them some warning about the fact that V is large.

Of course, the sample variance will correctly estimate V only once the number of independent points in the sample is of the order of the square of V.

But what this means in practice is that the sample variance is not a good estimator of the order of magnitude of the true variance. It is just a good estimator of the variance once you know the order of magnitude, and have adjusted your sample size accordingly.

It may be something obvious, but I guess many people are not aware of that (or else, they would not rely exclusively on the sample variance to feel confident about an estimator, as they often do).

Comment on The Harmonic Mean of the Likelihood: Worst Monte Carlo Method Ever by Radford Neal

Radford Neal — Fri, 01 May 2009 03:59:05 +0000

The possibility that the sample variance is far from the true variance is one that should be kept in mind in many contexts, such as time series with high autocorrelation. The Harmonic Mean Estimator is an extreme case, though. I don’t have any great ideas for convincing people of the problem. However, if they realize that the true variance may be infinite, but say it’s not a problem since the sample variance was finite, maybe one could ask them how one could possibly get an infinite sample variance….

Comment on The Harmonic Mean of the Likelihood: Worst Monte Carlo Method Ever by Nicolas Lartillot

Nicolas Lartillot — Fri, 01 May 2009 03:07:22 +0000

Dear Radford,

I am happy to hear you say all that. And glad to see that this post is among the top 4 hits when searching google for ‘harmonic mean estimator’, because it means that you (we) are not preaching in the desert…

I am afraid that this HME has done more harm to bayesian studies than any opponent to bayesian inference has ever done.

Incidentally, the HME is also a striking example of how misleading the sample variance can be. When I try to convince people that the HME is not reliable, they usually seem very disturbed by the fact that this ‘infinite variance problem’ I seem to be so worried about does not show up when they compute the sample variance.

I then try to explain that the sample variance, as an estimator of the true variance, ALSO has an infinite variance, but then, it usually gets rather helpless: people just do not get the point, think that I see problems where they aren’t any, and opt for using the HME (which is anyway so much simpler than the never ending path sampling approaches that I try to sell them) ..

I don’t know if there is any better way to explain this true variance versus sample variance issue, do you know of any ?

in any case. thank you for this post

Comment on Down Syndrome and Decision Theory by Corinna

Corinna — Fri, 24 Apr 2009 19:02:18 +0000

I just wanted to comment (enjoyed your post very much) that the question is not when the embryo/fetus becomes “human”. It is human right from the sperm & oocyte stage (i.e. it isn’t a dog or a cat or a Martian, it has the exact genetic makeup that causes us to call skin cells or hair “human skin cells” or “human hair”. It is a “human embryo/fetus”). I would say the question is actually when it becomes a person/its own individual…whether its personhood has equal status to the individual carrying it…whether it is a separate being with its own inherent rights, or part of the mother. Anyway, this is tangential to your point

Comment on Does coverage matter? by Corey

Corey — Sat, 11 Apr 2009 05:17:55 +0000

In the multi-door Monty Hall variant I’m thinking of, when the initial door is not correct Monty opens every door except the initial one and the correct one. In the ten-door version, you pick a door, Monty opens eight doors with booby prizes, and you choose whether to switch or stay with your original choice.

This variant is useful for getting people past the intuitive feeling that switching and sticking are equivalent in the 3-door version. When the number of doors is large it’s much easier to see that the probability of that the door initially picked is the winner doesn’t change when Monty does the reveal, so the remaining door almost certainly hides the big prize.