Topic: Episode #329

[Trinoc]

Bayes' Theorem can be seen as a probabilistic variation on Affirming The Consequent in which the argument is valid. It tells us that the probability of A given B is equal to the probability of A and B divided by the probability of B. If A implies B, then the probability of A and B equals the probability of A. Therefore, as long as B was not certain to be true, the discovery of the truth of B increases our assessment of the probability of the truth of A.

That's not quite right. Bayes' Theorem relates the probability of A given B to the probability of B given A and to the probabilities of A and B separately.

http://en.wikipedia.org/wiki/Bayes_theorem

(I'll resist the temptation to include my usual jibe about "It's only philosophy so getting it right isn't important". Except that I didn't resist the temptation. Is there a philosophical name for what I just did?)

[Chew]

Bayes' Theorem can be seen as a probabilistic variation on Affirming The Consequent in which the argument is valid. It tells us that the probability of A given B is equal to the probability of A and B divided by the probability of B. If A implies B, then the probability of A and B equals the probability of A. Therefore, as long as B was not certain to be true, the discovery of the truth of B increases our assessment of the probability of the truth of A.

That's not quite right. Bayes' Theorem relates the probability of A given B to the probability of B given A and to the probabilities of A and B separately.

http://en.wikipedia.org/wiki/Bayes_theorem

Wouldn't you say it is more closely related to the Conjunction fallacy?

(I'll resist the temptation to include my usual jibe about "It's only philosophy so getting it right isn't important". Except that I didn't resist the temptation. Is there a philosophical name for what I just did?)

Pedantium ad absurdum

[rlquinn1980]

That's not quite right. Bayes' Theorem relates the probability of A given B to the probability of B given A and to the probabilities of A and B separately.

http://en.wikipedia.org/wiki/Bayes_theorem

(I'll resist the temptation to include my usual jibe about "It's only philosophy so getting it right isn't important". Except that I didn't resist the temptation. Is there a philosophical name for what I just did?)

Mind elaborating? Bayesian statistics is not taught at my university, and so I am left to grasp as much of this on my own as I can until I get into a grad school where its importance is salient. (That Wiki page is dry as dirt.)

And I hardly think this "only philosophy," as one of the primary causes of the SBM blog (and in recent psychological news, the push for statistical change with Bem's paper as an example of what can go wrong) is to bring the Bayesean approach to the forefront of statistical approaches in science—something that has direct application not only how we interpret the data from our studies but whether a study is worth the limited resources we have toward pursuing it.

[Trinoc]

Mind elaborating? Bayesian statistics is not taught at my university, and so I am left to grasp as much of this on my own as I can until I get into a grad school where its importance is salient. (That Wiki page is dry as dirt.)

I'm no statistical math(s) expert, but in general terms Bayes' Theorem is a way of combining the prior probability of something being true with some new evidence which has come in either for or against it, to give the new perceived probability of it being true.

A good hand-waving example of Bayes is the skeptic's rule "extraordinary claims require extraordinary evidence". Roughly, an extraordinary claim has a much lower prior probability than something more plausible, and so requires a higher standard of new evidence in order to be accepted.

[rlquinn1980]

I'm no statistical math(s) expert, but in general terms Bayes' Theorem is a way of combining the prior probability of something being true with some new evidence which has come in either for or against it, to give the new perceived probability of it being true.

A good hand-waving example of Bayes is the skeptic's rule "extraordinary claims require extraordinary evidence". Roughly, an extraordinary claim has a much lower prior probability than something more plausible, and so requires a higher standard of new evidence in order to be accepted.

That much I knew.

[Trinoc]

That much I knew.

In that case, I'm afraid the rest is mathematics.

It's annoying sometimes that Wikipedia seems to have some articles that explain things in really basic terms for the layman, and others which explain them in terms that assume advanced mathematics, but very little for the person in between who wants to understand more but only has high school maths and science.

[werecow]

For those that are interested in the Berkeley study, it's discussed at some length on the latest "the climate show" with John Cook from skepticalscience.com:

The Climate Show 21: carbon, coal and Cook on BEST

Starts at about 38 mins in and lasts for about 20 minutes.

[JPC]

So science-by-press-release is OK sometimes.

Got it. Thanks.

Perhaps in a future episode you could discuss the conditions under which it receives your derision ...

[Tormod]

I think the panel overlooked a vital piece in the "new european GPS" story.

It's pretty shortsighted to decide the benefits of the new system by looking at todays car navigation, which was designed for the old level of precision.
The point is that the increased accuracy makes a new generation of products possible.
I predict that this new GPS system will, amongst other things, spawn a generation of augmented reality technologies.

[werecow]

Here's another lecture of interest for those who think the evidence for anthropogenic warming is not particularly strong (but are open to evidence to the contrary):

http://rce.csuchico.edu/Mediasite/Viewer/?peid=c4ef29c2484b44b2b2a0fa70d36bb6fe

[SkeptDC]

Were there any studies supporting the information on brushing your teeth, or did that all come from authorities?  The idea of orange juice softening tooth enamel sounds plausible, but implies that we shouldn't drink OJ before we eat either, right?  A crunchy cereal would do at least as much damage as a tooth brush.  Also, don't eat salad with vinaigrette dressing, since that is also acidic.

[Trinoc]

Were there any studies supporting the information on brushing your teeth, or did that all come from authorities?  The idea of orange juice softening tooth enamel sounds plausible, but implies that we shouldn't drink OJ before we eat either, right?  A crunchy cereal would do at least as much damage as a tooth brush.  Also, don't eat salad with vinaigrette dressing, since that is also acidic.

I did my own experiment to test the orange juice idea. All it needs are three cotton buds and some pH indicator papers. And of course some orange juice.

I dabbed some orange juice on an indicator paper: pH 3-3.5 as expected (mild acid). Then I swabbed some saliva from my teeth: pH 7-7.5, also as expected. Then I drank the orange juice, swishing it around my teeth to make sure it got everywhere, and as quickly as possible swabbed saliva from my teeth again: still pH 7-7.5.

I conclude that saliva is an effective enough buffer to neutralise any acidity from the orange juice almost as soon as it is swallowed. I wouldn't advise holding OJ (or other acid drinks like Coke) in the mouth for a long time, but why would anyone do that anyway?

Tests such as leaving an extracted tooth in OJ or Coke overnight are hardly realistic, as they simply leach enamel off dead tissue. A live mouth is very effectively pH regulated, so I'd think the effect is negligible.

Anyway, what is meant by "softening" the enamel? Is it being suggested that the outer layer of the tooth somehow becomes less hard for a short time, but if you don't brush it off it returns to its old, rock hard state. This seems implausible. Surely once calcium carbonate has been attacked by acid it has become CO₂ and something like calcium citrate, which no longer makes hard enamel, so any effect would be irreversible.

[Shadow Of A Doubt]

Were there any studies supporting the information on brushing your teeth, or did that all come from authorities?

I've heard it from my dentist and separately from a dentistry student and now from Steve Novella so it seems to be a fairly common belief amongst the authorities.

[Trinoc]

Were there any studies supporting the information on brushing your teeth, or did that all come from authorities?

I've heard it from my dentist and separately from a dentistry student and now from Steve Novella so it seems to be a fairly common belief amongst the authorities.

In that case I'd like to see an explanation of the mechanism believed to soften the enamel, and how/why it is supposed to harden again if the teeth are not brushed for a while.

[Shadow Of A Doubt]

Were there any studies supporting the information on brushing your teeth, or did that all come from authorities?

I've heard it from my dentist and separately from a dentistry student and now from Steve Novella so it seems to be a fairly common belief amongst the authorities.

In that case I'd like to see an explanation of the mechanism believed to soften the enamel, and how/why it is supposed to harden again if the teeth are not brushed for a while.

Oh yes, explanations are always appreciated.