Solo

Found a strange apprehension of Bayes theorem on Hoffmann's May 29 blog entry. He gives the following problem as an illustration:

Can anyone spot the problem in Hoffmann's reasoning ? How would you go around proving the 11% figure is in error ? What is the correct predictive probability of rain for Marie's wedding day ?

Best,
Jiri

andrewcriddle

I'm afraid I think Hoffmann is correct here. (I'm going to take a year as 365 days long and take a 2 year period.)

During this period there will be 10 days of rain and 720 days without rain. On 9 of the days with rain the forecaster will predict rain. On 72 of the days without rain the forecaster will predict rain. Hence it will only rain on 1/9 of the days on which the forecaster predicts rain. Which is what Hoffmann claims.

Andrew Criddle

Solo

Really ? So if the pattern holds and it rains only on 11% of the days the weatherman predicts rain how can it be said that the weatherman correctly forecasts rain nine times out of ten ?

The problem is that the weatherman's prediction is treated here both as a statistical factor and as the result of statistical processing of meteorological data. If the weatherman is said to 90% accurate in predictions, he/she needs to be 90% accurate for all instances regardless of precipitation frequencies. In other words, the weighing proposed in the exercise is self-contradictory as it contains a circular proposition. The value of the weatherman's prediction would sharply vary with the rate of precipitation, which is not only counter-intuitive but plainly wrong.

The weatherman may well be incorrect 72 times over two years but there is still by definition 90% statistical chance he/she is correct in predicting rain for any particular day.

The Bayesian Theorem would work for the example if instead the weatherman one the factor was, say, barometric pressure signifying such and such probability of rain the following day.

Best,
Jiri

Diogenes the Cynic

He's only correctly forecasts rain 9 times out of 81. If it rains, there is a 90% chance he predicted it, but most of the time he predicts it, it doesn't rain.

To take it to an extreme, if he predicts rain every single day of the year, he will successfully predict rain on 100% of the days it actually rains, but that does not translate into 100% accuracy as a predictor of rain. A stopped clock is 100% accurate twice a day.

Solo

My point is that the Bayes Theorem only yields meaningful results if the tasks are properly set up. In this example, the compounding of statistical factors does not make sense because one of the arguments itself is a statistical result which presumably is built on a model which takes into account the frequency of precipitation. What you are doing then in effect is discount the declared predictabilty, which of course makes no sense.

Basically, what the formula asserts the weatherman's prediction holds only in regions where it rains 50% of the time

(0.5*0.9)/(0.5*0.9+0.5*0.1) = 90.00 %.

But that is just not how the world works.


Best,
Jiri

andrewcriddle

The probabilities are clearly the probabilities for this desert region where it is assumed that the weather conditions and other factors remain on average constant over time.

The reliability of a prediction clearly does vary with the prior probability of the thing predicted. This is central to uses and misuses of probability in the legal system. If rain is frequent in an area then unusually low air pressure for that area is a good predictor of rain. If rain is infrequent then unusually low air pressure is a much weaker predictor.



The weatherman is by definition correct 90% of the time in predicting rain for any particular day. But this means that IF it will rain on day x then there is only a 10% chance that the weatherman will fail to predict rain for day x. This does not mean that if the weatherman predicts rain for day x there is only a 10% chance of failure.

Suppose the weatherman predicts rain every day. He will be corrrect 100% of the time in predicting rain. (There will never be rain on days when the weatherman has failed to predict it.) This does not mean that if the weatherman predicts rain on day x rain is likely.

I'll use the example of barometric pressure to try and explain what is going on. Suppose we have a computer that measures barometric pressure and when pressure is below value y prints in large red letters a message saying It will rain tomorrow.
Assume that in reality it rains only 5 days out of 365. Assume that in 90% of the days when it does rain the computer successfully predicted it the day before, (ie printed the message in large red letters) But in 10% of the days when it did not rain the computer wrongly predicted the day before that it would rain tomorrow (ie printed the message in large red letters).

The fact that the message has been printed in large red letters the day before the wedding gives a probability of a wet wedding of 11% as Hoffmann claims.

Andrew Criddle

Solo

withdrawn

Solo

Andrew,
my objection is not to the mechanics of the Bayes Theorem. I understand how it works. It is just that the example chosen is not a reasonable application of the tool. In the case, the rain prediction is actually postdicted and the arguments skewed such as to produce a seemingly paradoxical result. It obviously plays on the extra large "error" (10%) which is made to look like a complement to the 90% but isn't. It transparently seeks to skew the predicted probability. In real life, the expertise of the meteorologists is in predicting the occurence of rain with x% error, i.e. x% percent accuracy in prediction whether it will rain or not. For models said to have 90% accuracy, the number of errors in daily predictions of rain over 2 years is 72, regardless whether in the error readings rain or no-rain were predicted. The empirical frequency of rain in a given region would have no effect.


Best,
Jiri

spin

For the last week I have been attempting to engage the slugs of the Jesus Process. Jacob Aliet posted some material of mine from here over with RJoe and the Casey entry. Drusilla the Nun, she who plays Robin to Casey's Batman, didn't like what Jacob posted and so attacked it. I decided to engage and the result is interesting. Eventually a few hours ago, RJoe decided he wasn't going to post any more of my material. I post here to say that some might find the exchange revealing in the way people avoid dealing with things. RJoe's use and abuse of Jacob's information here shows RJoe to be quite horrid. What follows is my last reply to RJoe, which naturally he removed. It's best to have read the whole exchange first. I hope you enjoy.

[T2]I'm sorry, Joe. It appears you've caught a mild case of Geoff Hudson disease from hanging around the online bars looking for ways to express yourself. I'm sure Jacob is a lot of things but he's not me. You seem to think I have some allegiance with the mythicist brigade. You're wrong. But it's inconsequential. I've explained why I posted here. Jacob put excerpts from a casual post of mine up here on your blog. I didn't ask for that but I didn't ask Robin to spew all over the material in youthful exuberance either. As to Bayes, I've paid no attention to the discussion, so your comments to me about it seem to be spitting into the wind.

Lebanon is your burden. You were trying to give credence to the notion of a trilingual context through anecdote. When you commented about Lebanon and Israel "which I venture to say are just faraway places for you", I'd venture to say that you were just groping in the dark. My approach has been to try to deal with evidence, not to flail about with none, as you are doing here. (And on a personal note I have indeed briefly been to Lebanon, but not by choice, the bus I took from Banias to Homs went through a small tract.)

If we remove the preponderance of irrelevances from your response to my last post, let's look at "You have been unable to produce one whit of evidence to refute Professor Casey...", though I have never tried to refute "Emeritus Professor Maurice Casey". My interest has always been the location of Mark's production and the influence of Latin on it, with no attempt to deny the Aramaic component. However, his book has no theoretical framework or rationale: he begins by asserting that while the "Gospel of Mark is written in Greek,... Jesus spoke Aramaic" and that's as far as he goes. You don't want to know the alternative theories or whether there is sufficient evidence to support the assertion. And what does being able to translate a few sections of the Greek into Aramaic show exactly? How do they balance with the evidence for a Latin linguistic substratum? You just get the claim that it is centrally important to study "these very early traditions in their original language." (p.260) He hasn't shown that his translation provides their original language, merely the possibility. It could be that the writer translated Aramaic sources, or that his Aramaic linguistic habits came through his Greek writing, or even that he was a tradent in Greek traditions some of which were derived from Aramaic sources. Only one of these cases shows the Marcan writer as translator. Continuing your words, you said "...preferring instead to put a respectable title in scare quotes". You are willfully ignoring the fact that "steph" started the "scare quotes" on June 1 and "Emeritus Professor Maurice Casey" continued the trend while imputing my honesty.

Is there anything else in your response to me that even regards me? Perhaps a clarification regarding the Jesus Project train wreck. It seems to me to be reduced to petty conplaints about Jesus mythicism. Denigrating one ontology will not give substance to another. What you end up with is smoke without a fire and, as I said, this is all very sad.[/T2]

Grog

One striking characteristic of this exchange is Stephanie Fisher's handling of Casey. It is clear from his comments that spin is rude to "Steph," that he is being hand fed a one-sided account. He doesn't seem to realize that the one who is taking this debate into the gutter is his prized student, perhaps his self-appointed heir-apparent.