## STAT 330 August 28, 2012

Here is a link to the article by Tony O’Hagan that I mentioned in class.

Here is a link to the Ioannidis article I mentioned, “Why most published research findings are false”.

Today’s Dilbert cartoon talks about coin-tossing.

Links to the charts for the first few lectures:

### 2 Responses to “STAT 330 August 28, 2012”

1. Ahmed Says:

I emailed a couple of questions to Prof. Jefferys yesterday. I am sharing on the blog per his request. Please feel free to make any comments:
———-
Dear Professor Jefferys,

Sorry, I am still making sense of the first lectures notes and I have a question about class notes:

Page # 20, which discuss the plausibility and how it should be transitiv:

The sentence following that is explains that transitivity means that it should be possible to attach a real number P(A) to each proposition and rank accordingly. I am not sure who there transitivity means the attachment of real number to proposition. Please explain to me why is that.

Transitive just means that there is a relationship, which I will write >- for example, such that you can rank things that has the property that if A>-B and B>-C then A>-C. The usual example would be for >- to signify “greater than”, so we say if A is greater than B and B is greater than C then A is greater than C. Here we have >- signifying “more plausible than”, which just says that if A is more plausible than B and B is more plausible than C then A is more plausible than C. Since the relationship is similar, we ought to be able to attach real numbers to the plausibility of A, B and C, call them P(A), P(B) and P(C), so that P(A)>P(B)>P(C). In other words, we ought to be able to make a correspondence between plausibilities and real numbers so that we can represent plausibilities as real numbers. Not every relationship is transitive in this way. For example, “is the parent of” is not transitive because if A is the parent of B and B is the parent of C, it isn’t generally the case that A is the parent of C.

Page # 26:

I am not sure how the game works. There are two different types of bets going on:
1- First one if you the outcome of pc is negative vs positive and whether you and your opponent lose or win.
2- Second one whether the proposition A is true or false.

Each case sounds like a game by itself. Can you kindly clarify this slide for me?

Not sure quite what you are asking here. There is only one bet discussed on this page. That is the bet you make when you assign probability p to the proposition A. c is not a bet, it is what the opponent (e.g., the racetrack) decides what the payoff will be if you win (proposition A turns out to be true). The quantity pc is the bet that the racetrack requires for you to make the bet (analogous to the price you pay for the ticket prior to the race being run). So, for example, at the racetrack the standard price for a ticket is \$2. So, pc=\$2, and c=\$2/p, which will at a real racetrack be greater than \$2. The difference here is that if the opponent chooses a negative value of c (for example), it may be that the money will go the other direction, e.g., the opponent pays you \$2 if pc<0, and you pay the racetrack if c<0 and the bet is won.

Bill

Thanks very much!

-Ahmed

PS If you have questions, it's best to post them on the blog so that others in the class can benefit from the answers. It may even be that others will answer the question before I get around to it, and/or may give an answer that is better!

-B

2. Ahmed Says:

Thank you Professor Jefferys. The racetrack clarifies my doubt. I can explain to you after class what I mean by two bets, if you are still curious what I meant