Simple Probability Estimation with more than two outcomes

[steve_bank]

I agree it poorly defined.

What does s1 and s2 not separated mean? In statistical terms do you mean correlated vs uncorrelated(random) variables?

Pa does bot make sense in the table. if s is a random variable with two staes and s1 s2 are continget on s then s1 + s2 has to equal 50%.

Please explain Swami.

Wrte out the probailty equations fr Pa and Pb in the tables.

I'm not sure what your questions are..
P(A|.) is the label for one row; substitute the column label for the dot to get P(A|S), P(A|not.S), P(A|S1), P(A}S2).

Thus P(A|S1) = 90% means that in Scenario S1, A is true 90% of the time. (Never mind which is cause and effect, if any. Treat it as a pure math exercise with the probabilities given.)

Note that the source code provided ensures exactly that and may answer other questions as well. See something like

case 1: // S_1​

Clue_A = (random() < 0.90 * RAND_MAX);​

(I'd intended that source code to be easy-to-read, but looking now I see it assumes familiarity with C and its random() library.)

In the other thread's example. S is the proposition that Sam committed a certain robbery. One detective divides S into two scenarios (Sam hired George as his getaway driver OR Sam drove himself). Other detectives do not consider the getaway at all, due to oversight or perhaps afraid it might confuse them further.

As you can see from the table, the clues are useless for the detectives who do NOT subdivide into two scenarios. Clue B for example might be that George has a good alibi on the day of the robbery.

Then I am not sure you know what you are talking about. I am sure it is all very clear to yourself.

There is little math here, just the same posts that ended up in Elsewhere on the other hread.

I will try and avoid this kind of OPs in the future.

 

[Merle]

But you USED the .9's and .1's in your proposed Carrierite analysis. (Numbers that don't arise without considering the sub-scenarios.)

Huh? As I have explained, when confonted with a range of values to use for each factor, then one can simply argue from the two limits for each factor, and bracket a range of the final answer. In your example, P(A|S)/P(A|not.S) could be either 9 or 1/9. Likewise, P(B|S)/P(B|not.S) could be either 9 or 1/9, depending which sub-scenario is true. The simple Bayesian analysis is to argue first using both the high limits, then do a separate calculation using the low limits. If we take the high limits, we are multiplying by 9 * 9. If we take the low limits, we are multiplying by 1/9 * 1/9. Thus the high and low limits are very far off.

And yes, as I have said multiple times (would you like me to repeat it a dozen more times?) if the range in the end result is too wide for our purposes, we might be able to narrow down the conclusion by dividing the calculation into two or more scenarios. In the example you showed, breaking it into two scenarios does wanders, because it was specifically set up such that the scenarios are so widely divergent, it makes no sense to analyze them as a combined scenario.

Again, Carrier comes up with the odds of historicity as being somewhere between 1:1 to 1:1000. Yes, that is a wide range, but it is fine for his purposes. Again, all he is trying to prove in that book, according to the title, is that "we might have reason for doubt". If Bayesian analysis shows the odds of historicity are 1:1 to 1:1000 by his calculations, does that support his assertion?

 

[Merle]

As you know, I have contended emphatically that only some scenarios need to be split into two. Do you or do you not agree with me?

If you agree with me, then the fact that you found one scenario that has a feature that requires it to be split does not prove that Carrier's analysis needs to be split.

If you don't agree that only some scnarios need to be split, then yes, you yourself our saying that all scenarios must be split, and yes, that splitting would , by definition, go on ad infinitum.

So which way is it?

Again the implication that I am obsessed with multiple scenarios and will split them willy-nilly into an infinitude of cases. Ridiculous?

I take note that you completely dodged the question. It is a simple question and gets to the heart of the matter. Once again here is my question:

I assert that some scenarios can be best analyzed by breaking them into two scenarios. In other cases, we do not need to do this. Do you or do you not agree?

This question in no way implies that you are obsessed with multiple scenarios that you split willy-nilly. That is simply a dodge to avoid the question. Please answer the question.

 

[Merle]

(1) What is the Mythicist stand on Josephus' "brother of Jesus" mention? Does Carrier still think that was Jesus ben Damneus? I would want to address the different cases separately. (Unless all you Mythicists go along with Carrier's laughable solution.)

(2) Were Chrestus and Christ the same person or not? Argument details are VERY different for the two cases. Unless Mythicists have a consensus answer to this question, I would want to assess the scenarios separately.

I am not an expert on these questions, and don't have a lot of time to spend on this. I do know that Carrier analyzes these in a lot of detail in his book, looking at various interpretations. Then, based on his analysis, he estimates the high and low limits and uses those limits in his overall analysis.

Do you disagree with his analysis on these points? If you don't know what he says, you can read about both these things in his book. If you read his book and have a problem with what he says, then you can come here and tell us where you disagree.

I am not your personal research assistant. If you want to know what Carrier says about these things, read what he says. Don't ask me to look it up and tell you what he says.