Bayesian Reasoning: Is it reasonable?

[R2D2]

My understanding is that Bayesian reasoning assigns a probability for the evidence against a theory but also the evidence for a theory. By doing this they claim to be able to tell how likely something is true. How can this be taken seriously in regards to things that we have little data for? Where do they get the numbers for probability? Seems to me that they are pulling numbers out of thin air.

I have seen Bayesian reasoning used in regards to a theory that there are many different worlds and that there is not a God so I think this stuff is relevant to Catholic Apologetics.

Hello Cure of Ars,

Are you satisfied with the explanation on Bayes Theorem on this thread? Would a simpler explanation help?

 

[Cure_of_Ars]

Hello Cure of Ars,

Are you satisfied with the explanation on Bayes Theorem on this thread? Would a simpler explanation help?

I think I understand but just enough to make me dangerous. Seems to me that you really would have to play around with the actual numbers to really understand and I am not that motivated. But if you have a simpler explanation I definitely would like to hear it.

 

[R2D2]

Ooops… almost forgot about this thread…

I’m very sorry for the late post.

 

[R2D2]

I. My assumptions

1. 
   *]“reasonable” as in a pragmatic and simple application
   *]Corollary: from (1), absolutely zero (none, nada, zip, zilch) advanced Calculus, Partial Differential Equations and other math mumbo jumbo content, i.e., a simpler explanation
   *] math majors are magnitudes of orders smarter than physics majors
   *]You agree that the strict mathematical proof of Bayes’ Theorem is true and valid, therefore a mathematical critique is not warranted and is outside the scope of this post
   
   II. A gambler’s parable and a doctor’s dilemmaChuck wants to make a bet on the Lakers-Celtics finals’ series will go 7 games. What would be a fair probability (odds) to give Chuck? If his bookie gives him 1:7 (~14.29%), it would be advantageous to him but not for the bookie, given that best of 7 series has to go at least 4 games on a 2-3-2 format. (Supposing a 50-50 chance of any team wining a game)Fair odds would be 1:4 (25%) – Chuck loses in games 4, 5 & 6 if one team gets 4 wins. In other words, he only has a 25% chance of winning the bet. In classical statistics, that’s the end of the story. In Bayesian statistics however, you are to modify probabilities (odds) as new information (data) comes in.Say the Lakers get a split in Boston (1-1). That means there has to be a game 5 (new information). So Chuck’s “odds” should increase from 1:4 to 1:3 (~33.33%) and this becomes his new *“*odds”. If the Celtics win a game (again, new info) in Los Angeles, his “odds” should increase to 1:2 (50% chance of wining the bet). Notice that the Celtics has to win in Boston in game 6 for him to win, but the payout, “$1.00 wins $4.00”, is still in effect even though the “odds” just doubled to Chuck’s favor. Classical statisticians will argue that Bayesian reasoning is not necessary since gaining new information need not change the betting structure. I agree that it need not change the betting structure but disagree that Bayesian reasoning is not necessary. Consider the next problem.1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get a positive mammography. 9.6% of women without breast cancer will also get a positive mammography. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?The correct answer would be 7.8%. (Whew!) How? Eliezer Yudkowsky explains it neatly here. In this application, it is necessary to adjust the probability (pre-knowledge/a priori bias) according to the new information or else you will get the wrong diagnosis and prognosis.Continued…

 

[R2D2]

Continued from above…

III. The VerdictAs you can see, there are real world applications to Bayes’ Theorem. It models our learning methods quite nicely. It has been proven in searching tree algorithms on AI research. It is reasonable, and sometimes, necessary.Videos:youtube.com/watch?v=2fa3Z74_DjMyoutube.com/watch?v=pPTLK5hFGnQIV. CodaIn applying Bayesian reasoning to the existence of God, I would recommend the works of Dr. William Dembski for the affirmative, and Dr. Mark Perakh for the negative. I’d have to say (in my opinion) that Dr. William Dembski’s application of Bayes’ Theorem is simple and straightforward, but Dr. Mark Perakh sort of utilizes an Algebraic trick to make it work in his favor. Both are using the “Anthropic Principle” in their arguments. My Google skills are not very good-- but I’m sure there is a plethora of information on the net that’s been posted by the both of them. (So you need not buy any of their books to understand their arguments.)

 

[Orangebookbag]

All the Thomistic “proofs” for God’s existence are “cheats” in precisely this sense - alternative models are simply ruled out a priori, despite the claims to an a posteriori proof.

That’s not true at all. Thomas 5 ways are deductive, Bayesian reasoning is inductive. If they were to be phrased in a way that a Bayesian would understand, I suppose the premises would be the ‘priors’.

Take the argument from motion (or change). To assess the prior probability, we need to find the ratio of the number of possible worlds where motion exists, and the number of possible worlds where motion either exists or doesn’t exist.

Every single living person experiences motion, therefor Thomas is justified in treating this probability as 100%

 

[bsroufek]

As a Computer Scientist with some advanced training in Artificial Intelligence and Expert Systems, I was taught that the Bayesian model was very useful in Expert Systems, wherein a specific area of knowledge was represented through logic and probability models successfully.

So, a cardiac diagnosis through heart readings could be very accurate, for actual example.

But, using the Bayesian model on theology is probably not a good idea, since theological reasoning also includes faith-driven and grace-based reasoning which is not statistically measurable, IMHO.

 

[Alberti_Devoveo]

That’s not true at all. Thomas 5 ways are deductive, Bayesian reasoning is inductive. If they were to be phrased in a way that a Bayesian would understand, I suppose the premises would be the ‘priors’.

Take the argument from motion (or change). To assess the prior probability, we need to find the ratio of the number of possible worlds where motion exists, and the number of possible worlds where motion either exists or doesn’t exist.

Every single living person experiences motion, therefor Thomas is justified in treating this probability as 100%

Good job on responding to a thread that is 5 years old.