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Mortal Kolle

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Good evening all

I have encountered a counter-intuitive result while thinking about Bayesian networks and decided to ask the members of this group

Suppose A is the probability space of all possible events (with P(A)=1, of course)

Now suppose A is partitioned into A1 and A2 such that P(A1)=P(A2)=0.5 and let a be some event in A

According to Bayes' Rule, 

P(A1|a) +P (A2|a) = P(A1)/P(a) *P(a|A1)  + P(A2)/P(a)*P(a|A2) =

= 0.5/P(a) *(P(a|A1) + P(a|A2)) = 0.5          since P(A1)= P(A2) = 0.5

P(A1+A2)=1 and A1 and A2 are disjoint, yet P(A1+A2|a) ~= P(A1|a) + P(A2|a) = 0.5

But A1 and A2 are disjoint and P(A1) + P(A2) = 1 so a must be fully contained in the union of A1 and A2 since it is contained in the universal probability space A. 


Likewise, P(a|A1) + P(a|A2) = (P(a)/0.5) *  (P(A1|a) +P (A2|a))

My head is spinning from this. Is there a rationalization I don''t know about?
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Karthik K

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Mark Adams

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I have been asked to improve the way that predictions of reliability of my companies products are done. I think I understand Bayes' Theorem, but putting into practice is another thing. I have the number of hours that the sub system has before it fails, if we have a corrective action for the failure mode (I don't have a lot of confidence of the root causes or effectiveness), the total number of machines built in a quarter, the percent new content for the next generation of machine. So can I predict what the reliability will be at the start of production for the new product and a year into production? Can I use excel, R, mini tab? I use a mac by the way. 
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since none else answer you, I would do it: sure you can; and you can do it in excel and specially in R. You have to use survival analysis and use number of machines, etc as covariates. See for example:

http://www.hindawi.com/journals/mpe/2012/329489/

or

http://www.springer.com/statistics/physical+%26+information+science/book/978-0-387-77948-5
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João Neto
moderator

Discussion  - 
 
 
Interesting to think about. Bayesian statistics became popular when it became computationally feasible due to MCMC and Moore's Law. Could it become infeasible again due to new larger data sets and become less popular?
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João Neto
moderator

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"Some of my fellow scientists have it easy. They use predefined methods like linear regression and ANOVA to test simple hypotheses; they live in the innocent world of bivariate plots and lm(). Sometimes they notice that the data have odd histograms and they use glm(). The more educated ones use generalized linear mixed effect models."

http://www.r-bloggers.com/the-joy-and-martyrdom-of-trying-to-be-a-bayesian/
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Excellent article. Thanks for sharing!
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João Neto
moderator

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"The most important thing to note about these categorizations is that the type of randomness depends on your perspective. The cards you hold in your hand are Type 0 randomness to you, but to the person sitting across the poker table from you, they are Type 2 randomness."

http://www.statisticsblog.com/2012/02/a-classification-scheme-for-types-of-randomness/
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Big Data Analytics Master
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Hi Everyone,

I'm planning on finally studying some serious mathematical statistics, but I am trying to decide between starting on measure-theoretic foundations or current practices in, say, statistical machine learning.

The following is a quote from Larry Wasserman's book "All of Statistics":
 "The typical mathematical statistics course spends too much time on tedious and uninspiring topics (counting methods, two dimensional integrals, etc.) at the expense of covering modern concepts (boot- strapping, curve estimation, graphical models, etc.)."

Any suggestion is greatly appreciated.
Thanks.
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Larrys book is probably a good serious start. All I can say is that you need a healthy mix of rigorous probability, advanced modelling and a decent hand with numerical computing and efficient programming. 
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Could someone point me to some literature on setting priors? 
Specifically, I want to set a prior for Click Through Rate estimation but I want to penalize a subset of the results based on the cardinality of the set, but It doesn't sound like a very Bayesian thing to do. Naturally, some reading could help. Thanks!
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Splendid, thank you. I will go through this!
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help me solve
 
 "in research of 1000 people 8% tested to have tuberculosis.the 1000 people then given new test found that tuberculosis was in 96% of those who have it and 2% for those who dont have.whats the probability of randomly chosen perso
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High school conditional Probability, Please help

As a part of a bit complicated high school conditional probability question, I devised the following argument to get my answer to agree with the given answer. Please tell whether this argument is valid, by providing links for any theorems or so.

Below, 
Three genes M, N, O that are responsible for the color of eyes occur randomly among adults and one person can have only one of these genes. Among children, probabilities of having  Brown or Black eyes given that Parents are combination of MM, MN, MO...etc are given separately.

P(Ci) = Probabilities of parents having random genes M,N,O joining to produce a baby. 
            i.e, C1=MM C2=MN C3= MO C4= NM C5=NN C6=NO.... C9=OO
P(A)  = Probability of Both parents having Black eyes
P(B)  = Probability of child having brown eyes

****************************
P(A∩B)

= ⅀ P([A∩B] | Ci) P(Ci)

= ⅀ P(A | Ci) P(B | Ci) P(Ci)

= ⅀ P(A | Ci) (P(B∩Ci)

******************************

Note, in the second step, I assumed
P([A∩B] | Ci) = P(A | Ci) P(B | Ci)
because, A and B are both events that depend on C only. So, I take it that when given C has occurred (when the sample space is restricted to C only), Events A|C and B|C can be considered independent of each other.

Is this argument correct? Please support your answer with links or references to any theorems.
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Top 11 Free Software for Text Analysis, Text Mining, Text Analytics

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Read more: http://wp.me/p43LB9-o
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Able Lawrence

Discussion  - 
 
Weak statistics to blame for non-reproducible scientific results
Most scientific data are analysed and reported using Frequentist statistics and use a cut-off of P values <0.05 to define positive as opposed to negative study results. Now a new study that compares the traditional frequentist analysis with Bayesian inference has concluded that the choice of P values <0.05 as the reason for the excess of false positive results that never get reproduced. They suggest use of more stringent statistical standards with a cut off of at least 0.005 for reporting purposes. 
Revised standard for statistical inference http://goo.gl/Bo6S2H
Weak statistical standard implicated in scientific irreproducibility 
http://goo.gl/UY3DgN
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Interesting lies!
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Why Gamification Can Get Even The Uninterested Very Interested In Mathematics?
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Rasmey Yem

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Hi all of you I'm pleasure to be a member in this community. I'm a little man that start learn statistics, I hope get more advice from you.
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Welcome!
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Sajjit Thampy

Discussion  - 
 
The law of the unconscious statistician
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João Neto
moderator

Discussion  - 
 
"We can argue about whether or not the question we are answering is the correct question — but given that it is the question, the procedure to answer it and to verify the statistical validity of the results is perfectly appropriate."

http://www.win-vector.com/blog/2013/05/bayesian-and-frequentist-approaches-ask-the-right-question/
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