This might help:
Bayes, Thomas 1702-1761. An English theologian and mathematician who was the first to use probability assessments inductively. That is, calculating the probability of a new event on the basis of earlier probability estimates which have been derived from empiric data.
Bayes set down his ideas on probability in “Essay Towards Solving a Problem in the Doctrine of Chances” (1763, published posthumously). That work became the basis of a statistical technique, now called Bayesian statistics.
A key feature of Bayesian methods is the notion of using an empirically derived probability distribution for a population parameter. The Bayesian approach permits the use of objective data or subjective opinion in specifying a prior distribution. With the Bayesian approach, different individuals might specify different prior distributions. Classical statisticians argue that, for this reason, Bayesian methods suffer from a lack of objectivity.
Bayesian proponents argue, correctly, that the classical methods of statistical inference have built-in subjectivity (through the choice of a sampling plan and the assumption of ‘randomness’ of distributions) and that an advantage of the Bayesian approach is that the subjectivity is made explicit. However, a prior distribution cannot easily be argued to be strongly ‘subjective’.
Bayesian methods have been used extensively in statistical decision theory. In this context, Bayes's theorem provides a mechanism for combining a prior probability distribution for the states of nature with new sample information, the combined data giving a revised probability distribution about the states of nature, which can then be used as a prior probability with a future new sample, and so on. The intent is that the earlier probabilities are then used to make ever better decisions. Thus, this is an iterative or learning process, and is a common basis for establishing computer programmes that learn from experience.
http://www.abelard.org/briefings/bayes.htm
You have an expectation P(x) about an event 'x', called 'a priori'.
You have empirical data (or related event) 'y', that can change your expectation on 'x' to the 'a posteriori' P(x|y).
You had an expectation on the data P(y) before relating it to 'x', and a probability P(y|x) for 'y' if 'x' is true.
Bayes' theorem states: P(x|y)/P(x) = P(y|x)/P(y)
simple example: a bag with two balls. Each ball has 0.5 chance of being white and 0.5 of being black.
Call x= there are 2 white balls. P(x) = 0.25 ; the options are ww, wb, bw, bb
call y= we take one ball out and it is white P(y) = 0.5 (every ball has equal prob. of being white or black)
But if x were true, then P(y|x) = 1 if two white balls, then you pick a white
So after picking the white ball, the 'a postieriori' expectation of a ww combination is
P(x|y)= P(x).P(y|x)/P(y) = 0.25 * 1 /0.5 = 0.5 which is rather obvious in this simple example.
an example: ??
A drilling company has estimated a 40% chance of striking oil for their new well.
A detailed test has been scheduled for more information. Historically, 60% of successful wells have had detailed tests, and 20% of unsuccessful wells have had detailed tests.
Given that this well has been scheduled for a detailed test, what is the probability that the well will be successful?
mephisto, could u solve this only example? or anybody interested! dont make it complicated plz! <thanks Mephisto for the previous example, you defined everything clearly! am getting it (simple examples r always helpful) 🙂
~^kattY Queen^~
Originally posted by kattyAll you need to know about probability is this, and remember this sole fact got me through my Computer Engineering Degree. Maybe, it'd be a good idea to write it on you legs or something for reference.
i dont understand Bayes' Theorem
any helpers?
~^kattY Queen^~
Anyway, here it is...
The probability of a faulty chip is 13.
Sorted.
D BEng
Originally posted by kattywww.forumwars.us. Click 'The Round Table' and then the threads 'New Religion' and 'Companion Thread to the Chess Police' might be of use.
an example: ??
A drilling company has estimated a 40% chance of striking oil for their new well.
A detailed test has been scheduled for more information. Historically, 60% of successful wells have had detailed tests, and 20% of unsuccessful wells have had detailed tests.
Given that this well has been scheduled for a detailed test, what is the probabili ...[text shortened]... ned everything clearly! am getting it (simple examples r always helpful) 🙂
~^kattY Queen^~
Originally posted by kattyMy skills are a little rusty, but here my try:
an example: ??
A drilling company has estimated a 40% chance of striking oil for their new well.
A detailed test has been scheduled for more information. Historically, 60% of successful wells have had detailed tests, and 20% of unsuccessful wells have had detailed tests.
Given that this well has been scheduled for a detailed test, what is the probabili ...[text shortened]... ned everything clearly! am getting it (simple examples r always helpful) 🙂
~^kattY Queen^~
'x' = the well is successful
'y' = a test has been made
P(x) = 0.4 a priori
the question here is what % of wells have had tests:
- successful wells : 60% (with a weight of 40% a priori)
- unsuccessful wells: 20% (with a weight of 60% a priori)
So P(y)= 0.6 x 0.4 + 0.2 x 0.6 = 0.36
Given this then P (x|y) = P(x) * P(y|x) / P(y)
or P(x|y) = 0.4 x 0.6 / 0.36 = 2/3
Originally posted by Mephisto2Thanks Mephisto, that was helpful 😀
My skills are a little rusty, but here my try:
'x' = the well is successful
'y' = a test has been made
P(x) = 0.4 a priori
the question here is what % of wells have had tests:
- successful wells : 60% (with a weight of 40% a priori)
- unsuccessful wells: 20% (with a weight of 60% a priori)
So P(y)= 0.6 x 0.4 + 0.2 x 0.6 = 0.36
Given this then P (x|y) = P(x) * P(y|x) / P(y)
or P(x|y) = 0.4 x 0.6 / 0.36 = 2/3
~^kattY Queen^~
