Bayesian or not Bayesian,this is my problem

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In summary, the conversation discusses the use of an automatic test to determine the probability of correctness for a set of 10000 elements. The test has a 20% false positive rate and a 30% false negative rate. The conversation then delves into how to calculate the posterior probability of correctness for an element with a 75% estimated probability of correctness, and how to prioritize checking the remaining elements based on their probability of correctness. Finally, there is a request for confirmation and clarification on the calculations.
  • #1
Marione
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I have a set of 10000 elements to buy; I want to do some quality assurance activity in order to avoid to buy invalid elements. I have an automatic test that provides the probability of correctness of an element; moreover I know that the test gives a 20% of false positive and a 30 % of false negative.
1)Suppose that I have an element of which the test estimate a probability of correctness of 75%; which is the posterior probability?
I’m afraid I’m unable to apply the Bayesian theorem because I do not know the number of correct elements. My instinct tells me to count the frequency in the past in which an element was really correct when the estimated probability by the tool was less or equal then 75%; suppose that such frequency is 50%. Consequently, my instinct will say that an element of which the test estimate a probability of correctness of 75% has a posterior probability to be correct of 50%. Am I right?

2) Suppose that I cannot check all the elements by eye but I need to use the automatic test to prioritize the elements to check; suppose that I run the automatic test on all the elements and then I order the elements according to the probability of correctness provided by the test; suppose that I’ve analyzed all the elements with a probability of correctness lower 70%; how to calculate the probability that there is an incorrect elements in the remaining ones (i.e. the ones with a probability of correctness higher than 70%)?

Please help me!
 
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  • #2
Can you tell me if this is a proper question picked up from somewhere or is any data missing here? If all correct, tell me if the answer for 1. is 15/16?
 
  • #3
I don't understand your question.
 
  • #4
A way to check your calculation is to count the overall defective percentage p[0]. Suppose p[0] = p. Then the probability of having a defective part conditional on a "pass score" p[0|1] can be found as:

p[0|1]p[1] = p[0,1] = p[1|0]p[0]
p[0|1] = p[1|0]p[0]/p[1]
p[0|1] = 0.2 p[0]/p[1]
p[0|1] = 0.2 p[0]/(1-p[0])
p[0|1] = 0.2 p/(1-p).

EnumaElish
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I would definitely have logged in as EnumaElish had PF administration awarded that account the privilege of posting replies, after I reset my e-mail address Tuesday, October 28, 2008.
 

FAQ: Bayesian or not Bayesian,this is my problem

What is Bayesian analysis?

Bayesian analysis is a statistical approach that uses prior knowledge or beliefs about a problem to make predictions or draw conclusions. It involves updating these beliefs as new data is collected, resulting in a posterior probability distribution.

What is the difference between Bayesian and non-Bayesian methods?

The main difference between Bayesian and non-Bayesian methods is the use of prior knowledge or beliefs in Bayesian analysis. Non-Bayesian methods do not incorporate prior information and rely solely on the data for making predictions or drawing conclusions.

When should I use Bayesian analysis?

Bayesian analysis is best suited for problems where prior knowledge or beliefs are available and can be incorporated into the analysis. It is also useful for problems with limited data, as it allows for the use of prior information to make more accurate predictions.

What are the advantages of using Bayesian analysis?

One advantage of Bayesian analysis is its ability to incorporate prior knowledge or beliefs, which can lead to more accurate predictions and conclusions. It also allows for the updating of beliefs as new data is collected, resulting in a more refined analysis.

What are the limitations of Bayesian analysis?

Bayesian analysis relies heavily on the quality of the prior knowledge or beliefs used. If the prior information is incorrect or biased, it can lead to inaccurate predictions. Additionally, it can be computationally intensive and may require specialized software or expertise to perform the analysis.

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