How to calculate probabilities using Bayesian theorem

Question

Ricardo Duarte 2022-2-4

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https://ww2.mathworks.cn/matlabcentral/answers/1643310-how-to-calculate-probabilities-using-bayesian-theorem

回答： Pratyush 2023-12-14

Dear all,

I would like to calculate the probability of A, given B (p(a|b)) which can be done through the Bayesian theorem: p(a|b)=(p(b|a)/p(b))*p(a).

Im considering that: p(a)=normpdf(A) and p(b)=normpdf(B)

However, I'm not sure how to calculate p(b|a).

Can anoyone give me a hand on this?

Thank you in advance.

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Ive J 2022-2-5

I assume by "working with matrices" you mean each random variable is stored in a different column of the matrix, with rows being the observations. In that case, you still can follow the link above.

Ricardo Duarte 2022-2-5

I would like to say that each variable is a different matrix (24 x 36).

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Answer 1

Pratyush 2023-12-14

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https://ww2.mathworks.cn/matlabcentral/answers/1643310-how-to-calculate-probabilities-using-bayesian-theorem#answer_1371454

Hi Ricardo,

I understand that you want to calculate ( P(A|B) ) using Bayes' theorem.

To do that you need ( P(B|A) ), ( P(A) ), and ( P(B) ). In MATLAB, "normpdf" can be used to calculate the probability density function (PDF) for ( P(A) ) and ( P(B) ), but this gives the density, not the actual probability.

For ( P(B|A) ), you need to know the relationship between ( A ) and ( B ):

If ( A ) and ( B ) are independent, ( P(B|A) = P(B) ).
If ( A ) and ( B ) are dependent, you need their joint distribution to calculate ( P(B|A) ).

Without knowing how ( A ) and ( B ) are related or having their joint distribution, you cannot calculate ( P(B|A) ). Additional information about their covariance or relationship is required to proceed with the calculation.