(prerequisite-Kalman Filter) Bayes' Theorem(Baysianism)

• Bayes' Theorem(Baysianism)

 

 

The relationship between prior probability and post-probability.

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$P(B|A)=\frac{P(B\cap A)}{P(A)}$

The probability that event $B$ occurs on the premise that event $A$ has already occurred.

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Example

 

Q. What is the probability that this email is spam when the word A is visible?

 

$P(S)=0.3$ : Probability of spam mail

$P(N)=0.7$ : Probability of normal mail

$P(A|S)=0.4$ : Probability that spam mail contains A.

$P(A|N)=0.1$ : Probability that normal mail contains A.

$P(A)=0.19$ : Probability that both of normal and spam mail contains A.
$P(A)=(P(A|S)\ast P(S))+(P(A|N)\ast P(N))$
$(0.4\ast 0.3)+(0.1\ast 0.7)=0.19$ $P(A)=0.19$

Result :
$P(A|S)=\frac{P(A\cap S)}{P(S)}$ : Probability that this email is spam when the word A is visible.
$P(A|S)P(S)=P(A\cap S)$
$0.3\times 0.4=0.12$
$P(S|A)=\frac{P(S\cap A)}{P(A)}=\frac{0.12}{0.19}=0.6315$

 

 

https://gaussian37.github.io/autodrive-ose-bayes_filter/

https://roytravel.tistory.com/350

https://zzaebok.github.io/machine_learning/bayesian-statistics-and-machine-learning/