What Is a Posterior Probability?

Posterior probability is one of the basic concepts of information theory. In a communication system, after receiving a message, the probability that the receiver knows that the message is sent is called the posterior probability.

Suppose a school has 60% boys and 40% girls. The number of girls wearing pants is equal to the number of skirts, and all boys wear pants. A man randomly saw a student wearing pants in the distance. What is the probability that this student is a girl?

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In statistics and financial economics, the probability distribution of the random variable X is f (x | ), and the prior probability distribution is f ().

1. When the subjective probability is inferred based on experience and related materials, and it is not fully sure whether it is accurate, the Bayesian formula in probability theory can be used to modify it. The probability before the correction is called the prior probability, and the revised probability It is called posterior probability, and the risk analysis is performed by using posterior probability.

2. The information technology revolution has accelerated human progress towards the actual situation of the information society. The world's information service industry is becoming the most powerful in essence. It is based on new information as a condition for economic growth.

3. P {H0 | x} is the probability that H0 appears under the given observation x, which is collectively called posterior probability. According to the Bayesian formula, the posterior probability can be expressed as P {H0 | x} = P (H0) P {x | H0} / P (x), P {H1 | x} = P (H1) P {x | H1} / P (x). In the formula, P (x) is the probability density of x.

4, which is to obtain

To give a simple example: There are 3 red balls and 2 white balls in a pocket.

Probability of first touching a red ball (denoted as A);

The probability of touching the red ball (denoted as B) for the second time;

(3) It is known that the red ball is touched for the second time. Find the probability that the red ball is touched for the first time.

solution:

P (A) = 3/5, this is the prior probability;

P (B) = P (A) P (B | A) + P (A inverse) P (B | A inverse) = 3/5

P (A | B) = P (A) P (B | A) / P (B) = 1/2, this is the posterior probability.