The anterior probability and posterior probability have not yet occurred. The magnitude of the likelihood of this event is a prior probability.
Something has happened. The reason for this is the possibility of a factor, which is the posterior probability. i. A prior probability refers to the probability obtained based on past experience and analysis, such as the full probability formula, which often appears as a "cause" in the question of "result from result. Posterior Probability refers to the probability of re-correction after obtaining the "result" information. For example, in Bayesian formula, it is the "cause" in the "result finding" problem ". There is an inseparable relationship between the anterior probability and the posterior probability. The calculation of the posterior probability is based on the anterior probability. II. A prior probability is a marginal probability, interpreted as a description of what is known about a variable in the absence of some eviility. the posterior probability is then the conditional probability of the variable taking the evidence into account. the posterior probability is computed from the prior and the likelihood function via Bayes 'theorem. 3. There are n possibilities for the occurrence of anterior probability and posterior probability. We cannot control the occurrence of results or influence the results. The mechanism is that we do not know or are too complex to exceed our computing capabilities. Is it a cat or a tiger (classic example of Zhu daoyuan )? It is because of our ignorance that we cannot determine. Prior probability a prior probability describes a variable in the absence of a fact. A posterior probability is a conditional probability after a fact is taken into account. The prior probability is usually the subjective estimation of experienced experts. For example, in the French election, the support rate P of the female candidate Luo yaer can be expressed by a prior probability before a public opinion survey. Probability of outcomes of an experiment after it has been completed MED and a certain event has occured. the posterior probability can be calculated using the prior probability and likelihood function based on the Bayesian formula. 4. The ultimate solution to a typical probability question-Relationship Between Posterior facts and prior probability: There are three main questions, one of which has a car, if you select the right option, you can get the car. When the examinee selects a door, the host opens another door, empty. Ask the examinee if they want to change their choice. Suppose the host knows the door where the car is located. Classic solution: the probability of correct selection for the first time is 1/3, so the probability of a car in the other two doors is 2/3. The host points out that if you choose the wrong door (2/3 probability), 100% of the remaining door will have a car. If you choose the right door for the first time (1/3, there are 100% cars left in the door.
After the host prompts, if you do not change, the correct probability is 1/3 * 100% + 2/3*0 = 1/3. If you change, the correct probability is 1/3*0 + 2/3 * 100% = 2/3. The question of this solution is that the host has opened an empty door (and the host intends to open this door). After this "information" appears, can you tell me the probability of an error is 2/3? Does this posterior fact change our view of the anterior probability? The answer is yes. More specifically, when the host opens a door, the probability of an incorrect choice is not necessarily equal to 2/3. Start from scratch. Suppose I have selected door B and the host Opens Door C. Under what circumstances will the host Open Door C?
If A has A car (A prior probability P = 1/3), then host 100% opens the C door (he apparently won't open B );
If B has A car (A prior probability P = 1/3), then the host has two choices: A and C. Assume that B opens C with the probability of K (generally K = 1/2, but we have set it as a variable );
If C has a car (a prior probability P = 1/3), the probability that the host opens C is 0 (as long as he is not stupid ...) It is known that he opened C. According to Bayesian formula -- here P (M | N) indicates the probability of M event occurrence when N event occurs: P (B has a car | C opens) = P (C Open | B has a car) * p (B has a car)/P (C open) P (C Open | B has a car) * p (B has a car) = P (C Open | A has A car) * p (A has A car) + P (C Open | B has A car) * p (B has A car) K * 1/3 = 1*1/3 + K * 1/3 K = ------- K + 1
When is the value equal to 1/3 (that is, the assumption in the classical solution )? Only K = 1/2. That is, under normal circumstances. However, if the host prefers to open the door on the right (assuming C is on the right) and K is set to 3/4, the probability of B having a car is 3/5, not 1/3, the fact of posterior changes the estimation of the prior probability! However, this does not change the correct choice. We should still select door A as follows: P (A has A car | C opens) = P (C opens | A has A car) * p (A has A car)/P (C open) P (C Open | A has A car) * p (A has A car) = ---------------------------------------------- P (C Open | A has A car) * p (A has A car) + P (C Open | B has A car) * p (B has A car) = 1*1/3/1*1/3 + K * 1/3 = 1/k + 1 and K <1 (assuming that the host is not too extreme to a non-C deselected degree ), so there will always be P (B has A car | C opens) <P (A has A car | C opens ). A has A higher probability of having A car than B. we should change our choice.
