Theorem application of Bayes theorem, what is Yebes s theorem

1. Expressions and prior probabilities of known class conditional probability density parameters. 2. Use Bayesian formula to convert into posterior probability. 3. Classification of decisions according to the size of the posterior probability.

His main contribution to statistical reasoning was the use of"Inverse probability"and put it forward as a universal method of reasoning. Bayes' theorem is originally a theorem in probability theory, and this theorem can be expressed by a mathematical formula, which is the famous Bayesian formula.

Reasoning and decision-making based on uncertainty information requires estimating the probability of various conclusions, which is called probability-based reasoning.

1. Bayes' theorem is a conclusion in probability theory, which follows the conditional probability of machine variables and the marginal probability distribution. In some probability-based explanations, Bayes' theorems (Bayesian updates) can tell us how to modify existing beliefs using new evidence. In general, the probability of event A under the condition of event B (occurring) is not the same as the probability of event B under the condition of event A; However, there is a definite relationship between the two, and Bayes' theorem is a statement of this relationship.

2. Bayes' rule can be expressed as: posterior probability = (likelihood * prior probability) Normalized constant, that is, the posterior probability is proportional to the product of the prior probability and likelihood. In addition, the ratio pr(b|a) PR(b) is also sometimes referred to as standardised likelihood, and Bayes' rule can be expressed as:

Posterior probability = standard likelihood * prior probability.

Bayes' theorem can be understood as follows:

Posterior probability (the probability of a occurring after the new information appears) A priori probability (the probability of a occurrence) x probability function (the adjustment of the dust belt of the new information) The underlying idea of Bayes is:

If I can grasp all the information about a guess, Hu Zhaochan, I can certainly calculate an objective probability (classical probability, positive probability).

However, the vast majority of decisions in life are faced with incomplete information, and we only have limited information in our hands. Since we can't get comprehensive information, we try to make a good ** as much as possible in the case of limited information. That is, on the basis of subjective judgment, it is possible to estimate a value (a priori probability) and then continuously revise it based on new information observed (probability function).

p(a|b) is the probability that a occurs in the case of b;

p(a) is the probability of a occurrence;

p(b|a) is the probability of b occurring in the case of a;

The wheel p(b) is the probability of b occurring.

p(b) = p(b丨a)p(a) + p(b丨a')p(a').This is called the full probability formula.

p(a'), the probability that a does not occur, p(a') 1- p(a)。

Bayes' theorem is a method of solving for probabilities based on known other probabilities. Bayesian theorem, as a commonly used basic algorithm, has always had important significance and application in statistics, psychology, sociology, economics and other aspects. In the IT era, Bayesian theorem occupies an important place in computer science, especially in machine learning and industrial intelligence.

Especially in terms of data processing, it has a good effect on the probability of event occurrence and the credibility analysis of the event. In recent years, Bayesian theorem has received more and more attention and application in analysis and market.

Bayes (1701 – 1761) Thomas Bayes was an English mathematician. Born in London in 1701, he worked as a priest. He became a Fellow of the Royal Society in 1742.

He died on April 7, 1761. Bayes' main study in mathematics is the theory of probability. He first applied the inductive reasoning method to the basic theory of probability theory, and founded the Bayesian theory of statistics, which contributed to statistical decision functions, statistical inference, and statistical estimation.

1. Bayes' theorem is a posterior theorem about the conditional probabilities (or marginal probabilities) of random events a and b. where p(a|b) is the possibility of a occurrence in the case of b.

2. Bayesian theorem, also known as Bayesian inference, as early as the 18th century, the British scholar Bayes (1702-1763) proposed the formula of conditional probability to solve the following problems: hypothetical h[1], h[2]...., h[n] mutually exclusive and constitute a complete event, their probability p(h[i]), i=1,2,... is known, n, an event a and h[1], h[2]...., h[n] is accompanied by a machine, and the conditional probability p(a|) is knownh[i]), find p(h[i]|a)。