The cause of Bayesian (probability theory analysis)

Conditional probability: P (x| Y

Joint probability: P (X, Y)

Edge probability: P (X), P (Y).

Joint probability = conditional probability * Edge probability

The inverse problem is usually solved with conditional probabilities.

• Inverse problem refers to the problem that the cause should be reversed from the result;
• A positive problem is the introduction of results from a cause.
  • The inverse problems are common:
    • Communication: According to the received signal containing noise y presumably send a signal x;
    • Speech recognition: Based on the audio waveform data identified by Mioko, Y guesses the voice information x;
    • Text recognition: Based on the image read by the scanner y guess the text x written by the user;
    • Automatic message filtering: Based on the received message text y guess the type of the message x (whether it is advertising, etc.)
  • The relationship between x, Y is expressed by the random variable x, Y.

• The Bayesian formula discusses the following types of problems:
  • Consistent all P (cause) and P (Result | reason)
  • Ask P (cause | result)

where P (cause) is called a priori probability, p (cause | result) is called posterior probability, and the distribution of response is called prior distribution and posterior distribution.

• Independence:
  • If there are multiple random variables in the problem, we first look at whether there is a real association between these random variables:
    • If x is not related to Y, it is meaningless to push y by X.
    • "Independent" differs from "Uniform distribution": P (y=1| x=**) = P (y=2| x=**) = P (y=3| x=**) = .... (does not satisfy independence)
    • "Independent" differs from "Independent distribution": P (x=1) = P (y=1), p (x=2) = P (y=2), p (x=3) = P (y=3), ...
    • "Independent" differs from "mutex": independence does not mean that the "event x=1 and Y=1 do not occur simultaneously", whereas the mutex means that x and Y are not independent random variables.
    • Independence means that x is not associated with Y, and we cannot judge the value of x based on Y.
  Nature of Satisfaction:
  • Conditional probabilities are independent of condition: P (x| Y) = P (x|-y)
  • Add or remove conditions do not affect: P (x| Y) = P (X)
  • The joint probability is the product of the edge probability: P (x, Y) = P (x) *p (y)

The cause of Bayesian (probability theory analysis)