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1、决策理论与方法2_（Decision theory and method 2_）The second chapter is subjective probability and prior distributionSubjective, Probability, and, Prior, DistributionThe main references in this chapter are: 60, 52, how god throws diceThe basic concept of 2-1Probability (probability)1. frequencyFN (A) =Na/NP (
2、A) = FN (A). Definition of classical probabilityThe definition of 2. Laplace in the theoretical analysis of probability (1812)P (A) =k/NIn the formula, K is the basic event number contained in A,N is the total number of basic eventsApplicable conditions 1. basic events Limited2. each basic event, et
3、c.3. axiomatic definitionE is a random test, and S is the sample space of E. For each event of E, A corresponds to a definite real number P (A) if it satisfies:Non negative: 0 = P (A = 1)Normative: P (S) =1The countable additivity of 22 incompatible events (k=1,2 Ak. (Ai) Aj=.)P (Ak) = Sigma P (Ak)T
4、he P (A) is called the probability that the event A occursTwo, subjective probability (subjective, probability, likelihood)1. why introduce subjective probabilities?. Some natural states cannot be repeatedWill it rain tomorrow?Hows the new product going?What is the rate of national economic growth n
5、ext year?Can you take a PhD?. The cost of the experiment is too expensive and too costlyExample: Continental missile hit rateAn estimate of the enemys next move in a war2. subjective probability definition: a measure of rational beliefA possible measure of what happens to a particular event.The exte
6、nt to which he believed (or believed) the possibility of an event to occur.This degree of belief is a belief, subjective, but based on experience, knowledge, and knowledgeObjective analysis, reasoning, and synthetic judgment (Assignment) is different from subjective conjecture.Example: doctoral cand
7、idates, flip coins, flip pinsThree. The mathematical definition of probabilityThe non empty elements of Omega Omega, omega = Omega, that is, F is a subset of A Omega sigma Omega epsilon F domain (i.e.;If A is A, F, F;If Ai = F i=1,2,. Then, Ai, F)If P (A) is the real valued set function set on F, it
8、 satisfiesNon negative P (A) = 0Normative P (omega) =1The countable additivityP (A) is a straight (principal or objective) probability measure, referred to as probabilityOmega is the basic eventA for eventsThe $three population (omega, F, P) is called probability spaceNote: subjective probability an
9、d objective probability (objective, probability) have the same definitionFour. Comparison of subjective and objective probabilities(1) basic attributes:O: the inherent objective nature of a system, the limits of frequency passing under repeated tests in the same conditionsS: probability is the natur
10、e of the observer rather than the system, which is the degree to which the observer is trusting in the system(two) coin toss: positive upward, with a probability of 1 / 2O: as long as the coin is uniform, the throwing method is similar, and the number is enough. The positive upward probability is 1
11、/ 2, which is simpleDefinition。S: thats the definition. DMer thinks the coins are homogeneous. The likelihood of the positive and the negative is the same (1)2 is a subjective quantity.(three) the probability of a positive coin next time is 1 / 2O: this statement is wrong. Without repeated tests, th
12、e probability is out of the questionS: for DMer, next time a positive or negative is possible. But he does not mean that the coin itself is fair, it isThere may be a bias, as far as his knowledge is concerned, there is no reason to predict that one side may appear greater than the other, but repeate
13、dly throw itThe observation of the throw may change his belief.O: S: will the next coin be positive or negative, but I know?:Either the front or the back.The 2-2 distribution (Prior distribution) and setIn decision analysis, the information that is collected when the state information has not been t
14、ested is called a priori information, which is determined by a priori informationThe determined probability distribution is called a prior distribution.Setting a priori distribution is the need for Bayesean analysisA few assumptions about the prior distribution1. connectivity (Connectivity), also kn
15、own as comparabilityThat is, the likelihood B of events A and likelihood can be compared:A L, B or A, L, B or B L A, there must be one and only one* * A L B read as A, the likelihood of occurrence is greater than the likelihood of B occurrence,The likelihood of occurrence of A L B as A is comparable to the likelihood of B occurrence.2. transitivity (Transitivity)For events A, B, C, A, L, B, B, L, C, then A L CThe 3. part is less than the A B: if B L A?E
