This kind of understanding can be a certain theory, the experience accumulated in the past research on similar problems, this kind of experience is obtained before the experiment, called pre-knowledge or prior information.The joint density function of the sample, m(O is the prior density function of 6. joint density function of the sample, O is the estimated parameter, Suppose the density function of the overall X is f(x;O), and the prior density function is r().
Bayesian estimation believes that before conducting experiments to obtain samples, we should have some knowledge of estimators. Bayesian estimation believes that the parameter θ to be estimated is a random variable and has a certain probability distribution.,x), the joint density of sample X=(X12. This distribution is prior knowledge or prior information. Through experience or observations, prior knowledge or prior information of parameter 0 can be obtained.
Suppose X=(X,X) is a sample of the population, when the given sample value x=(x1.;xn) is the given sample, and x is the sample The ith observation of, n is the number of observations.,Xn|0)=1f(x16)2-50) where q(x(. This is very useful in actual estimation, and the prior knowledge or prior information of the parameters can be used to make more accurate estimates of the parameters. It pays attention to the collection, mining and processing of prior information, so that it can participate quantitatively in statistical inference, which can improve the quality of statistical inference.
Bayesian estimation of needle roller bearings is one of the important contents of modern statistical research. Reasonable use of the prior knowledge or prior information of the parameter θ to be estimated can improve The inferred quality of the parameter θ. Since θ is a random variable and has a prior density function, the overall density function f(x;O) can be regarded as Is the conditional distribution of x when θ is given.
From a common sense point of view, Bayes is undoubtedly correct to consider the prior information of the estimator.. The joint density function of samples X and 6 is f(x,0)=q(x|6)n(6(2-51) where f(x,0 is the joint probability density function of X and θ, q( x). It may be recognized through observations. Therefore, the distribution of the overall x needs to be replaced by).,Xn) is q(x10)=q(x ,. Regarding θ as a random variable China wheel bearing kits Manufacturers in the parameter space, there are two understandings: the first is that the parameter θ is random within a certain range; the second is that the parameter θ may be a certain constant, but it is impossible to accurately understand it