The bayesian estimation of rolling bearing modern statistics

Rolling bearing the bayesian estimation of modern statistics, bayesian estimation is an important content of modern statistical research of - 。 , bayesian estimation that before the experiment to get the sample, should have - in estimator - - - - - - Some understanding. This awareness can be a theory, past the research of the similar problem when the accumulated experience, is this kind of experience before experiment, known as the a priori knowledge or prior information. Look from the common sense, consider the bayesian estimator of a priori information is correct, attaches great importance to the a priori information collection, mining and processing, make quantitative participation in statistical inference, can improve the quality of statistical inference. Bayesian estimation that theta be estimated parameters as random variables, and with a certain probability distribution, the distribution of prior knowledge or prior information, reasonable use of prior knowledge or prior information of estimated parameters theta, can improve the quality of parameters theta inference. The theta is regarded as random variable parameter space, there are two kinds of understanding: the first - Is in a certain range, parameter 0 is random; The second is parameter 0 is likely to be a constant, but can not accurately understand it, can only through observation to know it. Parameters can be got through experience or observation, theta prior knowledge or prior information. This is very useful in the actual estimate, can use the parameter theta prior knowledge or prior information to make a more accurate estimates of parameters. Set the overall density function of x for f ( x; ) , theta prior density function as n ( 6) , as a result of theta as random variables with a prior density function, so the overall density function f ( x; ) Can be seen as the conditional distribution of x given theta. So, the overall distribution of the X need to switch to f ( x( 6) To represent. X = ( X; ”。 X,) Is one of the overall sample, when the given sample value x = ( 1、“xn) When the sample x = ( X; ”,Xn) The joint density of q ( X |) = ( , ,x,|,) =我] f( x) ( 2 - 50) The type of g ( xl) As samples of joint probability density function, 0 to estimate parameters ( 1, ', in a given sample of xn, x as samples of the ith observation, n is number of observations. Samples of joint probability density function of X and theta for f ( x,0) = q( x|⑥) r( @) ( 2 - 51) Type of f ( 。 ) As the joint probability density function of x and theta, q ( ) As samples of joint probability density function, A prior density function for theta.