Bayesian Methods for Inferring Representative Values of Variable Actions in Small Sample Situations

There is a need sometimes in engineering to infer the representative values of variable actions in cases when the test data is not sufficient, but the classical statistics methods do not take into account of the succedent influences of statistical uncertainty, and the inferred results are always on the aggressive side. In order to overcome the above shortcomings, applying the current linear regression estimation for inferring the fractiles of type I minimum distribution, the linear regression estimation of representative values of variable actions is proposed as a reference method for the precision inspection of other inference methods. According to Bayesian theory, applying Jeffreys non-informative prior distribution, a Bayesian method for inferring characteristic and frequent values of variable actions is put forward. The results show that the Bayesian inference method is more convenient than the liner regression estimation, and easy to use in a broader context. The method can give more advantageous results when standard deviation is known. If no parameter information is available, the Bayesian inference method has better precision when the guarantee rates of characteristic and frequent values are no less than 0.90. Compared with other confidence degrees, the inferred results are more close to the true value when the confidence degree equals 0.75; therefore, it is recommended to take a confidence degree of 0.75.