ISSN Online: **2379-1748**

8th Thermal and Fluids Engineering Conference (TFEC)

# UNDERSTANDING THE DIFFERENCES BETWEEN CLASSICAL AND BAYESIAN STATISTICS APPLIED TO THERMALLY FORMED POLYMERICMATERIALS

## 要約

Classical (or Frequentist) statistics attempts to understand how a sample of statistical information behaves over all possible random samples. It assumes that the numerical characteristics of the sample are fixed by unknown constants; the probabilities are treated as long run relative frequencies; the behavior of the statistical procedures are judged by how well they behave over an infinite number of hypothetical repetitions of the experiments.

Bayesian statistics assumes that parameters are random variables; the rules of probability make inferences about the parameters; probability statements are interpreted as degrees of belief. Every statistician can have a unique set of priors that contains the weights that are assigned to each parameter. Consequently, the conclusions are based upon the priors and the data actually observed. Essentially the Classical approach looks at how a method depends upon a random sample, i,e., a sampling distribution of the estimator. Bayesian treats the parameter as a random variable and depends upon the sample actually used. As a result, we find that Bayesian analysis often has better performance than the frequentist's estimator in terms of the mean squared error over the range of possible values.

In contrast to elastic problems where history can be ignored, viscoelastic materials require a knowledge of the entire history that the material has experienced. In many papers the viscoelastic properties have been entered into commercial FEM systems and the time history been obtained. In this paper we make use of an iterative process involving a Lagrangian approach based upon the matching of a second order Piola-Kirchoff and Cauchy analyses of the current spatial description of the system using Schapery material model.

Bayesian statistics assumes that parameters are random variables; the rules of probability make inferences about the parameters; probability statements are interpreted as degrees of belief. Every statistician can have a unique set of priors that contains the weights that are assigned to each parameter. Consequently, the conclusions are based upon the priors and the data actually observed. Essentially the Classical approach looks at how a method depends upon a random sample, i,e., a sampling distribution of the estimator. Bayesian treats the parameter as a random variable and depends upon the sample actually used. As a result, we find that Bayesian analysis often has better performance than the frequentist's estimator in terms of the mean squared error over the range of possible values.

In contrast to elastic problems where history can be ignored, viscoelastic materials require a knowledge of the entire history that the material has experienced. In many papers the viscoelastic properties have been entered into commercial FEM systems and the time history been obtained. In this paper we make use of an iterative process involving a Lagrangian approach based upon the matching of a second order Piola-Kirchoff and Cauchy analyses of the current spatial description of the system using Schapery material model.