**2. Robust Bayesian procedure**

We also noted earlier that the concept of Bayes theory depends on prior information so that prior information is combined with the distribution of observations according to the Bayes rule, for the purpose of obtaining the posterior distribution, from here we may have a problem, which is a problem that prior data conflict. Whereas prior data they are the default values that are assumed for the parameters of the prior distribution, to find out this problem by updating the parameters of the prior distribution through two methods, namely Expected Conditional or Canonical Exponential Family and provided that the prior distribution is conjugate prior, after obtaining the prior distribution with the updated parameters, we extract the posterior distribution and then extract the standard deviation of the distribution if the value of the standard deviation of the prior distribution is greater than the standard deviation of the posterior distribution, then this means that there is a problem of prior data conflict, Thus, this problem can be addressed through the steps that we will explain later, This method is called the robust Bayesian method [1].

After the default values for the parameters of the prior distribution are chosen, the standard deviation of the prior distribution and the posterior distribution are extracted. If the value of the standard deviation of the prior distribution is greater than the standard deviation of the posterior distribution, this means that there is a problem of prior data conflict and provided that the posterior distribution is conjugate prior, this is the method that will be used in this chapter to verify the prior data conflict.

There are other ways to verify the prior data conflict that we did not used in this chapter, for example (Conflict checks based on relative belief, Connections between the relative belief and score checks and Other approaches to prior-data conflict checking) [2].

Then we move on to addressing the problem of prior data conflict through the proposal presented by (Walter and Augustin; 2009), this is for the purpose of generating a set of prior parameters, in short <sup>Q</sup><sup>0</sup> <sup>¼</sup> *<sup>n</sup>*0, *<sup>n</sup>*�<sup>0</sup> ½ �*<sup>x</sup> <sup>y</sup>*0, �*y*<sup>0</sup> � � h i , So that this model that generates a set of prior parameters is called generalized iLuck-model and therefore we will get a set of posterior distributions, And then a Bayes estimator is obtained according to the type of loss function used, and thus this method is called the robust Bayesian method [3].
