My main goal is to use four independent variables (y~x1,x2,x3,x4) and develop a Bayes Linear Regression model. However when I ran a simple linear regression model using these same four independent variables I found out that none of these independent variables are significant.

Does this matter at all that these independent variables were insignificant in predicting y to begin with, when I build a Bayes Linear model?

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    $\begingroup$ It depends on what, and how strong, your prior information is. A weak or uninformative prior will tend to replicate the classical frequentist analysis. But if your question is "is it valid to use a Bayesian model if a null frequentist model cannot be rejected?" then the answer is yes. Why wouldn't it be? $\endgroup$ – Andrew M Dec 18 '14 at 1:17
  • $\begingroup$ @AndrewM that is perfect, I did feel the same way..."Using Bayesian model because Freqentist model is insignificant in the first place" $\endgroup$ – Science11 Dec 18 '14 at 1:43

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