Bayes Theorem between Continuous-valued Parameters

4 Bayes Theorem between Continuous-valued Parameters 

In most engineering applications, the updating concern is on continuous-valued uncertain parameters with measurements of continuous-valued variables. Even though there is quantization for the measurements, it is more convenient to treat them as continuous-valued variables and probability density functions are used to characterize their statistical behavior. With the same treatment for event B, event A can also represent the occurrence of another parameter vector  

Bayesian Methods for Structural Dynamics and Civil Engineering 

This form with probability densities is useful for most engineering applications and the methodologies presented in this book are built on it. The vector 9 represents the uncertain parameters for identification and the vector f represents the measurements of the system. Further discussion will be given in the following sections. 

---