sentences:  Generally, formula_1 has a set of parameters that can be grouped together and called formula_12, and formula_2 has its own vector of parameters that may be of different dimensionality, but is still termed formula_12.The marginalization for formula_1 is
  
  and likewise for formula_2.This integral is often analytically intractable, and in these cases it is necessary to employ a numerical algorithm to find an approximation.