Give an in-depth explanation of how and why mixture density models are used in HMMs.

SHOW COMPLETE AND CLEAR SOLUTION. SHOW ILLUSTRATION IF NECESSARY.  EXPLAIN YOUR ANSWER FOR ME TO UNDERSTAND

When evaluating models, why is it essential to first analyze measurement models before structural models?

The flow of glycerine (kinematic viscosity Vg = 5 x 104 m²/s) in an open channel is to be modeled in laboratory flume using water (vw) 10-6 m²/s) as the flowing fluid. If both gravity and viscosity are important, what should be the length scale (i.e, ratio of prototype to model dimensions) for maintaining dynamic similarity?