What is the difference between a response, output, hidden and latent variables in modeling?

A hidden variable is a variable that you cannot measure by a sample process. For instance, this appears in the hidden Markov model (HMM), where you can sample output data $(y_1,\ldots,y_n)$ but not the states $(x_1,\ldots,x_n)$ which led to the output.

Note that the difference is between observable and hidden variables. The observable variables are instantiated (there are values for these variables) while there are no values for the hidden variables.

In the HMM (which is a specific Bayesian network), given the observable (here output) variables (values for them), estimate the most probable values of the state variable that led to the output.

The initial application of the HMM is speech recognition by Viterbi in the 1960s. Basically, the output are spoken siblings (output observed) and the corresponding states (hidden) are the written (real) siblings. The aim is to find the most probable sequence of written siblings (sentences) corresponding to the spoken words. The associated algorithm is named after its inventor Viterbi.

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Statistics

Data Analysis

Mathematical Modeling

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