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To illustrate the goal, I'll provide an example.

Suppose we'd like model someone's foot-size, in inches, with a Gaussian distribution of unknown mean and variance. We'd like to infer through N observations of them trying on a shoes of different sizes (continuous, in inches)

However, the N observations binary only, e.g {Fit, No_Fit}.

What would be the appropriate model structure to tie the binary observations to the latent Gaussian distribution? Or more generally, mixed discrete-observations/continuous-model scenarios?

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