Dealing with multivariate x, errors in both x and y, and posterior predictive for y

  1. You can represent multiple x variables (e.g., repeated measurement) as a matrix, and do tt.dot(gradient * true_x) for matrix multiplication. Of course, you need to be careful of the shape in gradient and true_x

  2. It is hard to say, in general use a normal distribution with large standard deviation (e.g., 10x std of x) is a good starting point

  3. You can have a look at this blogpost and related discussion in OOS predictions with missing input values for some inspiration.

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