Regression adjustment returns point estimate in specific case about elfi HOT 3 CLOSED

Hi! I think that linear regression adjustment actually works as intended for an observation model without noise, which essentially is a linear system of equations (L) in this case. The adjustment "corrects" all the samples as the same solution to (L).

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What do you mean by "an observation model without noise"? Is this in reference to the original observed data (i.e. theoretical quantiles of the chi-squared in my example), or the lack of random simulation from the parameters in the rejection sampling stage?

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I see what you mean. The system can be described as y = XB where y is the vector of samples for a single parameter, X is a matrix with samples over rows and summary statistics (selected quantiles in this case) over the columns, and B is a vector of coefficients. When fitting this model manually using sklearn.linear_model.LinearRegression().fit(X, y), I get an r-squared of 1, i.e. a perfect fit. As it turns out, the quantile function for the Normal distribution is a linear function of the location and scale parameters so the point estimate is actually the correct result. This is not an issue with ELFI at all, just my own understanding!

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