Observations errors or values have no effect on posterior's variance?

Python usage
1

hello,
i’ve tried running the official code (GaussianLinearCalibration — OpenTURNS 1.19 documentation) documenting Linear Gaussian Calibration. When i change the observed values, for instance by replacing the observed values by a constant vector, [y = ot.Sample(np.array([50]*m).reshape(-1,1))], the posterior’s variance is unchanged…

i obtained this variance using this line of code :
algo.getResult().getParameterPosterior().getMarginal(0).getStandardDeviation()[0]

i will also add that does not happen when i use the GaussianNonLinearCalibration class.

thanks a lot
regards,
sanaa

2

Hi @sanaaZ, this behavior is adequate: the posterior is a multivariate normal distribution whose covariance matrix does not depend on the values of the observations. Its formula is given in the theoretical doc page Gaussian calibration — OpenTURNS 1.19 documentation. It only depends on the distribution of the observations conditionally to the parameters, not the actual values of the observations.

Note that this is true because the prior is normal and the model for the observations is linear. Remove one of those assumptions and the posterior variance very much depends on the values of the observations.

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