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astrosonnen / allZeLenses

Cosmology with every single gravitational lens ever.
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Model checking discussion #6

Open drphilmarshall opened 9 years ago

drphilmarshall commented 9 years ago

Needs working into plan (introduction) and then experimental sections. Can we tell when we have reached sufficient model flexibility? Can we detect the likely presence of residual systematics this way?

General principle: define test statistic $T(d)$ that only depends on the data vector at hand. Then, form the posterior predictive distribution for $T$, ie $P(T(d^p);d) where $d^p$ is a predicted data vector (drawn from the posterior PDF for the parameters, and then the sampling distribution to capture the noise) and look at where $T(d)$ (the test statistic of the observed data) lies. More discussion in Gelman and Shalizi (2012)

drphilmarshall commented 9 years ago

Gelman and Shalizi (2012) is well worth reading in full.