lkunik / bayesian-osse-r-sample Goto Github PK
View Code? Open in Web Editor NEWSource code for Bayesian urban inversion OSSE [Kunik et al., 2019] written in R and equipped with sample inputs (run it out-of-the-box!)
Source code for Bayesian urban inversion OSSE [Kunik et al., 2019] written in R and equipped with sample inputs (run it out-of-the-box!)
The paper referencing this code mentions that
X2 = spriorT B-1 sprior + zT R-1 z
is distributed as a χ2 variable on ν = Nobservations + Nfluxes. This is true.
The paper then goes on to generate an ensemble of pseudo-observations, calculate X2/ν for each member, and states that the expected value of this latter quantity is one. This is also true.
The difficulty I am having is that I can decompose X2 into two random variables:
Xflux2 = spriorT B-1 sprior
and
Xobs2 = zT R-1 z,
which are distributed as χ2 variables on Nfluxes and Nobservations, respectively. The ensemble in the paper generates multiple realizations of the second variable, but I only see one realization of the first.
E(X2 / ν) is still one;
E(E(X2 | Xflux2)) is also one;
E(X2 | Xflux2) is a function of Xflux2 and is what I think the paper has.
Is this an accurate description of what is going on? Is this a known and intended behavior of this package? It is entirely possible I just missed this section of the paper while reading. If that is th case, a pointer to the section of the paper where this is described would be welcome.
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