The paper makes (among other arguments) the point that model selection is difficult to interpret correctly because the result depends on the priors. The authors use an analogy which I didn't quite grasp:

*Rather than discussing mathematical niceties, consider searching for, say, the smartest person in the world: applying a uniform prior across the population would lead a model selector to conclude that the evidence favors that person living in England rather than the US, because the US represents a larger parameter volume.*

The authors also write, as an example of the adequacy of parameter fitting, that

*A standard cosmological fit analysis of actual SNAP + SNF + Planck data will produce a central value in the ([tex]w_0,w_a[/tex]) plane (recall that [tex]w_a[/tex] = −2[tex]w[/tex]′(z = 1)) and a contour around it encompassing some chosen confidence level (CL), typically 68, 90, or 95%. The point corresponding to a cosmological constant (-1,0) may or may not lie inside the contour. If it does not, we may say that we exclude [tex]\Lambda[/tex]CDM at that CL.*

More precisely, in a frequentist analysis in which one aims to prove or disprove [tex]\Lambda[/tex]CDM, one would simulate the expected SNAP + SNF + Planck data sample assuming a [tex]\Lambda[/tex]CDM universe, and, analyzing this synthetic data sample as if it were the real data, one would draw a, say, 90% CL contour around the (-1,0) point, much like the one depicted as the inner contour in Fig. 1. That contour tells us that, if [tex]\Lambda[/tex]CDM is true, we expect to get a central value inside that contour in 90% of the observations like SNAP + SNF + Planck that we may perform. Therefore, if our one real SNAP + SNF + Planck observation delivers a central value outside that contour, irrespectively of its associated error ellipse, we will be able to say that we have excluded [tex]\Lambda[/tex]CDM at greater than 90% CL.

More precisely, in a frequentist analysis in which one aims to prove or disprove [tex]\Lambda[/tex]CDM, one would simulate the expected SNAP + SNF + Planck data sample assuming a [tex]\Lambda[/tex]CDM universe, and, analyzing this synthetic data sample as if it were the real data, one would draw a, say, 90% CL contour around the (-1,0) point, much like the one depicted as the inner contour in Fig. 1. That contour tells us that, if [tex]\Lambda[/tex]CDM is true, we expect to get a central value inside that contour in 90% of the observations like SNAP + SNF + Planck that we may perform. Therefore, if our one real SNAP + SNF + Planck observation delivers a central value outside that contour, irrespectively of its associated error ellipse, we will be able to say that we have excluded [tex]\Lambda[/tex]CDM at greater than 90% CL.

It would be interesting to hear comments from people who advocate model selection.