From: Alexander Conley (AJConley@lbl.gov)
Date: Tue Sep 07 2004 - 10:20:34 PDT
Hello Mark,
Thank you kindly for the comments.
> In Fig. 9, errors corresponding to a peculiar velocity of 300 km/sec
> are
> displayed horizontally. In quadrature, scaled by the local Hubble
> slope,
> are they also included in the vertical errors? If not, perhaps this
> should
> be considered; it would help to dispel the false impression that the
> lowest-z points contribute disproportionately to chi^2.
I see your point. My first reaction was that the horizontal errors
encode
all of the information, but once you subtract off the best fit line
that is
no longer the case. I will consider modifying the plot.
> ----------
>
> From Fig. 10, one hopes to judge whether the stretch-luminosity
> relationship
> is systematically different for high-z and low-z SNe. However, since
> the
> chi^2 of the low-z points with respect to the solid line is obviously
> unacceptable, one is led not to take seriously their displayed error
> bars.
> In turn this confounds the judgment.
>
> Is this conundrum avoidable? Perhaps the following supplement to Fig.
> 10
> should be considered for inclusion: Start from the residuals and their
> errors (relative to "Best Fit") from Fig. 9 (see above comment).
> Modify
> these residuals by backing out the stretch correction to each point
> (but
> retain the stretch-correction-related contribution to the error in the
> plotted residual). Using these residuals and their errors, construct
> the
> analog to Fig. 10.
>
What you are suggesting is essentially to do the plot the same way but
add in the propagated stretch uncertainty. That is probably a
reasonable
thing to include because it does effectively go into the fit. I will
make this
change.
One thing worth noting is that the error bars here don't include the
intrinsic
error, which would make things look better. Maybe I should consider the
inner error bar/outer error bar approach.
> ----------
>
> In Fig. 12, no errors are shown. Based on the points displayed there,
> a
> Pearson coefficient and two best-fit (slopes + errors) are quoted. Do
> the
> Pearson coefficient and best-fit slopes take into account the known
> point-by-point errors, both in B_BV residual and B_max residual, that
> could
> have been displayed in Fig. 12?
>
You must have a slightly older version of the paper. Version 1.27 does
include
the error bars in plot 12.
The fitted slope does include the error bars, the Pearson's
coefficients do not.
Is there a way to include them in the Pearson's coefficient
meaningfully? I
was under the impression that you couldn't include errors.
However, the fitted slopes do not include any correlation information
between B_BV0.6 and m_B. Inspired by your work, at the least I should
try to include the peculiar velocity correlation in the fit.
Alex
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