David Jones:

> "It is discontinuous in that the raw data are
> discontinuous" .. That explains nothing. An "error" that
> is squared is derived from an an observed and a modelled
> value. Given the quantisation, the "observed" part of this
> for a single observation is either just a single value
> (usually the centre of the interval), or two values
> denoting the end points of the interval. In either case
> these values are fixed and don't depend on the mode
> parameters and hence cannot contribute a discontinuity to
> the objective function.

I misunderstood you. I thought you were talking about the
systematic drift model, which consists of a set of points
and is of course discontinous in time. The least-squares
objective function, however, need not be discotinous in the
parameters being fitted, yet Mr. Roberts chose to make it
so. Had he kept it natually continous, he would have been
able to find the optimum by solving it in partial
derivatives.

> Now it may be that the "error" is being constructed as a
> comparison of the quantised observation with a quantised
> version of the continuous modelled values. This seems to
> be very inadvisable, but it would produce a discontinuous
> objective function.

I think Mr. Roberts did the inadvisable thing.

> It is unfortunate that the 2006 paper provides no actual
> details about what is being done by way of defining the
> objective function.

Oh, no, it does explain that in part IV, albeit not very
clearly. I have tried to re-express his procedure with the
clarity and unambiguity of mathematical language, see my
post here:

From : Anton Shepelev <anton.txt@gmail.moc>
Subject : Re: statistics in Roberts' paper on Miller
Date : Wed, 8 Mar 2023 15:33:02 +0300
Message-ID: <20230308153302.2e74b7a62f096863323df7dd@gmail.moc>

Perhaps if you ask specific questions I can help you better.

> > David Jones:
> >
> > > There is an implication that this discontinuity was
> > > derive from whatever allowance is made for the effect
> > > of quantisation, but there are no details given.
> >
> > Can you please quote the relevant parts of the article?
>
> Well on page 6 there is this ..
>
> "As the data are quantized at 0.1 fringe, so are the
> parameters, and instead of the usual minimization programs
> an enumeration of all reasonable sets of parameters was
> used with an algorithm that finds the minimum X2. The
> result of the fit is a complete quantitative model of
> systematic(time) for the run. This fit has 313 degrees of
> freedom, and the histogram of X2 for all runs has a mean
> of 300, indicating that the estimate of the individual
> measurement resolution (0.1 fringe) is reasonable. Fitting
> each run took about 3 minutes of computer time to
> enumerate several million combinations of the 7 parameters
> to find both the best fit and the errorbar"

The only justification is in the first sentence. Mr. Roberts
thinks he should use quantised model parameters because the
input data is quantised, whereas I see no logical connection
between the premise and conclusion. The least-squares method
works well with quantised data and a continuous objective
function.

> I might well have misinterpreted this use of a search over
> "several million combinations" and the use of a
> "quantised" set of possible parameter values as being a
> response to discontinuity.

Mr. Roberts first /created/ that discontinuity by deciding
to quantise the naturally continous model parameters, and
then responded to his own decision by brute-force
enumeration of the several million combinations. He also
had to "fold" earch interferometer turn in two, because
partly the brute-force enumeration could not handle the 16
azimuth orientations.

> How the parameters can be "quantised at 0.1 fringe" and
> what this means is a mystery,

`ringe' is the unit of measurement, and also the quantum.
Each of the paramters may assume a fixed set values: 0.0,
0.1. 0.2, &c up the the practical maximum obvious from the
data.

> but it seems to be what is being said. But perhaps this
> part of the overall data analysis is not what I thought it
> was. But, if the objective function is actually continuous
> and well-behaved, I don't see why you would choose to do a
> multi-dimensional grid search.

Nor do I.

> Well yes, one would need to include in a model all of the
> effects that need to be modelled.

His model of the systematic drift includes them.

> But the point was that the quantisation should be treated
> properly as it seems to have been judged to be of such
> importance. This means having a model describing what
> would have been observed if there were no quantisation
> being done and then to treat the consequences of the
> quantisation.

In that case, the consequences of the quantisation are the
quantised values of the model parameters and a potential
small loss of precision -- nothing catastophiic. But still
idea artificially to quanise the naturally continuous
parameters seems unjustified.

> The above may sound a simple approach but, without
> thinking too deeply about this, I am worried that the
> "data manipulation" that is going on may make it
> infeasible. If the data-manipulation were simply that the
> data actually being analysed were simply the differences
> of two quantised observations, I think the approach could
> be carried through. But the steps being taken seem more
> complicated than that ... possibly in an attempt to
> remove certain effects that are of no interest but which
> need to be included in a full model of the observations
> actually made.

Well, this sound rather vague to me, so I can only refer you
to the 2006 article and my explanatory post mentioned above.
I will be glad to answer whatever specific questions you may
have.

> > Please, see the paragraph starting with: "While Fig. 3
> > shows the inadequacy of assuming a linear drift, it is
> > still useful to obtain quantitative errorbars for these
> > data analyzed in this manner," and let us know whether
> > you agree with the author.
>
> Well yes error bars would be useful, but one would need to
> know what they are error bars for, and one would need to
> know that they have been derived in a way that is
> statistically valid.

The paragraph referred-to above contains the entire
explanation of how those error bars were obtained. If you
brew some tea and take the time to read and understand the
2006 article, with my help when/if you need it, I am sure
you will understand those error bars and will be able judge
their correcness.

> Well I did look up a description of Java. This confuses
> the issue, but a summary is that the Java package itself
> is compiled, but that the treatment by the package of a
> supplied script is that it interprets and executes it line
> by line.

Well, Java is not an interpreted language at the top level.
It is compiled into `bytecode', which may be either
interpreted or compiled into machine code.

> Now there may be some version that compiles a script into
> executable code, but that is not really the point ...
> which is that Java is not usually counted as producing
> quickly-executing code as would be the case for Fortran or
> C(plus?). It may even be that there is some version of
> Java that is capable of calling subroutines written in
> Fortran or C, as is the case with the R package.

There is nothing wrong with interpreted languages for data
analysis as long as they defer the number-crunching to
compiled submodules. Python, Julia, or Wolfram Mathematica
are all good great choices. I don't know about R, but it too
seems great for the purpose.

> Obviously I know nothing about concepts of "Aether drift"

The aether is a hypothetical substance that fills all space,
because "nature brooks no emptiess", and "empty space cannot
be the arena of whatsoever interactions." If the Solar
system, -- and the Earth with it, -- moves through the
aether, the effect should be similar to the wind one feels
on one's face when riding a bicyle fast, whence the term
`aether wind', e.g.:

The Earth moving though aether, bound votixes causing
the phenomena of "the roaring forties":
https://freeshell.de//~antonius/file_host/ether-wind.png

> and how this might fit into modern versions of cosmology.

I have come hither to discuss the statistical model in the
2006 article regardless of theoretical cosmology :-)

> But there seems to be an assumption that, if it exists, it
> is in some way constant in size and direction.

Yes, especially in direction.

> Why wasn't the experiment constructed so as to determine a
> direction for rthe drift if it existed?

But it was! He measured the ether wind during several full-
days sessions at four different seasons, which let him
estimate the direction of the aether wind. No sceptic has
been able to answer how all his measurements made at
different times of day and of the year might have conspired
to point at a fixed direction in the galaxy. That is, every
day they show a clearly sinusoidal dependency on the time of
day with exactly the phase that would result from an
galactic aether wind rather than an earthly factor. Miller
reports his findings in the 1933 article. Do read
it -- clear and well-written.

> I guess the point is that there are certain mathematical
> theories in which things related to reality either do or
> do not interact and one is either; (a) looking for things
> already in the model that interact when the theory says
> they do not; or (b) looking for evidence that there are
> things not already in the theory that do have an effect on
> things that are.

Yes, as well as I could understand that rather philosophical
passage :-)

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