Take a parameter space theta, indexed by delta in [0,1], so

theta(delta) = {standard model+delta}

prior over theta values: p(theta)

results space x; higgs results x = x0.

Connect by mathematical model of relevant physics, p(x|theta)

Then

p(x) = integral p(x|theta)p(theta) dtheta

p(x|x = x0) = integral p(x|theta,x=x0)p(theta|x=x0) dtheta

p(x|x = x0) = integral p(x|theta)p(theta|x=x0) dtheta [same mathematical model]

p(theta|x=x0)/p(theta) = p(x=x0|theta)/p(x=x0)

standard model: theta = 0

evidence for standard model given Higgs results:

p(theta=0|x=x0)/p(theta=0) = p(x=x0|theta=0)/p(x=x0)

*: http://www.utstat.utoronto.ca/mikevans/papers/mayoevansdiscuss.pdf

]]>“For a Bayesian the difference between prior and posterior measures quantifies the ‘evidence’ the data provides, given the model”.

That is why Royall and other say that Bayesians and likelihoodlums agree on evidence. ]]>

I’m reminded of a recent post on Jim Frost, a statistical advisor from Minitab. Despite posting several very sensible things on significance tests, he falls into confusion by echoing, with inadequate scrutiny, what he heard from J. Berger (mixed in with Colquihoun and others), and apparently has 0 interest in straightening things out:

http://errorstatistics.com/2016/01/19/high-error-rates-in-discussions-of-error-rates-i/

]]>I’m just not sure how I would express the rules other than in mathematics (and to me logic is a subset of mathematics). And then we end up with a mathematical structure representing the rules which is the game. An applied mathematician would probably call that a mathematical model of the game.

To get forward predictions we plug in info like team quality (with uncertainty) and propagate through to get output like a predicted score (with uncertainty).

The inverse problem is to do something like predict team quality (with uncertainty) given observed scores and holding the mathematical structure fixed (same game – still football).

Contra the forward problem this is generally ill-posed so we regularise via various means. For Bayesians that means a prior, but for others something else. For a Bayesian the difference between prior and posterior measures quantifies the ‘evidence’ the data provides, given the model through which we connected inputs and outputs.

I’ve now lost track of what we were talking about. Hope only weirdos are reading.

]]>I think your trial example makes my point better, actually. A person claiming to be a witness will be questioned and their testimony rigorously checked. If it is found to be unsound– as when the person was not at the scene to witness the event– then the testimony is not treated as evidence. No one just takes witness testimony at face value. Likewise, experts who are asked to testify must go through a vetting process and their analysis/test results subject to a review to determine if proper methods were used properly (called a Daubert hearing in US) prior to being admitted into evidence. Again, if the work was found to be flawed, then no testimony and no evidence.

That is the legal system, not science, but it makes sense.

]]>Oliver, Michael: OED model 2.e. A simplified or idealized description or conception of a particular system, situation, or process (often in mathematical terms: so mathematical model) that is put forward as a basis for calculation, predictions, or further investigation.

The rules of football define football just as the rules of chess define chess The rules of a game are not a model of the game, they are the game so to speak. This now sounds a bit like Searle and the construction of social reality. Nor is a real football game is a model of the rules.

Any non-statistician reading this must think we are all a bit weird.

]]>I think that we currently lack any agreed usage of the word evidence, and that is hindering our ability to talk about the appropriate ways of making inferences, and preventing many students from being able to put the various schools of statistical thought into a unified framework.

]]>http://homepages.warwick.ac.uk/~masdr/BOOKCHAPTERS/stuart15c.pdf ]]>