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This commit updates the chi2 script to add scale factors for the
atmospheric neutrino scale and muon scale parameters. The reason for
this is that these parameters should now have a much easier
interpretation than before. Now, the atmospheric neutrino scale
parameter is relative to the expected atmospheric neutrino flux (i.e. we
expect the fit to return something close to 1), and the muon scale
parameter is the total number of expected muons in our sample, which is
exactly what the data cleaning analysis gives us.
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This commit updates the chi2 script to skip minimzing the likelihood
before running the MCMC. The reason for this is that I was occasionally
seeing a linear algebra error about a singular matrix when running the
MCMC with the KDEMove which I suspect is caused by too many points being
in the same place.
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This commit updates the chi2 script to only merge the weights dataframe
with the Monte Carlo dataframe after we have selected the universe for
the weights. This *greatly* reduces the memory usage.
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This commit fixes the chi2 analysis so that it is no longer biased.
Previously, the chi2 analysis pull plots showed a consistent bias. At
first, I thought this was due to the fact that the posterior wasn't
gaussian, but even after switching to percentile plots based on the
algorithm outlined in "Validating Bayesian Inference Algorithms with
Simulation-Based Calibration", I was still seeing a bias. I finally
tracked it down to the fact that I was applying the energy scale
parameters to the data instead of the Monte Carlo. Therefore, in this
commit I update the posterior to now apply the energy scale parameters
to the Monte Carlo instead of the data. This has the slight disadvantage
that the final histograms will be binned in the biased energy, but
that's not really a big deal.
In addition, this commit contains several other updates:
- switch to plotting percentile plots based on the algorithm in
"Validating Bayesian Inference Algorithms with Simulation-Based
Calibration" instead of pull plots
- apply both the energy scale and resolution at the individual particle
level, i.e. there is no longer an energy resolution term for electron
+ muon fits
- separate pull plots and coverage plots. Previously I was making both
the p-value coverage plots and the pull plots at the same time.
However, the pull plots shouldn't have anything to do with the GENIE
weights whereas the p-value coverage plots should draw samples
weighted by the GENIE weights. In addition, for the pull plots we draw
new truth parameters on every iteration whereas for the p-value
coverage plots we only draw them once.
- switch to using KDEMove() for the MCMC since I think it samples
multimodal distributions a lot better than the default emcee move.
- I now correct for the reconstruction energy bias in plot-michel and
plot-muons
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This commit updates how the energy bias is applied when we correct for
the energy bias in correct_energy_bias(). The correct way to apply this
correction is to compute:
T_corrected = T_reco/(1+bias)
whereas previously we were multiplying by (1-bias).
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This commit updates the chi2 analysis with two big changes:
- I now apply the energy bias correction in the likelihood per particle
and not per fit. So there is no longer an energy bias parameter for
electron + muon fits, instead we just apply the energy bias correction
for electrons to the electron and the energy bias correction for muons
to the muon and then add the two kinetic energies.
- I now apply the energy bias correction terms to the data instead of
the Monte Carlo. This does introduce an issue with discontinuities in
the likelihood but it makes everything easier to interpret. The
discontinuities *should* be correctly taken into account by the MCMC.
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This commit updates the chi2 script to correct for the energy bias of
the reconstruction relative to Monte Carlo.
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This commit updates the estimate_errors() function so that it works
without a list of constraints and uses arrays of low and high bounds
passed in instead of hardcoded constraints.
I can now call this function from the chi2 analysis to get the stepsizes
before running the MCMC.
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This commit updates the chi2 script to make sure that the energy
resolution is nonzero otherwise we get nans.
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This commit updates the first bins that we use before applying the
energy resolution in the chi2 script. The reason we do this is because
when adding the energy resolution, events outside of the original bins
may migrate into the first and last bin.
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- add get_multinomial_prob() function to stats.py
- add plot_hist2_data_mc() function to do the normal particle id plot
but also print p values
- other small bug fixes
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This commit adds the new file sddm/stats.py to and adds a function to
correctly sample a Monte Carlo histogram when computing p-values. In
particular, I now take into account the uncertainty on the total number
of expected events by drawing from a gamma distribution, which is the
posterior of the Poisson likelihood function with a prior of 1/lambda.
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This commit adds a first draft of a script called chi2. This script calculates
a chi2 for the null hypothesis test if the events in the energy range 20 MeV -
10 GeV match what we expect from atmospheric neutrino events.
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