From 8738ec1f2416f80a26f867e43f089b76fb351b53 Mon Sep 17 00:00:00 2001 From: tomeichlersmith Date: Tue, 14 Oct 2025 07:02:07 -0500 Subject: [PATCH 1/5] start EoT page with appendix from EaT internal note --- src/SUMMARY.md | 1 + src/physics/stats/electrons-on-target.md | 59 ++++++++++++++++++++++++ 2 files changed, 60 insertions(+) create mode 100644 src/physics/stats/electrons-on-target.md diff --git a/src/SUMMARY.md b/src/SUMMARY.md index 39902e10..7f9e0992 100644 --- a/src/SUMMARY.md +++ b/src/SUMMARY.md @@ -26,6 +26,7 @@ - [Averages](physics/stats/averages.md) - [Resolution](physics/stats/resolution.md) - [Multi-Bin Exclusion with Combine](physics/stats/multi-bin-combine.md) + - [Electrons on Target (EoT)](physics/stats/electrons-on-target.md) - [ECal](physics/ecal/intro.md) - [Layer Weights](physics/ecal/layer-weights.md) diff --git a/src/physics/stats/electrons-on-target.md b/src/physics/stats/electrons-on-target.md new file mode 100644 index 00000000..8af6b674 --- /dev/null +++ b/src/physics/stats/electrons-on-target.md @@ -0,0 +1,59 @@ +# Electrons on Target +Generally, we find the equivalent electrons on target ($N_\text{EoT}^\text{equiv}$) +by multiplying the simulated number of electrons on target ($N_\mathrm{thrown}$) +by the biasing factor ($B$) increasing the rate of the process focused on for the sample. +If there is filtering in the simulation, the simulated number of electrons on target +_is not_ equal to the number of events in the output file. + +Currently, the simulated number of electrons on target is stored as the "number of tries" +in the `RunHeader`. + +~~~admonish note title="Caveat Depending on ldmx-sw Version" collapsible=true +Samples created with ldmx-sw verions newer than v3.3.4 ($\geq$ v3.3.5) have an update +to the processing framework to store this information more directly +(in the `numTries_` member of the RunHeader or $\leq$ v4.4.7 and the `num_tries_` member +for newer). +Samples created with ldmx-sw versions older than v3.1.12 ($\leq$ v3.1.11) have access +to the "Events Began" field of the `intParameters_` member of the RunHeader. + +The easiest way to know for certain the number of tries is to just set the maximum +number of events to your desired number of tries $N_\mathrm{thrown}$ and limit the +number of tries per output event to one `p.maxTriesPerEvent = 1` and `p.maxEvents = Nthrown` +in the config script. +~~~ + +In the thin-target regime, this is satisfactory since the process we care about either +happens (with the biasing factor applied) or does not (and is filtered out). +In thicker target scenarios (like the Ecal), we need to account for events where +unbiased processes happen to a particle _before_ the biased process. +Geant4 accounts for this while stepping tracks through volumes with +biasing operators attached and we include the weights of all steps in the overall event +weight in our simulation. +We can then calculate an effective biasing factor by dividing the total number of events +in the output sample ($N_\mathrm{sampled}$) by the sum of their event weights ($\sum w$). +In the thin-target regime (where nothing happens to a biased particle besides the +biased process), this equation reduces to the simpler $B N_\mathrm{thrown}$ used in other +analyses since biased tracks in \textsc{Geant}4 begin with a weight of $1/B$. +$$ +N_\text{EoT}^\text{equiv} = \frac{N_\mathrm{sampled}}{\sum w}N_\mathrm{thrown} +$$ + +## Event Yield Estimation +Each of the simulated events has a weight that accounts for the biasing that was applied. +This weight quantitatively estimates how many _unbiased_ events this single +_biased_ event represents. +Thus, if we want to estimate the total number of events produced for a desired EoT +(the "event yield"), we would sum the weights and then scale this weight sum by the ratio +between our desired EoT $N_\text{EoT}$ and our actual simulated EoT $N_\text{thrown}$. +$$ +N_\text{yield} = \frac{N_\text{EoT}}{N_\text{thrown}}\sum w +$$ +Notice that $N_\text{yield} = N_\text{sampled}$ if we use +$N_\text{EoT} = N_\text{EoT}^\text{equiv}$ from before. +Of particular importance, the scaling factor out front is constant across all events +for any single simulation sample, so (for example) we can apply it to the contents of a +histogram so that the bin heights represent the event yield within $N_\text{EoT}$ events +rather than just the weight sum (which is equivalent to $N_\text{EoT} = N_\text{thrown}$). + +## More Complexity +Include Einar's notes here... From 33f5054e0659cec1a64f0181baed41c113905ada Mon Sep 17 00:00:00 2001 From: tomeichlersmith Date: Tue, 14 Oct 2025 08:42:45 -0500 Subject: [PATCH 2/5] update eot notes while drafting --- src/physics/stats/electrons-on-target.md | 127 ++++++++++++++++++----- 1 file changed, 101 insertions(+), 26 deletions(-) diff --git a/src/physics/stats/electrons-on-target.md b/src/physics/stats/electrons-on-target.md index 8af6b674..cb48c9b1 100644 --- a/src/physics/stats/electrons-on-target.md +++ b/src/physics/stats/electrons-on-target.md @@ -1,27 +1,102 @@ # Electrons on Target -Generally, we find the equivalent electrons on target ($N_\text{EoT}^\text{equiv}$) -by multiplying the simulated number of electrons on target ($N_\mathrm{thrown}$) -by the biasing factor ($B$) increasing the rate of the process focused on for the sample. -If there is filtering in the simulation, the simulated number of electrons on target -_is not_ equal to the number of events in the output file. +The number of "Electrons on Target" (EoT) of a simulated or collected data sample +is an important measure on the quantity of data the sample represents. +Estimating this number depends on how the sample was constructed. -Currently, the simulated number of electrons on target is stored as the "number of tries" -in the `RunHeader`. +## Real Data Collection +For real data, the accelerator folks at SLAC construct a beam that has a few parameters we can +measure (or they can measure and then tell us). +- duty cycle \\(d\\): the fraction of time that the beam is delivering bunches +- rate \\(r\\): how quickly bunches are delivered +- multiplicity \\(\mu\\): the Poisson average number of electrons per bunch -~~~admonish note title="Caveat Depending on ldmx-sw Version" collapsible=true -Samples created with ldmx-sw verions newer than v3.3.4 ($\geq$ v3.3.5) have an update +The first two parameters can be used to estimate the number of bunches the beam delivered to LDMX +given the amount of time we collected data \\(t\\). +\\[ + N_\text{bunch} = d \times r \times t +\\] + +For an analysis that only inspects single-electron events, we can use the Poisson fraction of these +bunches that corresponds to one-electron to estimate the number of EoT the analysis is inspecting. +\\[ + N_\text{EoT} \approx e^{-\mu} N_\text{bunch} +\\] +If we are able to include all bunches (regardless on the number of electrons), then we can replace +the Poisson fraction with the Poisson average. +\\[ + N_\text{EoT} \approx \mu N_\text{bunch} +\\] +A more precise estimate is certainly possible, but has not been investigated or written down +to my knowledge. + +## Simulation +For the simulation, we configure the sample generation with a certain number of electrons +per event (usually one) and we decide how many events to run for. +Complexity is introduced when we do more complicated generation procedures in order to +access rarer processes. + +~~~admonish warning title="Single Electron Events" +All of the discussion below is for single-electron events. +Multiple-electron events are more complicated and have not been studied in as much detail. +~~~ + +In general, a good first estimate for the number of EoT a simulation sample represents is +\\[ +N_\text{EoT}^\text{equiv} = \frac{N_\text{sampled}}{\sum w} N_\text{attempt} +\\] +where +- \\(N_\text{sampled}\\) is the number of events in the file(s) that constitute the sample +- \\(\sum w\\) is the sum of the event weights of those same events +- \\(N_\text{attempt}\\) is the number of events that were attempted when simulating + +~~~admonish note title="Finding Number of Attempted Events" +Currently, the number of attempted events is stored as the `num_tries_` member of +the `RunHeader` + +Samples created with ldmx-sw verions newer than v3.3.4 (>= v3.3.5) have an update to the processing framework to store this information more directly -(in the `numTries_` member of the RunHeader or $\leq$ v4.4.7 and the `num_tries_` member +(in the `numTries_` member of the RunHeader or <= v4.4.7 and the `num_tries_` member for newer). -Samples created with ldmx-sw versions older than v3.1.12 ($\leq$ v3.1.11) have access +Samples created with ldmx-sw versions older than v3.1.12 (<= v3.1.11) have access to the "Events Began" field of the `intParameters_` member of the RunHeader. The easiest way to know for certain the number of tries is to just set the maximum -number of events to your desired number of tries $N_\mathrm{thrown}$ and limit the -number of tries per output event to one `p.maxTriesPerEvent = 1` and `p.maxEvents = Nthrown` -in the config script. +number of events to your desired number of tries \\(N_\mathrm{attempt}\\) and limit the +number of tries per output event to one (`p.maxTriesPerEvent = 1` and `p.maxEvents = Nthrown` +in the config script). ~~~ +### Inclusive +The number of EoT of an inclusive sample (a sample that has neither biasing or filtering) +is just the number of events in the file(s) that constitute the sample. + +The general equation above still works for this case. +Since there is no biasing, the weights for all of the events are one \\(w=1\\) so the sum +of the weights is equal to the number of events sampled \\(N_\text{sampled}\\). +Since there is no filtering, the number of events attempted \\(N_\text{attempt}\\) is also equal +to the number of events sampled. +\\[ + N_\text{EoT}^\text{inclusive} = N_\text{sampled} +\\] + +### Filtered +Often, we filter out "uninteresting" events, but that should not change the EoT the sample +represents since the "uninteresting" events still represent data volume that was processed. +This is the motivation behind using number of events attempted \\(N_\text{attempt}\\) instead +of just using the number in the file(s). +Without any biasing, the weights for all of the events are one so the sum of the weights +is again equal to the number of events sampled and the general equation simplifies to +just the total number of attempts. +\\[ + N_\text{EoT}^\text{filtered} = N_\text{attempt} +\\] + + +### Biased +Generally, we find the equivalent electrons on target (\\(N_\text{EoT}^\text{equiv}\\)) +by multiplying the attempted number of electrons on target (\\(N_\mathrm{attempt}\\)) +by the biasing factor (\\(B\\)) increasing the rate of the process focused on for the sample. + In the thin-target regime, this is satisfactory since the process we care about either happens (with the biasing factor applied) or does not (and is filtered out). In thicker target scenarios (like the Ecal), we need to account for events where @@ -30,13 +105,13 @@ Geant4 accounts for this while stepping tracks through volumes with biasing operators attached and we include the weights of all steps in the overall event weight in our simulation. We can then calculate an effective biasing factor by dividing the total number of events -in the output sample ($N_\mathrm{sampled}$) by the sum of their event weights ($\sum w$). +in the output sample (\\(N_\mathrm{sampled}\\)) by the sum of their event weights (\\(\sum w\\)). In the thin-target regime (where nothing happens to a biased particle besides the -biased process), this equation reduces to the simpler $B N_\mathrm{thrown}$ used in other -analyses since biased tracks in \textsc{Geant}4 begin with a weight of $1/B$. -$$ +biased process), this equation reduces to the simpler \\(B N_\mathrm{thrown}\\) used in other +analyses since biased tracks in Geant4 begin with a weight of \\(1/B\\). +\\[ N_\text{EoT}^\text{equiv} = \frac{N_\mathrm{sampled}}{\sum w}N_\mathrm{thrown} -$$ +\\] ## Event Yield Estimation Each of the simulated events has a weight that accounts for the biasing that was applied. @@ -44,16 +119,16 @@ This weight quantitatively estimates how many _unbiased_ events this single _biased_ event represents. Thus, if we want to estimate the total number of events produced for a desired EoT (the "event yield"), we would sum the weights and then scale this weight sum by the ratio -between our desired EoT $N_\text{EoT}$ and our actual simulated EoT $N_\text{thrown}$. -$$ +between our desired EoT \\(N_\text{EoT}\\) and our actual simulated EoT \\(N_\text{thrown}\\). +\\[ N_\text{yield} = \frac{N_\text{EoT}}{N_\text{thrown}}\sum w -$$ -Notice that $N_\text{yield} = N_\text{sampled}$ if we use -$N_\text{EoT} = N_\text{EoT}^\text{equiv}$ from before. +\\] +Notice that \\(N_\text{yield} = N_\text{sampled}\\) if we use +\\(N_\text{EoT} = N_\text{EoT}^\text{equiv}\\) from before. Of particular importance, the scaling factor out front is constant across all events for any single simulation sample, so (for example) we can apply it to the contents of a -histogram so that the bin heights represent the event yield within $N_\text{EoT}$ events -rather than just the weight sum (which is equivalent to $N_\text{EoT} = N_\text{thrown}$). +histogram so that the bin heights represent the event yield within \\(N_\text{EoT}\\) events +rather than just the weight sum (which is equivalent to \\(N_\text{EoT} = N_\text{thrown}\\)). ## More Complexity Include Einar's notes here... From bbcf119c5033354d6d4ced5b16834216c7deabd0 Mon Sep 17 00:00:00 2001 From: tomeichlersmith Date: Tue, 14 Oct 2025 09:25:46 -0500 Subject: [PATCH 3/5] copy in Einar's notes from almost 2yr ago --- src/physics/stats/electrons-on-target.md | 61 +++++++++++++++--- .../eot/ecal-pn-extrapolate-loglog-scale.png | Bin 0 -> 46750 bytes .../stats/figs/eot/ecal-pn-linear-scale.png | Bin 0 -> 49083 bytes .../stats/figs/eot/kaon-pn-resampling.png | Bin 0 -> 43064 bytes 4 files changed, 53 insertions(+), 8 deletions(-) create mode 100644 src/physics/stats/figs/eot/ecal-pn-extrapolate-loglog-scale.png create mode 100644 src/physics/stats/figs/eot/ecal-pn-linear-scale.png create mode 100644 src/physics/stats/figs/eot/kaon-pn-resampling.png diff --git a/src/physics/stats/electrons-on-target.md b/src/physics/stats/electrons-on-target.md index cb48c9b1..b4422c54 100644 --- a/src/physics/stats/electrons-on-target.md +++ b/src/physics/stats/electrons-on-target.md @@ -62,7 +62,7 @@ to the "Events Began" field of the `intParameters_` member of the RunHeader. The easiest way to know for certain the number of tries is to just set the maximum number of events to your desired number of tries \\(N_\mathrm{attempt}\\) and limit the -number of tries per output event to one (`p.maxTriesPerEvent = 1` and `p.maxEvents = Nthrown` +number of tries per output event to one (`p.maxTriesPerEvent = 1` and `p.maxEvents = Nattempt` in the config script). ~~~ @@ -107,10 +107,10 @@ weight in our simulation. We can then calculate an effective biasing factor by dividing the total number of events in the output sample (\\(N_\mathrm{sampled}\\)) by the sum of their event weights (\\(\sum w\\)). In the thin-target regime (where nothing happens to a biased particle besides the -biased process), this equation reduces to the simpler \\(B N_\mathrm{thrown}\\) used in other +biased process), this equation reduces to the simpler \\(B N_\mathrm{attempt}\\) used in other analyses since biased tracks in Geant4 begin with a weight of \\(1/B\\). \\[ -N_\text{EoT}^\text{equiv} = \frac{N_\mathrm{sampled}}{\sum w}N_\mathrm{thrown} +N_\text{EoT}^\text{equiv} = \frac{N_\mathrm{sampled}}{\sum w}N_\mathrm{attempt} \\] ## Event Yield Estimation @@ -119,16 +119,61 @@ This weight quantitatively estimates how many _unbiased_ events this single _biased_ event represents. Thus, if we want to estimate the total number of events produced for a desired EoT (the "event yield"), we would sum the weights and then scale this weight sum by the ratio -between our desired EoT \\(N_\text{EoT}\\) and our actual simulated EoT \\(N_\text{thrown}\\). +between our desired EoT \\(N_\text{EoT}\\) and our actual simulated EoT \\(N_\text{attempt}\\). \\[ -N_\text{yield} = \frac{N_\text{EoT}}{N_\text{thrown}}\sum w +N_\text{yield} = \frac{N_\text{EoT}}{N_\text{attempt}}\sum w \\] Notice that \\(N_\text{yield} = N_\text{sampled}\\) if we use \\(N_\text{EoT} = N_\text{EoT}^\text{equiv}\\) from before. Of particular importance, the scaling factor out front is constant across all events for any single simulation sample, so (for example) we can apply it to the contents of a histogram so that the bin heights represent the event yield within \\(N_\text{EoT}\\) events -rather than just the weight sum (which is equivalent to \\(N_\text{EoT} = N_\text{thrown}\\)). +rather than just the weight sum (which is equivalent to \\(N_\text{EoT} = N_\text{attempt}\\)). -## More Complexity -Include Einar's notes here... +Generally, its a bad idea to scale too far above the equivalent EoT of the sample, so usually +we keep generating more of a specific simulation sample until \\(N_\text{EoT}^\text{equiv}\\) +is above the desired \\(N_\text{EoT}\\) for the analysis. + +## More Detail +This is a copy of work done by Einar Elén for [a software development meeting in Jan 2024](https://indico.fnal.gov/event/63045/). + +The number of selected events in a sample \\(M = N_\text{sampled}\\) should be binomially distributed +with two parameters: the number of attempted events \\(N = N_\text{attempt}\\) and probability \\(p\\). +To make an EoT estiamte from a biased sample with \\(N\\) events, we need to know +how the probability in the biased sample differs from one in an inclusive sample. + +Using "i" to stand for "inclusive" and "b" to stand for "biased". +There are two options that have floated around in LDMX. +1. \\(p_\text{b} = B p_\text{i}\\) where \\(B\\) is the biasing factor. +2. \\(p_\text{b} = W p_\text{i}\\) where \\(W\\) is the ratio of the average event weights between the two samples. Since the inclusive sample has all event weights equal to one, \\(W = \sum_\text{b} w / N\\) so it represents the EoT estimate described above. + +### Binomial Basics +- Binomials are valid for distributions corresponding to some number of binary yes/no questions. +- When we select \\(M\\) events out of \\(N\\) generated, the probability estimate is just \\(M/N\\). + +We want \\(C = p_\text{b} / p_\text{i}\\). + +The ratio of two probability parameters is not usually well behaved, but the binomial distribution is special. +A 95% Confidence Interval can be reliably calculated for this ratio: +\\[ + CI[\ln(C)] = 1.96 \sqrt{\frac{1}{N_i} - \frac{1}{M_i} + \frac{1}{N_b} - \frac{1}{M_b}} +\\] +This is good news since now we can extrapolate a 95% CI up to a large enough sample size using smaller +samples that are easier to generate. + +For example, a very common sample is the so-called "Ecal PN" sample where we bias and filter for a high-energy +photon to be produced in the target and then have a photon-nuclear interaction in the Ecal mimicking our missing +momentum signal. +Up to a sample size \\(N\\) of 1e8 (\\(10^8\\) both options for estimating \\(C\\) look okay (first image), +but we can extrapolate out another order of magnitude and observe that the second option \\(W\\) stays within +the CI. + +![EoT Estimate for ECal PN Sample on a Linear Scale](figs/eot/ecal-pn-linear-scale.png) +![EoT Estimate for ECal PN Sample Extrapolated on a LogLog Scale](figs/eot/ecal-pn-extrapolate-loglog-scale.png) + +Now, this estimate \\(W\\) ends up being a slight over-estimate for samples produced via a more complicated process. +Specifically, a "Kaon" sample where there is not an explicit biasing but the photon-nuclear interaction is re-sampled during the event already shows difference between the "true" value for \\(C\\) and our two short-hand estimates from before. + +![EoT Estimate Failure for Kaon PN Resampling](figs/eot/kaon-pn-resampling.png) + +I (Tom) do not know how to resolve this. 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deletions(-) diff --git a/src/physics/stats/electrons-on-target.md b/src/physics/stats/electrons-on-target.md index b4422c54..751c1f97 100644 --- a/src/physics/stats/electrons-on-target.md +++ b/src/physics/stats/electrons-on-target.md @@ -19,7 +19,7 @@ given the amount of time we collected data \\(t\\). For an analysis that only inspects single-electron events, we can use the Poisson fraction of these bunches that corresponds to one-electron to estimate the number of EoT the analysis is inspecting. \\[ - N_\text{EoT} \approx e^{-\mu} N_\text{bunch} + N_\text{EoT} \approx \mu e^{-\mu} N_\text{bunch} \\] If we are able to include all bunches (regardless on the number of electrons), then we can replace the Poisson fraction with the Poisson average. @@ -139,15 +139,15 @@ This is a copy of work done by Einar Elén for [a software development meeting i The number of selected events in a sample \\(M = N_\text{sampled}\\) should be binomially distributed with two parameters: the number of attempted events \\(N = N_\text{attempt}\\) and probability \\(p\\). -To make an EoT estiamte from a biased sample with \\(N\\) events, we need to know +To make an EoT estimate from a biased sample with \\(N\\) events, we need to know how the probability in the biased sample differs from one in an inclusive sample. Using "i" to stand for "inclusive" and "b" to stand for "biased". -There are two options that have floated around in LDMX. +There are two options that we have used in LDMX. 1. \\(p_\text{b} = B p_\text{i}\\) where \\(B\\) is the biasing factor. 2. \\(p_\text{b} = W p_\text{i}\\) where \\(W\\) is the ratio of the average event weights between the two samples. Since the inclusive sample has all event weights equal to one, \\(W = \sum_\text{b} w / N\\) so it represents the EoT estimate described above. -### Binomial Basics +~~~admonish note title="Binomial Basics" - Binomials are valid for distributions corresponding to some number of binary yes/no questions. - When we select \\(M\\) events out of \\(N\\) generated, the probability estimate is just \\(M/N\\). @@ -156,24 +156,50 @@ We want \\(C = p_\text{b} / p_\text{i}\\). The ratio of two probability parameters is not usually well behaved, but the binomial distribution is special. A 95% Confidence Interval can be reliably calculated for this ratio: \\[ - CI[\ln(C)] = 1.96 \sqrt{\frac{1}{N_i} - \frac{1}{M_i} + \frac{1}{N_b} - \frac{1}{M_b}} + \text{CI}[\ln(C)] = 1.96 \sqrt{\frac{1}{N_i} - \frac{1}{M_i} + \frac{1}{N_b} - \frac{1}{M_b}} \\] This is good news since now we can extrapolate a 95% CI up to a large enough sample size using smaller samples that are easier to generate. +~~~ + +### Biasing and Filtering +For "normal" samples that use some combination of biasing and/or filtering, \\(W\\) is a good (unbiased) +estimator of \\(C\\) and thus the EoT estimate described above is also good (unbiased). For example, a very common sample is the so-called "Ecal PN" sample where we bias and filter for a high-energy photon to be produced in the target and then have a photon-nuclear interaction in the Ecal mimicking our missing momentum signal. +We can use this sample (along with an inclusive sample of the same size) to directly calculuate \\(C\\) with +\\(M/N\\) and compare that value to our two estimators. Up to a sample size \\(N\\) of 1e8 (\\(10^8\\) both options for estimating \\(C\\) look okay (first image), -but we can extrapolate out another order of magnitude and observe that the second option \\(W\\) stays within -the CI. +but we can extrapolate out another order of magnitude and observe that only the second option \\(W\\) stays within +the CI (second image). ![EoT Estimate for ECal PN Sample on a Linear Scale](figs/eot/ecal-pn-linear-scale.png) ![EoT Estimate for ECal PN Sample Extrapolated on a LogLog Scale](figs/eot/ecal-pn-extrapolate-loglog-scale.png) -Now, this estimate \\(W\\) ends up being a slight over-estimate for samples produced via a more complicated process. -Specifically, a "Kaon" sample where there is not an explicit biasing but the photon-nuclear interaction is re-sampled during the event already shows difference between the "true" value for \\(C\\) and our two short-hand estimates from before. +### Photon-Nuclear Re-sampling +Often we want to not only require there to be a photon-nuclear interaction in the Ecal, but we also want +that photon-nuclear interaction to produce a specific type of interaction (usually specific types of particles +and/or how energetic those particles are) -- known as the "event topology". + +In order to support this style of sample generation, ldmx-sw is able to be configured such that when the +PN interaction is happening, it is repeatedly re-sampled until the configured event topology is produced +and then the simulation continues. +The estimate \\(W\\) ends up being a slight over-estimate for samples produced via this more complicated process. +Specifically, a "Kaon" sample where there is not an explicit biasing of the photon-nuclear interaction but +the photon-nuclear interaction is re-sampled until kaons are produced already shows difference between the +"true" value for \\(C\\) and our two short-hand estimates from before (image below). ![EoT Estimate Failure for Kaon PN Resampling](figs/eot/kaon-pn-resampling.png) -I (Tom) do not know how to resolve this. Perhaps a different estimate for \\(C\\) is able to handle the PN resampling and accomodate biasing in which case we can update our advice on how to estimate the EoT. +The overly-simple naive expected bias \\(B\\) is wrong because there is no biasing, +but the average event weight ratio estimate \\(W\\) is also wrong +in this case because the current (ldmx-sw v4.5.2) implementation of the re-sampling procedure updates the event +weights incorrectly. +[Issue #9999](https://github.com/LDMX-Software/ldmx-sw/issues/9999) documents what we believe is incorrect +and a path forward to fixing it. +In the meantime, just remember that if you are using this configuration of the simulation, the estimate for the +EoT explained above will be slighly higher than the "true" EoT. +You can repeat this experiment on a medium sample size (here 5e7 = 50M events) where an inclusive sample can +be produced to calculate \\(C\\) directly. From bbcaeea9c101922d185ba45d3319e7cd573433b1 Mon Sep 17 00:00:00 2001 From: tomeichlersmith Date: Wed, 15 Oct 2025 09:17:34 -0500 Subject: [PATCH 5/5] link to issue --- src/physics/stats/electrons-on-target.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/physics/stats/electrons-on-target.md b/src/physics/stats/electrons-on-target.md index 751c1f97..15d22ef9 100644 --- a/src/physics/stats/electrons-on-target.md +++ b/src/physics/stats/electrons-on-target.md @@ -197,7 +197,7 @@ The overly-simple naive expected bias \\(B\\) is wrong because there is no biasi but the average event weight ratio estimate \\(W\\) is also wrong in this case because the current (ldmx-sw v4.5.2) implementation of the re-sampling procedure updates the event weights incorrectly. -[Issue #9999](https://github.com/LDMX-Software/ldmx-sw/issues/9999) documents what we believe is incorrect +[Issue #1858](https://github.com/LDMX-Software/ldmx-sw/issues/1858) documents what we believe is incorrect and a path forward to fixing it. In the meantime, just remember that if you are using this configuration of the simulation, the estimate for the EoT explained above will be slighly higher than the "true" EoT.