Help Integrating Poisson Errors on Histograms

In summary, the speaker has a histogram with bins representing the expected number of events at a specific energy, generated using a Monte Carlo. They need to integrate the bins in a section of the histogram and find the error, but the number of events is very small, making it difficult to calculate the error. They ask for advice on how to calculate the error, specifically mentioning the Euler-Maclaurin formula.
  • #1
Karatechop250
16
1
So I have a histogram with bins that contain the number of events expected at a specific energy (which I generated with a Monte Carlo).. I need to add (integrate) all the bins in a section of this histogram and find the error of this value. However, the number of events are very small approx 10^(-1) so I can't just add the error of each bin in quadrature. So how do I calculate the error on the result of my integration over a section of the bins?
 
Physics news on Phys.org
  • #2

FAQ: Help Integrating Poisson Errors on Histograms

1. What are Poisson errors on histograms?

Poisson errors on histograms are a type of statistical error that occur when counting discrete events, such as the number of particles in a sample or the number of occurrences of a certain event. These errors arise from the inherent randomness in the events being counted and can be represented by a Poisson distribution.

2. How do you integrate Poisson errors on histograms?

To integrate Poisson errors on histograms, you can use the Poisson error propagation formula, which takes into account the uncertainty in the counts and the bin width of the histogram. This formula involves calculating the standard deviation of the counts and propagating it through the integration process.

3. Why is it important to account for Poisson errors on histograms?

It is important to account for Poisson errors on histograms because they can significantly affect the accuracy and precision of your results. Ignoring these errors can lead to underestimation or overestimation of the true values and can also affect the statistical significance of your findings.

4. What can cause Poisson errors on histograms?

Poisson errors on histograms can be caused by a variety of factors, such as random fluctuations in the data, measurement errors, or limitations in the experimental setup. These errors are inherent in any counting process and cannot be completely eliminated, but their impact can be minimized through careful experimental design and analysis.

5. How can Poisson errors on histograms be minimized?

Poisson errors on histograms can be minimized by increasing the number of events or measurements being counted, which reduces the relative size of the errors. Additionally, using smaller bin widths in the histogram can also help to reduce these errors by providing a more accurate representation of the data. It is also important to properly analyze the data and account for these errors in statistical calculations.

Similar threads

I Poisson Error Q: Can I Add Errors in Quadrature?
Replies
5
Views
2K
I How Should You Approach Fitting Multiple Gaussians to Data with Poisson Errors?
Replies
28
Views
3K
I How to Bin Data for Spectrum Fitting with Poisson Errors?
2
Replies
37
Views
4K
I Computing uncertainties in histogram bin counts
Replies
3
Views
7K
A Normalized differential cross section
Replies
9
Views
2K
A Mixture density neural network prediction bias
Replies
1
Views
1K
A Monte Carlo to compute uncertainties, why report the mean and SD?
Replies
2
Views
1K
Simple error analysis for probabilities
Replies
1
Views
2K
I How accurate are the peak values from different binning sizes?
Replies
18
Views
3K
I How Should Systematic Errors Be Estimated When Experiment Results Differ?
Replies
25
Views
2K

Hot Threads

Recent Insights

Back
Top