In many fields of science, it is important to understand the relevance of new theories or hypotheses in a description of experimental data, assuming that such data are already well represented by predictions of some well-accepted theory. A popular statistical method for setting upper limits (also called exclusion limits) on model parameters of a new theory is based on the CLs method.

Let us show how to set an exclusion limit in case of a counting experiment. We will use particle physics, as an example of hardcore science, where a new theory is considered to be excluded at the 95% confidence level (CL) if CLs = 0.05, and at more than the 95% CL if CLs< 0.05, assuming the presence of a signal that represents a new theory.

In this small tutorial, we will set the exclusion limits at the 95% CL on empirical distributions ("histograms"). We will use 3 histograms: (1) first histogram represents counts of actual measurements, (2) second histogram is the prediction of a well-established theory, (3) third distribution is a prediction ("signal") from some new theory. We will use the DataMelt program for this task that allows to use the Python language together with the Java scientific libraries.

Let us generate these histograms using one-tailed Gaussian distributions. The first histogram includes 10,000 events distributed according to one-tailed Gaussian distribution with the standard deviation 1. The second histogram represents our expectation for a known theory ("background"). The latter histogram has a similar shape and the number of events. The third histogram ("signal") corresponds to the prediction of a new theory. We assume that the new theory contributes to the tail of the experimental data (near x=2). We want to find the maximum number of events of signal (which is a parameter of this new theory) which can be reliable excluded, assuming that the given experimental data is already well described by the well-established theory.

*Read full article, with Python code, here. *

© 2020 Data Science Central ® Powered by

Badges | Report an Issue | Privacy Policy | Terms of Service

**Upcoming DSC Webinar**

- DataOps: How Bell Canada Powers their Business with Data - July 15

Demand for data outstrips the capacity of IT organizations and data engineering teams to deliver. The enabling technologies exist today and data management practices are moving quickly toward a future of DataOps. DataOps is an automated, process-oriented methodology, used by analytic and data teams, to improve the quality and reduce the cycle time of data analytics. Register today.

**Most Popular Content on DSC**

To not miss this type of content in the future, subscribe to our newsletter.

- Book: Statistics -- New Foundations, Toolbox, and Machine Learning Recipes
- Book: Classification and Regression In a Weekend - With Python
- Book: Applied Stochastic Processes
- Long-range Correlations in Time Series: Modeling, Testing, Case Study
- How to Automatically Determine the Number of Clusters in your Data
- New Machine Learning Cheat Sheet | Old one
- Confidence Intervals Without Pain - With Resampling
- Advanced Machine Learning with Basic Excel
- New Perspectives on Statistical Distributions and Deep Learning
- Fascinating New Results in the Theory of Randomness
- Fast Combinatorial Feature Selection

**Other popular resources**

- Comprehensive Repository of Data Science and ML Resources
- Statistical Concepts Explained in Simple English
- Machine Learning Concepts Explained in One Picture
- 100 Data Science Interview Questions and Answers
- Cheat Sheets | Curated Articles | Search | Jobs | Courses
- Post a Blog | Forum Questions | Books | Salaries | News

**Archives:** 2008-2014 |
2015-2016 |
2017-2019 |
Book 1 |
Book 2 |
More

**Upcoming DSC Webinar**

- DataOps: How Bell Canada Powers their Business with Data - July 15

Demand for data outstrips the capacity of IT organizations and data engineering teams to deliver. The enabling technologies exist today and data management practices are moving quickly toward a future of DataOps. DataOps is an automated, process-oriented methodology, used by analytic and data teams, to improve the quality and reduce the cycle time of data analytics. Register today.

**Most popular articles**

- Free Book and Resources for DSC Members
- New Perspectives on Statistical Distributions and Deep Learning
- Time series, Growth Modeling and Data Science Wizardy
- Statistical Concepts Explained in Simple English
- Machine Learning Concepts Explained in One Picture
- Comprehensive Repository of Data Science and ML Resources
- Advanced Machine Learning with Basic Excel
- Difference between ML, Data Science, AI, Deep Learning, and Statistics
- Selected Business Analytics, Data Science and ML articles
- How to Automatically Determine the Number of Clusters in your Data
- Fascinating New Results in the Theory of Randomness
- Hire a Data Scientist | Search DSC | Find a Job
- Post a Blog | Forum Questions

## You need to be a member of Data Science Central to add comments!

Join Data Science Central