A Data Science Central Community

In some applications, using the standard precision in your programming language of choice, may not be enough, and can lead to disastrous errors. In some cases, you work with a library that is supposed to provide very high precision, when in fact the library in question does not work as advertised. In some cases, lack of precision results in obvious problems that are easy to spot, and in some cases, everything seems to be working fine and you are not aware that your simulations are completely wrong after as little as 30 iterations. We explore this case in this article, using a simple example that can be used to test the precision of your tool and of your results.

Such problems arise frequently with algorithms that do not converge to a fixed solution, but instead generate numbers that oscillate continuously in some interval, converging in distribution rather than in value, unlike traditional algorithms that aim to optimize some function. The examples abound in chaotic theory, and the simplest case is the recursion *X*(*k* + 1) = 4 *X*(*k*) (1- *X*(*k*)), starting with a seed *s* = *X*(0) in [0, 1]. We will use this example - known as the logistic map - to benchmark various computing systems.

*Read full article for explanations about this picture*

Examples of algorithms that can be severely impacted by aggregated loss of precision, besides ill-conditioned problems, include:

- Markov Chain Monte Carlo (MCMC) simulations, a modern statistical method of estimation for complex problems and nested or hierarchical models, including Bayesian networks.
- Reflective stochastic processes, see here. This includes some some types or Brownian or Wiener processes.
- Chaotic processes, see here (especially section 2.) These include fractals.
- Continuous random number generators, see here.

The conclusions based on the faulty sequences generated are not necessarily invalid, as long as the focus is on the distribution being studied, rather than on the exact values from specific sequences.

© 2021 TechTarget, Inc. Powered by

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

**Most Popular Content on DSC**

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

- 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

**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 AnalyticBridge to add comments!

Join AnalyticBridge