Robust statistical analysis

In summary, the conversation revolved around quantitatively modeling error in models versus experiment and the challenge of determining the accuracy of a model for a sparse phase space of measurements. The topic of using median-based statistics as a more robust measure of central tendency was also brought up. Book recommendations for understanding robust statistical analysis were given.
  • #1
Norman
897
4
I have been doing a lot of work recently on quantitatively modeling error in models versus experiment.

One of the problems I currently have is with a model and a sparse phase space of experimental measurements and how to determine the accuracy of the model for the entire phase space. One the problems here is that the usual mean based statistics we all know is not very good and I need a much more robust measure of the central tendency of the data. So, I started looking into median based statistics. Has anyone done any work using a Root Median Squared Error?

And can anyone point me towards some good texts on robust statistical analysis? Especially one dumbed down for a theoretical physicist (ie. someone without much (any?) formal statistics training).

Thanks.
 
Physics news on Phys.org
  • #2
I'm in a similar boat as you, trying to figure out how to best measure the accuracy of models with sparse phase spaces. I've had some success with using Root Mean Squared Error (RMSE). It's not a median-based statistic, but it has worked well for me so far.

As for good texts on robust statistics, I'd suggest looking into Robust Statistics: The Approach Based on Influence Functions by Frank R. Hampel et al. It's a great book that explains the basic principles of robust statistics in an accessible way. Another great resource is An Introduction to Robust Estimation & Hypothesis Testing, 3rd Edition by Rand R. Wilcox. It provides a good overview of the principles of robust statistics and has lots of examples to illustrate the concepts.
 

1. What is robust statistical analysis?

Robust statistical analysis is a method of statistical analysis that is designed to be resistant to outliers and assumptions about the underlying distribution of data. It aims to provide more accurate and reliable results, even when certain assumptions are violated.

2. Why is robust statistical analysis important?

Robust statistical analysis is important because it can provide more accurate and reliable results, especially in cases where traditional statistical methods may be affected by outliers or assumptions that do not hold true. It can also help identify potential issues with the data and improve the overall validity of the analysis.

3. What are some common techniques used in robust statistical analysis?

Some common techniques used in robust statistical analysis include non-parametric methods, such as the median and trimmed mean, which are less affected by outliers than traditional parametric methods. Other techniques include bootstrapping, which involves repeatedly resampling the data to create a distribution of the statistic of interest, and robust regression methods, such as the Huber and M-estimators.

4. When should robust statistical analysis be used?

Robust statistical analysis should be used when there are concerns about the assumptions of traditional statistical methods being violated, or when there are potential outliers in the data. It can also be useful when the data is not normally distributed or when the sample size is small, as traditional methods may not be as reliable in these situations.

5. What are the limitations of robust statistical analysis?

While robust statistical analysis can provide more accurate and reliable results in certain situations, it is not a perfect solution and has its own limitations. For example, it may not be able to handle extremely large or complex datasets. Additionally, some robust methods may sacrifice efficiency for robustness, meaning they may not be as powerful in detecting small effects as traditional methods.

Similar threads

  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
996
  • Set Theory, Logic, Probability, Statistics
Replies
6
Views
3K
  • Programming and Computer Science
Replies
1
Views
946
  • Set Theory, Logic, Probability, Statistics
Replies
5
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
5
Views
3K
  • Set Theory, Logic, Probability, Statistics
2
Replies
64
Views
3K
  • Set Theory, Logic, Probability, Statistics
Replies
7
Views
898
Replies
2
Views
1K
  • Programming and Computer Science
Replies
3
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
3
Views
1K
Back
Top