Comparing Best-fits of different data sets that have different noise levels

In summary, the conversation discusses the challenge of comparing two sets of data, day1 and day2, when one set has significantly noisier data than the other. The difficulty lies in the fact that the root mean square (RMS) of the fit for day1 will naturally be larger due to the noise, making it difficult to determine which set fits the model better. One possible solution is to create a probability model that includes the distribution of the noise and use a computation based on the "likelihood ratio test" to make the comparison.
  • #1
zachzach
258
1
Suppose I have 2 sets of data: day1 and day2. I want to fit a model to both data sets and then compare them to each other to see which one fits the model the best (the fit is done with a computer using non-linear least squares method). The RMS of the fit would be fine except that day1 has much noisier data than day2 and the noise level is unknown. This makes the RMS of the fit for day1 (the noisy data) intrinsically larger than the RMS for day2 simply because of the noise. Is there anyway to compare the fits that is independent of the noise level?
 
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  • #2
I don't see how you can make a comparision unless you are willing to create a probability model for the data that includes the distribution of the noise. If you are willing to characterize the noise then you could consider a computation based on the "liklihood ratio test".
 

1. What is the purpose of comparing best-fits of different data sets?

The purpose of comparing best-fits of different data sets is to determine which data set provides the most accurate and reliable results. By comparing the best-fits, scientists can evaluate the quality of the data and make informed decisions about the validity of their findings.

2. How do you handle data sets with different noise levels when comparing best-fits?

When comparing best-fits of data sets with different noise levels, scientists often use statistical methods such as standard deviation or mean square error to quantify the level of noise in each data set. They can then use this information to make adjustments or apply weighting factors to the data sets to ensure a fair comparison.

3. What challenges do scientists face when comparing best-fits of data sets with different noise levels?

One of the main challenges is determining the appropriate method for handling the different noise levels. Additionally, scientists must carefully consider the potential biases or confounding factors that may affect the comparison and adjust their analysis accordingly.

4. Can best-fits of data sets with different noise levels be compared using visualizations?

Yes, visualizations can be used to compare best-fits of data sets with different noise levels. Graphs, charts, and other visual representations can help scientists to easily identify any patterns or differences between the data sets and make informed decisions about the quality of the data.

5. How important is it to choose the correct comparison method when comparing best-fits of data sets with different noise levels?

Choosing the correct comparison method is crucial when comparing best-fits of data sets with different noise levels. The method chosen should be based on sound statistical principles and should be appropriate for the type of data being analyzed. Using an incorrect method could lead to inaccurate conclusions and undermine the validity of the research.

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