Calculating Correlations and Sensitivity Coefficients

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SUMMARY

This discussion focuses on estimating the change in the means of output parameters B and C due to variations in input parameter A, while accounting for their correlations. The user suggests using sensitivity coefficients to analyze these relationships. A recommended approach involves rerunning the simulation with slightly altered input parameters to obtain new outputs A', B', and C', followed by calculating the means and standard deviations of the new data to assess changes. The importance of clear correlations in data analysis is emphasized, avoiding reliance on nested calculations.

PREREQUISITES
  • Understanding of numerical simulations and statistical distributions
  • Familiarity with correlation and sensitivity analysis
  • Knowledge of mean and standard deviation calculations
  • Experience with data analysis tools such as Python or R
NEXT STEPS
  • Explore sensitivity analysis techniques in Python using libraries like NumPy and SciPy
  • Learn about correlation coefficients and their interpretation in statistical analysis
  • Investigate methods for simulating random variables and their distributions
  • Study the implications of normal distribution in multivariate data analysis
USEFUL FOR

This discussion is beneficial for data analysts, engineers, and researchers involved in numerical simulations and statistical analysis, particularly those interested in understanding the relationships between correlated variables.

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I have a numerical simulation where I'm randomly varying an input parameter.

This results in variations in three output parameters: A, B and C. The output parameters can be assumed to have normal distributions, but are correlated to each other.

If I calculate the mean and standard deviation on the range of values of A, B and C is there any way I could estimate the change in the mean of B and C due to a small change in the mean of A, making some account of the correlations? I was thinking of an approach based on sensitivity coefficients, but I'm not sure that's appropriate.

Any help/advice would be very welcome! Thanks!
 
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It sounds to me like the only way you could make a valuable correlation would be if you ran your experiment again with slightly tweaked input parameter, giving you new outputs A', B', C'. Then I'd calculate mean and SD and whatever else you think is good for the new data, and then see the changes between correlated outputs (i.e. A vs A').

I have no idea about the order of magnitude for the relationship of the correlation, or if one could exist, but as an engineer who has often been presented with data that is "supposed to be useful", this is how I would define useful, meaning that the correlation between data is clear and not based on nested calculations if possible.
 

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