Gaussian fit score
I would like to know how to determine how well a Gaussian function fits my data.
Here are some of the plots I've tested the methods with. Currently I am just using RMSE as per the sample (red is appropriate, blue is sample).
For example, here are two good options:
And here are 2 scary prefixes that should be flagged as bad data:
In general, I'm looking for suggestions for additional metrics to measure good fit. Also, as you can see in the second "good" fit, there may sometimes be other out-of-data peaks. They are currently penalized with RSME, although they should not be.
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I'm looking for suggestions for additional metrics to gauge the goodness of the fit.
The Kolmogorov-Smirnov (KS) test with one sample would be a good starting point.
I offer the Wikipedia article as an introduction.
The test is available in SciPy as scipy.stats.kstest
. The function calculates and returns both the KS statistic and the p-value .
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You can try quantile-quantile (qq) with probplot from statistics:
import pylab
from stats import probplot
plot = probplot(data, dist='norm', plot=pylab)
pylab.show()
Calculate the quantile for the probability diagram and, if desired, show the plot.
Plots the probability of the sampled data against the quantiles of a specified theoretical distribution (default normal distribution). probplot optionally calculates a best fit line for the data and displays the results using Matplotlib or a given plot function.
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There are other ways of assessing good fit, but most of them are not emission resistant.
There MSE
is - the RMSE
root mean square error, which you already know, and which is its root.
But you can also measure it using MAE
- Average absolute error and MAPE
- Average absolute percentage error.
Also, there is the Kolmogorov-Smirnov test which is much more complicated and you will probably need a library for that while MAE
, MAPE
and MSE
you can easily implement yourself calmly.
(If you are dealing with uncontrolled data and / or classification that does not fit your case, curves ROC
and confusion matrix are also metrics of accuracy.)
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