Should You Use One or Two Gaussians to Fit Sparse Poisson-Distributed Data?

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Another option is to visually inspect the data and see if there are clear indications of two distinct peaks, which would suggest a two Gaussian model may be more appropriate. However, with sparse data and large error bars, this may not be a reliable approach. In summary, to determine whether your data is best described by one or two Gaussians, you could use a model selection technique such as the BIC or visually inspect the data.
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Gerenuk
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I have data points which depend on a parameter and for each parameter they are Poisson distributed. Usually I fit them with a Gaussian as a function of that parameter.

An important question is whether I should use one or two Gaussians (close together). Apparently two Gaussian close enough together look similar to one and therefore fit well. Even more, if both Gaussians fits converge to the same center point. However my sparse data has large error bars and flattish looking peak rather converge to two separated Gaussians.

How could I get a meaningful measure whether my data is one or two Gaussians? I know only basic statistics, but I'm quite OK with general maths.
 
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One approach you could take is to use a model selection technique to determine which model best describes your data. A common approach is to use the Bayesian Information Criterion (BIC), which uses the likelihood of the model to determine its fit to the data, as well as penalizing more complex models with additional parameters. You can then compare the BIC values for the one and two Gaussian models to determine which best fits the data.
 

FAQ: Should You Use One or Two Gaussians to Fit Sparse Poisson-Distributed Data?

What is the purpose of testing for one or two peaks?

The purpose of testing for one or two peaks is to determine the distribution of a data set and whether it follows a normal distribution or not. This information is important in statistical analysis and making accurate conclusions.

How do you test for one or two peaks?

One way to test for one or two peaks is by visually inspecting a histogram or line graph of the data. If there is only one prominent peak, the data is likely to be normally distributed. If there are two distinct peaks, the data may indicate a bimodal distribution.

What does it mean if the data has one peak?

If the data has one peak, it means that the values are clustered around a central point and decrease symmetrically on either side. This is also known as a unimodal distribution and is characteristic of a normal distribution.

What does it mean if the data has two peaks?

If the data has two peaks, it means that there are two distinct groups or patterns within the data. This is known as a bimodal distribution and may indicate the presence of two underlying populations or subgroups within the data.

What factors can affect the number of peaks in a data set?

The number of peaks in a data set can be affected by various factors such as the sample size, the type of data being collected, and the underlying distribution of the data. It is important to consider these factors when interpreting the results of a one or two peak test.

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