How do I average over a number of Histograms?

So, I have 100 histogram plots each for different time instant. To analyze the system, I need a histogram plot which is the average of all these plots. How do I do it? I don't want to do it by image processing and all that. Can I do something like generating the histograms with equal number of bins and add the frequencies and then do the average and re-plot the average histogram. But, the problem will be in the histograms of the plots for the different instants, the range might be different. Please help. Thank you.

[John BG]

Hi Arghadwip Paul

This is John BG ( <mailto:[e-mail] [e-mail]> )

In general, one can average partial histograms (the different times you mention) when the stochastic process is ergodic.

This happens if the average value doesn't change throughout each sample, and is not null.

From

https://en.wikipedia.org/wiki/Ergodicity

https://en.wikipedia.org/wiki/Ergodic_theory

So, why don't you start taking small enough time windows and let us know?

John BG

<mailto:[e-mail] [e-mail]>

[Arghadwip Paul]

Ergodic means when the process will be independent of the initial state. I have done simulations till the time when I don't observe significant changes in my system. I would now want to average over the data of time instants(delta t=10^(-4)). What do you think?

Answer 1

[Walter Roberson]

Do not histogram with an equal number of bins: histogram with consistent edges to the bins. Then you can just put all the results together and mean() as appropriate.

In the below example, numedges-1 and edges(1:end-1) relates to the fact that the number of bins produced by histcounts is one fewer than the number of edges, because the final edge marks the end of the range.

   num_datasets = 100;

   edges = sort(rand(1, 14) * 5);
   numedges = length(edges);

   counts = zeros(numedges-1, num_datasets);

   for dataset_idx = 1 : 100
      counts(:, dataset_idx) = histcounts( datasets{dataset_idx}, edges );
   end

   avg_counts = mean(counts);
   bar(edges(1:end-1), avg_counts)

[Arghadwip Paul]

I would try this. But, do you want me to store my data of each instant in datasets? And, edges- how do I specify? Here you use rand function, but in my case, it won't be so.

[Image Analyst]

counts is a 2-D array. Each row of counts is the histogram for a dataset. Replace edges with something not using rand and using your data, something like

edges = linspace(minPossibleValue, maxPossibleValue, numBins);

where the two values are something you determine in advance, perhaps by pre-scanning your data to check what those values might be if you don't have advance expert knowledge of the values would be.

[Arghadwip Paul]

Thanks. It worked.

[Shubhani Paliwal]

What is datasets variable here?

Answer 2

[Steven Lord]

Generate each set of bin counts using histcounts with the same set of bin edges for each call. Once you have the bin counts for each trial, add them together and call histogram with the bin counts and bin edges to plot it.