How can I represent a stochastic process in 2D?

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SUMMARY

This discussion focuses on representing two stochastic processes in 2D using matrices of size 9x500, where 9 represents time points and 500 represents realizations. The suggested approach involves calculating the correlations between the two sets of outputs, X and Y, and visualizing these correlations through histograms. The user seeks effective graphical representations, having previously attempted 3D histograms and contour plots but found them unsatisfactory. The conversation emphasizes the importance of illustrating the relationship between the stochastic processes clearly.

PREREQUISITES
  • Understanding of stochastic processes and their representation
  • Proficiency in statistical correlation analysis
  • Familiarity with data visualization techniques, particularly histograms
  • Experience with matrix manipulation in programming environments (e.g., Python, R)
NEXT STEPS
  • Learn how to calculate and interpret correlation coefficients using Python's NumPy library
  • Explore advanced data visualization techniques using Matplotlib or Seaborn for better representation of correlations
  • Investigate the use of 2D density plots to visualize the relationship between two stochastic processes
  • Research best practices for presenting stochastic data in academic papers or reports
USEFUL FOR

Data scientists, statisticians, researchers in stochastic modeling, and anyone involved in visualizing complex data relationships will benefit from this discussion.

Frank Einstein
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Hello everyone.

I have recently started working with a model whose output are two stochastic process which evolve trough time. Now, I have two 9*500 matrices, being 9 the number of times for which the model offers a value and 500 the number of realizations.

I was wondering if someone could suggest me what is the best way to represent this, since I want to illustrate graphically the correlation or lack of between both matrices, let's call them X and Y.

If someone could point me in the right direction I would be extremely thankful.
 
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Just to be sure I understand:
You ran an experiment 500 times.
Each time you got 9X values and 9Y values.
You want to show the relationship, if any, between the X and Y output.

So the first thing I would think of in presenting this data would be to calculate the 500 correlations between the X sets and the Y sets.
Then I would present a histogram of the result - showing the distribution of the correlations.

But really, I would need to know more about what you wanted to demonstrate.
 
.Scott said:
Just to be sure I understand:
You ran an experiment 500 times.
Each time you got 9X values and 9Y values.
You want to show the relationship, if any, between the X and Y output.

So the first thing I would think of in presenting this data would be to calculate the 500 correlations between the X sets and the Y sets.
Then I would present a histogram of the result - showing the distribution of the correlations.

But really, I would need to know more about what you wanted to demonstrate.

You have understood right. That's exactly what I have.

My question is if someone has ever plotted something like that.
What I have done is showing each pair of points at each realization, a 3D histogram and a contour, but I don't feel satisfied with the results.

jg7Cgo

https://ibb.co/jg7Cgo

cmrzST

https://ibb.co/cmrzST

cqQb7T

https://ibb.co/cqQb7T

So if someone has done something like this before, any hindsight would be very appreciated.
 

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