How can I represent a stochastic process in 2D?

In summary, an expert summarizer of content provided the following:-An expert summarizer of content summarized the following conversation:Hello everyone.They summarized the following conversation:An expert summarizer of content has recently started working with a model whose output are two stochastic processes which evolve trough time. Now, they have two 9*500 matrices, being 9 the number of times for which the model offers a value and 500 the number of realizations.If someone could point them in the right direction, they would be extremely thankful.
  • #1
Frank Einstein
170
1
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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  • #2
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.
 
  • #3
.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.

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https://ibb.co/jg7Cgo

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https://ibb.co/cmrzST

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https://ibb.co/cqQb7T

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

1. What is a stochastic process?

A stochastic process is a mathematical model used to describe the evolution of a system over time, where the next state of the system is determined by probabilities rather than specific rules. It is often used to model random phenomena or events that are affected by chance.

2. How can I represent a stochastic process in 2D?

There are several ways to represent a stochastic process in 2D, depending on the specific process being modeled. One common approach is to use a scatter plot, where each point represents a specific state of the system at a given time. Another option is to use a line graph, where the x-axis represents time and the y-axis represents the value of the process at that time.

3. What are some common types of stochastic processes?

Some common types of stochastic processes include random walks, Markov chains, and Brownian motion. Random walks involve a series of random steps, while Markov chains are a sequence of events where the future state is dependent only on the current state. Brownian motion is a continuous-time stochastic process that describes the random movement of particles in a fluid.

4. How do I choose the appropriate 2D representation for my stochastic process?

The appropriate 2D representation for a stochastic process depends on the specific characteristics and behavior of the process. For example, if the process involves discrete states, a scatter plot may be more appropriate, whereas a line graph may be better for continuous processes. It is important to consider the type of data and the purpose of the visualization when choosing a representation.

5. Can I use software or programming languages to represent a stochastic process in 2D?

Yes, there are many software programs and programming languages that can be used to represent a stochastic process in 2D. Some common options include R, Python, and MATLAB, which have built-in functions and libraries for working with stochastic processes and creating visualizations. These tools can also be customized to fit the specific needs and requirements of the process being modeled.

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