options for analyzing simulation results. Looking for suggestions

I have developed a Markov Model and got 100000 simulations for a time period of 57 years. That means my output is 100000 by 57 matrix.

Now I want to use analyze the results of those simulations by using various graphical forms. I have not used MATLAB much before, therefore, I am looking for the suggestions for graphs/plots/figures that can give meaningful visualization of the simulations.

I have used following command which works perfectly for a small number of simulations but the results look clumsy to make any analysis. Any suggestions?

plot(timePeriod,simulations(1,1:end))

Answer 1

[Parag]

To visualize a large set of simulations from a Markov Model like 100000 simulations for 57 years there are several techniques and plots that can help you gain insights from your data.

Here’s a complete MATLAB script that initializes a random dataset and demonstrates various visualization techniques for analyzing the results of 100,000 simulations over 57 years.

% Initialize random data for simulations 
numSimulations = 100000; % 100,000 simulations 
numYears = 57; % 57 time steps 
timePeriod = 1:numYears; % Time axis (1 to 57 years) 
simulations = randn(numSimulations, numYears); % Random normal distributed data

% 1. Plot the mean of all simulations over time 
figure; 
meanSim = mean(simulations, 1); 
plot(timePeriod, meanSim, 'b', 'LineWidth', 2); 
title('Mean of Simulations Over Time'); 
xlabel('Time (Years)'); 
ylabel('Mean Value'); 
grid on; 

% 2. Boxplot for distribution at each time step 
figure; 
boxplot(simulations, 'Labels', string(timePeriod)); 
title('Distribution of Simulations at Each Time Step'); 
xlabel('Time (Years)'); 
ylabel('Simulation Values'); 
set(gca, 'XTickLabelRotation', 45); % Rotate labels for better visibility 

% 3. Heatmap for visualizing the trends 
figure; 
imagesc(simulations); 
colorbar; 
title('Heatmap of Simulations Over Time'); 
xlabel('Time (Years)'); 
ylabel('Simulation Index'); 
set(gca, 'YDir', 'normal'); % Ensures proper orientation 

% 4. Histogram of the final state values (last column) 
figure; 
histogram(simulations(:, end), 50, 'FaceColor', 'g', 'EdgeColor', 'k'); 
title('Distribution of Final State Across Simulations'); 
xlabel('Final State Value'); 
ylabel('Frequency'); 
grid on; 

You can check the documentation of plots in MATLAB for more details on the types of plots in MATLAB.

https://www.mathworks.com/help/matlab/creating_plots/types-of-matlab-plots.html

You can also include waterfall plot as described in one of the MATLAB answers.

https://www.mathworks.com/matlabcentral/answers/1570708-plotting-1d-conditional-distributions-with-kdensity-stacked-in-a-3d-figure#answer_1464776