Calculating different levels of confidence and drawing the corresponding graph

I have monthly results of a natural process, obtained from 32 numerical models.

They show monthly rate of a process. How can I calculate different level of confidence (e.g., 10 %, 20%, 50%, 95%) for each months and draw a graph showing the mean of results and level of confidence for each bound.

Cheers,

Amin

[amin zarif]

Pls see the results in the attched figure.

Answer 1

[Aashray]

Hi @amin zarif,

For calculating and visualizing the confidence intervals in a plot, you can do the following:

1. Calculate the mean of all 32 models for each month using “mean()” function.
2. Compute confidence intervals (90%, 80%, and 50%) using percentiles “prctile()” function.
3. Plot shaded bands to represent the confidence intervals using “fill()” function.

This is how I implemented the above steps, you can see different confidence intervals shaded in different shades of blue in the plot:

% Using example data: 32 models × 12 months
rng(1);
data = randn(32, 12) * 2e4 + linspace(1e5, 2.5e5, 12);

meanVals = mean(data, 1);
ci_90 = prctile(data, [5 95], 1);
ci_80 = prctile(data, [10 90], 1);
ci_50 = prctile(data, [25 75], 1);

months = 1:12;
figure; hold on;

% Confidence bands (shaded areas)
fill([months fliplr(months)], [ci_90(1,:) fliplr(ci_90(2,:))], [0.8 0.8 1], 'EdgeColor', 'none');
fill([months fliplr(months)], [ci_80(1,:) fliplr(ci_80(2,:))], [0.6 0.6 1], 'EdgeColor', 'none');
fill([months fliplr(months)], [ci_50(1,:) fliplr(ci_50(2,:))], [0.3 0.3 1], 'EdgeColor', 'none');

% Plot each model line in a different color
colors = lines(32);
colors = [colors ones(32,1)*0.69];
for i = 1:32
    plot(months, data(i,:), '-', 'Color', colors(i,:), 'LineWidth', 1);
end

% Plot mean line
plot(months, meanVals, 'k-', 'LineWidth', 2);

% Axes and labels
xticks(1:12);
xticklabels({'Jan','Feb','Mar','Apr','May','Jun','Jul','Aug','Sep','Oct','Nov','Dec'});
ylabel('Rate (m^3)');
title('Mean & Confidence Intervals from 32 Model Simulations');
legend({'90% CI', '80% CI', '50% CI', 'Models', 'Mean'}, 'Location', 'northwest');
grid on;                                 

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I am also attaching the documentation links of the functions used for your reference:

1. “prctile()”: https://www.mathworks.com/help/matlab/ref/prctile.html
2. “fill()”: https://www.mathworks.com/help/matlab/ref/fill.html