How can I add confidence bounds to the plot?

Hello guys,

I need to add confidence bounds to the plots. As can be seen, plot show a comparison between two climate models and observations.(Time serie).My question is that how can I add confidence bounds to the plot? I have added the figure plus mat file shows models and observation yearly data. I plot it with the code below:

please help me.

figure;
hold('on');
plot(w_mash_yearly.Time,w_mash_yearly.MI_obs,'b-o','LineWidth',1)
plot(w_mash_yearly.Time,w_mash_yearly.MI_obs-detrend(w_mash_yearly.MI_obs),'b--')
hold on
plot(w_mash_yearly.Time,w_mash_yearly.MI_alaro,'r-o','LineWidth',1)
plot(w_mash_yearly.Time,w_mash_yearly.MI_alaro-detrend(w_mash_yearly.MI_alaro),'r--')
hold on
plot(w_mash_yearly.Time,w_mash_yearly.MI_remo,'m-o','LineWidth',1)
plot(w_mash_yearly.Time,w_mash_yearly.MI_remo-detrend(w_mash_yearly.MI_remo),'k--')
grid on
ylabel({'moisture Index'},'FontSize',20)
%legend({'Observation','Observation','ALARO-0','ALARO-0', 'REMO','REMO'},'FontSize',18)
title({' Mashhad '},'FontSize',20)
ax = gca;
ax.XAxis.FontSize = 20;
ax.YAxis.FontSize = 18;

[Walter Roberson]

Have you looked at boxplot() ?

[Hamed Hedayatnia]

I need to show it in annual time series.

[Walter Roberson]

It is not obvious to me that adding confidence intervals would help at all in establishing that.

[Hamed Hedayatnia]

My issue is that one of reviewers asked to add it in my plots.

[Hamed Hedayatnia]

He mentioned: In the figures showing the linear trend lines (Figures 2, 6, 10, 13, 14) it would be correct to add the corresponding confidence bounds.

[Walter Roberson]

Confidence intervals only make sense if you have a model with parameters and you want to describe the confidence in the parameter values. But in what you posted, you have no obvious model: you only appear to have observations, and for observations you do not calculate confidence intervals: you calculate quantiles.

[Hamed Hedayatnia]

No Walter. Actually, I have compared 2 climate model with the observations. ALARO-0 and REMO are climate models.

[Walter Roberson]

Assuming that those models estimate parameters, and that MI_alaro and MI_remo are values based upon their predictions, then you need to go back to the models and find the parameters being estimated and the certainty on the parameters, and have it re-run the value estimations based upon the 2-sigma variations in the possible values, and display those predictions as well. If multiple parameters are being estimated, then you might need to run a number of different predictions... e.g., first parameter being 2 standard deviations up, second and third parameter being 2 standard deviations down, and so on (assuming that the estimates are independent.)

Answer 1

[Scott MacKenzie]

Seems you are working with a linear model.

Also, your attached plot is quite cluttered. It will get worse if you add confidence intervals. I suggest you do a separate analysis and plot for each data set.

Adding confidence intervals is easy using polyfit. Here's a solution using the Year vs. MI_obs data:

load('test.mat'); % w_mashhad_yearly data

% data for Year vs. MI_obs
x = w_mash_yearly.Time.Year;
y = w_mash_yearly.MI_obs;

% build linear model with confidence intervals
[p, S] = polyfit(x, y, 1)
[y_fit, delta] = polyval(p, x, S);

plot(x,y,'b-o','LineWidth',1);
hold on;
plot(x,y_fit);
plot(x,y_fit+2*delta,'m--',x,y_fit-2*delta,'m--');
legend('MI\_obs','Linear Fit','95% Prediction Interval');
xlabel('Year');
ylabel('Moisture Index');