How to estimate 95% probability contour in bivariate kernel density function MATLAB

Hello:

I have fitted bivariate kernel density function using ksdensity in MATLAB and obtained contour as the method described here: https://stackoverflow.com/questions/44398251/matlab-contour-data-for-2d-normal-cumulative-probability-density

I want to show the area encompassed 95% probability field and related contour for the bivariate density field. I am looking for some thing like this as implemented in R : https://stackoverflow.com/questions/23437000/how-to-plot-a-contour-line-showing-where-95-of-values-fall-within-in-r-and-in

Does MATLAB has such facility to show 95% contours for the joint probability fields?

Answer 1

[Bruno Luong]

I'm not sure if there is a standard definition of area of 95 confidence in 2D pdf since it like asking what if the shape of 95% of the cake, one can cut in many way provide the remaning is 95%.

Assuming one cut on a level of pdf, here is one way

% Invent some fake 2D pdf
pdf=abs(peaks(100));
pdf=pdf-min(pdf,[],'all');

maxp = max(pdf,[],'all');
minp = 0;
smin = 1;
smax = 0;
spdf = sum(pdf,'all');
starget = 0.95;
sold = NaN;
while true
    l = (minp+maxp)/2;
    i = find(pdf >= l);
    s = sum(pdf(i)) / spdf
    if s > starget
        minp = l;
    else
        maxp = l;
    end
    if s==sold || ... % stuck due to quantification of pixels
       abs(smax-smin) < 0.001
        break
    end
    sold = s;
end

s = 0.3217

s = 0.6847

s = 0.8667

s = 0.9439

s = 0.9769

s = 0.9607

s = 0.9525

s = 0.9488

s = 0.9504

s = 0.9494

s = 0.9498

s = 0.9501

s = 0.9500

s = 0.9499

s = 0.9500

s = 0.9500

close all
figure;
surf(pdf+10)
hold on
contourf(pdf,[l l])

Note that estimation of the integration

    %i = find(pdf >= l);
    %s = sum(pdf(i)) / spdf

is very crude. One can do much better but a it cumbersome to implement more precise integration.