function [imfl,imfh,imfl1,imfh1] = demarw(xpo,xprob)
%  [imfl,imfh,imfl1,imfh1] = fn_demarw(xpo,xprob)
%    Demarcate the .68 and .90 error bands given positions and properly scaled probabilities (weights).
%
% xpo:  ndraws-by-n.  Centered position
% xprob:  ndraws-by-n.  Must be properly scaled probabilities corresponding to xpo.
%-----------------
% imfl:  lower .90 bound, n-by-1
% imfh:  higher .90 bound, n-by-1
% imfl1: lower .68 bound, n-by-1
% imfh1: higher .68 bound, n-by-1
%
% August 1999 Tao Zha; Revised, August 2000

[ndraws,n]=size(xpo);

%$$$ .68 and .95 probability bands
imfl = zeros(n,1);     % preallocating
imfh = zeros(n,1);     % preallocating
imfl1 = zeros(n,1);     % preallocating
imfh1 = zeros(n,1);     % preallocating
imfpo = zeros(4,n);    % 4 positions: l,h,l1,h1.
%
%tic
tem = cumsum(xprob);    % cumulative probability
tem = tem .* 100;
%
%@@@ the following operations are valid only because tem are increasing!
for k = 1:n
   %
   %@@@ the following operations are valid only because tem are increasing!
   %** 5% low tail
   if isempty(max(find(tem(:,k)<5)))
      imfl(k) = xpo(1,k);
   else
      imfl(k) = xpo(max(find(tem(:,k)<5)),k);
   end
   %** 16% low tail
   if isempty(max(find(tem(:,k)<16)))
      imfl1(k) = xpo(1,k);
   else
      imfl1(k) = xpo(max(find(tem(:,k)<16)),k);
   end
   %** 2.5% high tail
   imfh(k) = xpo(min(find(tem(:,k)>95)),k);
   %** 16% low tail
   imfh1(k) = xpo(min(find(tem(:,k)>84)),k);
end