messv_g3.m

计量工具箱

iter = 1;
in = ones(n,1);
sige = sig0;
V = ones(n,1);

% storage for draws
          bsave = zeros(ndraw-nomit,k);
          asave = zeros(ndraw-nomit,1);
          ssave = zeros(ndraw-nomit,1);
          rsave = zeros(ndraw-nomit,1);
          msave = zeros(ndraw-nomit,1);
          if mm ~= 0
          rdraw = zeros(ndraw-nomit,1);
          else
          rdraw = 0;
          end;
          vmean = zeros(n,1);
	       lsave = 0;
          rtmp = zeros(nomit,1);

hwait = waitbar(0,'MCMC sampling ...');
t0 = clock;                  
iter = 1;
          while (iter <= ndraw); % start sampling;


          
          % lookup Ymat based on alpha, rho, neigh values
          gsize = rmat(2,1) - rmat(1,1);
          i1 = find(rmat <= rho + gsize);
          i2 = find(rmat <= rho - gsize);
          i1 = max(i1);
          i2 = max(i2);
          indexr = round((i1+i2)/2);
          if isempty(indexr)
          indexr = 1;
          end;
          gsize = mmat(2,1) - mmat(1,1);
          i1 = find(mmat <= neigh + gsize);
          i2 = find(mmat <= neigh - gsize);
          i1 = max(i1);
          i2 = max(i2);
          indexm = round((i1+i2)/2);
          if isempty(indexm)
          indexm = 1;
          end;

          Ycap = squeeze(Ymat(:,:,indexr,indexm));
          Ycaps = matmul(Ycap,sqrt(V));
          % create Sy based on Y
          [junk nq] = size(Ycap);
          nq1 = nq-1;
          v = ones(nq,1);
          for i=2:nq;
          v(i,1) = alpha.^(i-1);
          end;
          W = (1./[1 cumprod(1:nq1)]);
          Sy = Ycap*diag(W)*v;
          Sys = Ycaps*diag(W)*v;
          xs = matmul(x,sqrt(V)); 

          % update beta   
          AI = inv(xs'*xs + sige*TI);
          b = x'*Sys + sige*TIc;
          b0 = AI*b;
          bhat = norm_rnd(sige*AI) + b0;  
         
          % update sige
          nu1 = n + 2*nu; 
          e = (Sys - xs*bhat);
          d1 = 2*d0 + e'*e;
          chi = chis_rnd(1,nu1);
          sige = d1/chi;

          % update vi
          e = Sy - x*bhat;
          chiv = chis_rnd(n,rval+1);   
          vi = ((e.*e./sige) + in*rval)./chiv;
          V = in./vi; 
  
          % update rval
          if mm ~= 0           
          rval = gamm_rnd(1,1,mm,kk);  
          end;
                       
          % metropolis step to get alpha update
          if pflag == 0
          alphax = cn_mess3(alpha,y,x,Ymat,bhat,sige,rho,neigh,rmat,mmat); 
          elseif pflag == 1
          alphax = cn_mess3(alpha,y,x,Ymat,bhat,sige,rho,neigh,rmat,mmat,palpha,S); 
          end;
          
          accept = 0; 
          alpha2 = alpha + cc*randn(1,1);
          while accept == 0 
           if (alpha2 <= 0)
           accept = 1;  
           else
           alpha2 = alpha + cc*randn(1,1);
           cnta = cnta+1; % counts accept rate for alpha
           end; 
          end; 
          if pflag == 0
           alphay = cn_mess3(alpha2,y,x,Ymat,bhat,sige,rho,neigh,rmat,mmat);
          elseif pflag == 1
           alphay = cn_mess3(alpha2,y,x,Ymat,bhat,sige,rho,neigh,rmat,mmat,palpha,S);
          end;
    
          ru = unif_rnd(1,0,1);
          if ((alphay - alphax) > exp(1)),
          p = 1;
          else,          
          ratio = exp(alphay-alphax);
          p = min(1,ratio);
          end;
              if (ru < p)
                 alpha = alpha2;
              end;

          rtmp(iter,1) = alpha;

          % update rho using metroplis-hastings step
          rhox = rn_mess3(rho,y,x,Ymat,bhat,alpha,neigh,rmat,mmat); 
          rho2 = unif_rnd(1,rmin,rmax);

          rhoy = rn_mess3(rho2,y,x,Ymat,bhat,alpha,neigh,rmat,mmat);
           ru = unif_rnd(1,0,1);
          if ((rhoy - rhox) > exp(1)),
          p = 1;
          else,          
          ratio = exp(rhoy-rhox);
          p = min(1,ratio);
          end;
              if (ru < p)
                 rho = rho2;
              end;

          % update neigh using metroplis-hastings step
          neighx = nn_mess3(neigh,y,x,Ymat,bhat,alpha,rho,rmat,mmat); 
          neigh2 = round(unif_rnd(1,mmin,mmax));

          neighy = nn_mess3(neigh2,y,x,Ymat,bhat,alpha,rho,rmat,mmat);
           ru = unif_rnd(1,0,1);
          if ((neighy - neighx) > exp(1)),
          p = 1;
          else,          
          ratio = exp(neighy-neighx);
          p = min(1,ratio);
          end;
              if (ru < p)
                 neigh = neigh2;
              end;
	  
     % evaulate the likelihood using current draws
     if lflag == 0
                like = -(n/2)*log(2*pi*sige) - (e'*e)/(2*sige);
     end;
                       
     % update rval
     if mm ~= 0           
     rval = gamm_rnd(1,1,mm,kk);  
     end;
              
    if iter > nomit % if we are past burn-in, save the draws
    bsave(iter-nomit,:) = bhat';
    ssave(iter-nomit,1) = sige;
    asave(iter-nomit,1) = alpha; 
    rsave(iter-nomit,1) = rho;
    msave(iter-nomit,1) = neigh;
    vmean = vmean + vi;
    if mm~= 0
    rdraw(iter-nomit) = rval;
    end;

     if lflag == 0
       lsave = lsave + like;
     else
       lsave = lsave + 0;
     end;
    end;
                    
    if iter == nomit % update cc based on initial draws
         tst = 2*std(rtmp(1:nomit,1));
         if tst > 0.05
         cc = tst;
         end;
    end;

iter = iter + 1; 
waitbar(iter/ndraw);         
end; % end of sampling loop
close(hwait);

stime = etime(clock,t0);

% compute posterior means
if lflag == 0
lmean = lsave/(ndraw-nomit);
else 
   lmean = 0;
end;
vmean = vmean/(iter-nomit);
amean = mean(asave);
bmean = mean(bsave);
astd = std(asave);
bstd = std(bsave);
smean = mean(ssave);
rmean = mean(rsave);
rstd = std(rsave);
mmean = mean(msave);
mstd = std(msave);

% find acceptance rate
results.accept = 1 - cnta/(iter+cnta);
% NOTE: this could be interpreted as the
% probability that alpha is in the mesh grid

% compute Sy based on posterior means for rho, neigh, alpha
mround = round(mmean);
tmp = rmean.^(0:mround-1);
tmp = tmp/sum(tmp);

% find index into nearest neighbors
nnlist = nnlistall(:,1:mround);

wy = y;
Y = y(:,ones(1,q));
for i=2:q;
wy = wy(nnlist)*tmp';
Y(:,i) = wy;
end;
Ys = matmul(Y,sqrt(vmean));

[junk nq] = size(Y);
nq1 = nq-1;
v = ones(nq,1);
for i=2:nq;
v(i,1) = amean.^(i-1);
end;
W = (1./[1 cumprod(1:nq1)]);
sy = Y*diag(W)*v;
sys = Ys*diag(W)*v;

e = sy - x*bmean';
yhat = y - e;

sigu = e'*e;
ym = y - mean(y);
rsqr1 = sigu;
rsqr2 = ym'*ym;
rsqr = 1.0 - rsqr1/rsqr2; % r-squared
rsqr1 = rsqr1/(n-k);
rsqr2 = rsqr2/(n-1.0);
rbar = 1 - (rsqr1/rsqr2); % rbar-squared

time = etime(clock,timet);

results.meth  = 'messv_g3';
results.bdraw = bsave;
results.rdraw = rsave;
results.adraw = asave;
results.bmean = bmean';
results.bstd  = bstd';
results.amean = amean;
results.astd  = astd;
results.smean = smean;
results.sdraw = ssave;
results.rmean = rmean;
results.rstd  = rstd;
results.rdraw = rsave;
results.mmean = mmean;
results.mstd  = mstd;
results.mdraw = msave;
results.lmean = lmean;
results.vmean = vmean;
results.rvdraw = rdraw;
results.bprior = c;
results.bpstd  = sqrt(diag(T));
results.nobs  = n;
results.nvar  = k;
results.ndraw = ndraw;
results.nomit = nomit;
results.time  = time;
results.stime = stime;
results.ntime = gtime;
results.nu = nu;
results.d0 = d0;
if mm~= 0
results.m = m;
results.k = k;
else
results.rval = rval;
end;
results.tflag = 'plevel';
results.pflag = pflag;
results.palpha = palpha;
results.acov = S;
results.y = y;
results.yhat = yhat;
results.resid = e;
results.rsqr = rsqr;
results.rbar = rbar;
results.neigh = neigh;
results.q     = q;
results.nobs = n;
results.nvar = k;
results.xflag = xflag;
results.nflag = nflag;

case{1} % case of x-variables transformed
   
   xone = x(:,1);
   if all(xone == 1)
      xsub = x(:,2:k);
   else
      xsub = x;
   end;

results.rmin = rmin;
results.rmax = rmax;
results.mmin = mmin;
results.mmax = mmax;

rgrid = rmin:0.01:rmax;
mgrid = mmin:1:mmax;
nrho = length(rgrid);
nneigh = length(mgrid);

t1 = clock;   % time this operation

% storage for Y,X over the grid
Ymat = zeros(n,q,nrho,nneigh); % vectors of Sy for various alpha,rho,neigh values
Xmat = zeros(n,2*k-1,nrho,nneigh); % matrices of Sx for various alpha,rho,neigh values
rmat = zeros(nrho,1);   % save rho values
mmat = zeros(nneigh,1); % save neigh values

% we have to construct the weight matrix using neighbors
if nflag == 0
nnlistall = find_nn(latt,long,mmax);
elseif nflag == 1
nnlistall = find_nn(latt,long,mmax,3);
else
error('messv_g3: bad nflag option');
end;

% check for empty nnlist columns
chk = find(nnlistall == 0);
if length(chk) > 0; 
 if nflag == 1 % no saving the user here
 error('messv_g3: trying too many neighbors, some do not exist');
 else % we save the user here
 nnlistall = find_nn(latt,long,mmax,4);
 end;
end;

% do grid over rho, neigh values
hwait = waitbar(0,'computing grid over rho and neighbors ...');
ngrid = nneigh*nrho;
iter = 1;

for kk=1:nneigh;
neigh = mgrid(kk);
nnlist = nnlistall(:,1:neigh);
for jj=1:nrho;
rho = rgrid(jj);

tmp = rho.^(0:neigh-1);
tmp = tmp/sum(tmp);

% construct and save Y
wy = y;
Y = y(:,ones(1,q));
for i=2:q;
wy = wy(nnlist)*tmp';
Y(:,i) = wy;
end;

Ymat(:,:,jj,kk) = Y;
% create and save X
[junk nk] = size(xsub);
xout = x;
for i=1:nk;
xi = xsub(:,i);
tmpp = xi(nnlist)*tmp';
xout = [xout tmpp];
end;
Xmat(:,:,jj,kk) = xout;
% save rho
rmat(jj,1) = rho;

end; % end of loop over rho values 
mmat(kk,1) = neigh;
iter = iter + nrho; 
waitbar(iter/ngrid);         

end; % end of loop over neighbors

close(hwait);

% end of up front stuff with Sy saved in Symat
gtime = etime(clock,t1);

% ====== initializations
% compute this stuff once to save time
[junk kk] = size([x xsub]); % need to add diffuse priors 
                          % to the spatial lags of x-variables
Tnew = eye(kk)*1e+12;
Tnew(1:k,1:k) = T;
TI = inv(Tnew);
tmp = zeros(kk,1);
tmp(1:k,1) = c;
c = tmp;
TIc = TI*c;
cc=0.2; % initial metropolis value
cntr = 0; 
iter = 1;
alpha = astart;
rho = 1;
in = ones(n,1);
sige = sig0;
V = ones(n,1);

% storage for draws
          bsave = zeros(ndraw-nomit,kk);
          asave = zeros(ndraw-nomit,1);
          ssave = zeros(ndraw-nomit,1);
          rsave = zeros(ndraw-nomit,1);
          msave = zeros(ndraw-nomit,1);
          if mm ~= 0
          rdraw = zeros(ndraw-nomit,1);
          else
          rdraw = 0;
          end;

          vmean = zeros(n,1);
	       lsave = 0;
          rtmp = zeros(nomit,1);

hwait = waitbar(0,'MCMC sampling ...');
t0 = clock;                  
iter = 1;
          while (iter <= ndraw); % start sampling;

          % lookup Sx based on rho values
          gsize = rmat(2,1) - rmat(1,1);
          i1 = find(rmat <= rho + gsize);
          i2 = find(rmat <= rho - gsize);
          i1 = max(i1);
          i2 = max(i2);
          indexr = round((i1+i2)/2);
          if isempty(indexr)
          indexr = 1;
          end;
          gsize = mmat(2,1) - mmat(1,1);
          i1 = find(mmat <= neigh + gsize);
          i2 = find(mmat <= neigh - gsize);
          i1 = max(i1);
          i2 = max(i2);
          indexm = round((i1+i2)/2);
          if isempty(indexm)
          indexm = 1;
          end;

          Ycap = squeeze(Ymat(:,:,indexr,indexm));
          Ycaps = matmul(Ycap,sqrt(V));

          Xcap= squeeze(Xmat(:,:,indexr,indexm));
          Xcaps = matmul(Xcap,sqrt(V));

          % construct Sy based on look up values
          [junk nq] = size(Ycap);
          nq1 = nq-1;
          v = ones(nq,1);
          for i=2:nq;