《Computational Statistics with Matlab》硬译2
T=;
sigma=;
thetamin=-;thetamax=;
theta=zeros(,T);
seed=;rand('state',seed);randn('state',seed);
theta()=unifrnd(thetamin,thetamax);
t=; while t<T
t=t+;
theta_star=normrnd(theta(t-),sigma);
alpha=min([ cauchy(theta_star)/cauchy(theta(t-))]);
u=rand;
if u<alpha
theta(t)=theta_star;
else
theta(t)=theta(t-);
end
end figure();clf;
subplot(,,);
nbins=;
thetabins=linspace(thetamin,thetamax,nbins);
counts=hist(theta,thetabins);
bar(thetabins,counts/sum(counts),'k');
xlim([thetamin thetamax]);
xlabel('\theta');ylabel('p(\theta)');
y=cauchy(thetabins);
hold on;
plot(thetabins,y/sum(y),'r--','LineWidth',);
set(gca,'YTick',[]);
subplot(,,:);
stairs(theta,:T,'k-');
ylabel('t');xlabel('\theta');
set(gca,'YDir','reverse');
xlim([thetamin thetamax]);
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" alt="" />
function y=bivexp(theta1,theta2)
lambda1=0.5;
lambda2=0.1;
lambda=0.01;
maxval=;
y=exp(-(lambda1+lambda)*theta1-(lambda2+lambda)*theta2-lambda*maxval);
T=;
thetamin=[ ];
thetamax=[ ];
seed=;
rand('state',seed);
randn('state',seed);
theta=zeros(,T);
theta(,)=unifrnd(thetamin(),thetamax());
theta(,)=unifrnd(thetamin(),thetamax()); t=;
while t<T
t=t+;
theta_star=unifrnd(thetamin,thetamax);
pratio=bivexp(theta_star(),theta_star())/bivexp(theta(,t-),theta(,t-));
alpha=min([ pratio]);
u=rand;
if u<alpha
theta(:,t)=theta_star;
else
theta(:,t)=theta(:,t-);
end
end figure();clf;
subplot(,,);
nbins=;
thetabins1=linspace(thetamin(),thetamax(),nbins);
thetabins2=linspace(thetamin(),thetamax(),nbins);
hist3(theta','Edges',{thetabins1 thetabins2});
thetabins1=linspace(thetamin(),thetamax(),nbins); xlabel('\theta_1');ylabel('\theta_2');zlabel('counts');
az=;el=;
view(az,el);
subplot(,,);
nbins=;
thetabins1=linspace(thetamin(),thetamax(),nbins);
thetabins2=linspace(thetamin(),thetamax(),nbins);
[theta1grid,theta2grid]=meshgrid(thetabins1,thetabins2);
ygrid=bivexp(theta1grid,theta2grid);
mesh(theta1grid,theta2grid,ygrid);
xlabel('\theta_1');ylabel('\theta_2');
zlabel('f(\theta_1,\theta_2)');
view(az,el);
function tau=kendalltau(order1,order2)
[dummy,ranking1]=sort(order1(:)',2,'ascend');
[dummy,ranking2]=sort(order2(:)',2,'ascend');
N=length(ranking1);
[ii,jj]=meshgrid(:N,:N);
ok=find(jj(:)>ii(:));
ii=ii(ok);
jj=jj(ok);
nok=length(ok);
sign1=ranking1(jj)>ranking1(ii);
sign2=ranking2(jj)>ranking2(ii);
tau=sum(sign1~=sign2);
lambda = 0.1; % scaling parameter
labels = { 'Washington' , 'Adams' , 'Jefferson' , 'Madison' , 'Monroe' };
omega = [ ]; % correct ordering
L = length( omega ); % number of items in ordering
T = ; % Set the maximum number of iterations
seed=; rand( 'state' , seed ); randn('state',seed ); % set the random seed
theta = zeros( L , T ); % Init storage space for our samples
theta(:,) = randperm( L ); % Random ordering to start with
t = ;
while t < T % Iterate until we have T samples
t = t + ;
lasttheta = theta(:,t-); % Get the last theta
whswap = randperm( L ); whswap = whswap(:);
theta_star= lasttheta;
theta_star( whswap()) = lasttheta( whswap());
theta_star( whswap()) = lasttheta( whswap());
dist1 = kendalltau( theta_star , omega );
dist2 = kendalltau( lasttheta , omega );
pratio = exp(-dist1*lambda) / exp(-dist2*lambda);
alpha = min( [ pratio ] );
u = rand; % Draw a uniform deviate from [ ]
if u < alpha % Do we accept this proposal?
theta(:,t) = theta_star; % proposal becomes new theta
else
theta(:,t) = lasttheta; % copy old theta
end
if mod( t, ) ==
fprintf( 't=%3d\t' , t );
for j=:L
fprintf( '%15s' , labels{ theta(j,t)} );
end
fprintf( '\n' );
end
end
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