对目标函数target_dist = @(x) x(1).*x(2)-1500用M-H生成 MCMC链的代码

以下是使用 Metropolis-Hastings 算法生成 MCMC 链的 MATLAB 代码，其中目标函数为 $target\_dist(x) = x_1 \cdot x_2 - 1500$：

% Define the target distribution
target_dist = @(x) x(1).*x(2) - 1500;

% Define the proposal distribution (a normal distribution centered at the current sample)
prop_dist = @(x) [normrnd(x(1), 1), normrnd(x(2), 1)];

% Define the initial sample
x0 = [1, 1500];

% Set the number of iterations and burn-in period
n_iter = 10000;
burn_in = 1000;

% Initialize the MCMC chain
chain = zeros(n_iter, 2);
chain(1,:) = x0;

% Run the MCMC algorithm
for i = 2:n_iter
    % Propose a new sample
    x_prop = prop_dist(chain(i-1,:));
    
    % Calculate the acceptance probability
    alpha = min(1, target_dist(x_prop)/target_dist(chain(i-1,:)));
    
    % Accept or reject the proposed sample
    if rand() < alpha
        chain(i,:) = x_prop;
    else
        chain(i,:) = chain(i-1,:);
    end
end

% Remove the burn-in period from the chain
chain = chain((burn_in+1):end,:);

在上述代码中，我们首先定义了目标函数 `target_dist` 和建议分布 `prop_dist`。然后，我们定义了初始样本 `x0`，设置了迭代次数 `n_iter` 和燃烧期 `burn_in`。接着，我们初始化了 MCMC 链 `chain`，并在循环中运行了 M-H 算法。最后，我们从链中删除了燃烧期的样本，并返回得到的 MCMC 链。