write the full code for parameter estimation of several parametrs using mcmc in matlab, consider input parameters have uniform prior and take values for example in matlab in matlab

main.m
% Define the log likelihood function you want to estimate
log_likelihood = @(parameters) -0.5 * sum((data - model(parameters)).^2);

% Define the log prior function with uniform prior
log_prior = @(parameters) 0; % Assuming uniform prior

% Define the log posterior function
log_posterior = @(parameters) log_likelihood(parameters) + log_prior(parameters);

% Set the MCMC parameters
n_iter = 10000; % Number of iterations
n_param = 5; % Number of parameters
proposal_width = 0.1; % Proposal width for random walk Metropolis-Hastings

% Initialize the chain
chain = zeros(n_iter, n_param); % Create a matrix to store chain
accepted = zeros(n_iter, 1); % Vector to store acceptance information

% Initialize parameters
params = [1, 2, 3, 4, 5]; % Initial guess

% Run the MCMC algorithm
for i = 1:n_iter
    % Propose new parameters
    proposed_params = params + proposal_width * randn(1, n_param);
    
    % Calculate acceptance probability
    log_alpha = log_posterior(proposed_params) - log_posterior(params);
    
    % Accept or reject the proposal
    if log(rand) < log_alpha
        params = proposed_params;
        accepted(i) = 1; % Proposal accepted
    end
    
    % Store the parameters in the chain
    chain(i, :) = params;
end

% Plot the parameter chain
figure;
for i = 1:n_param
    subplot(n_param, 1, i);
    plot(chain(:, i));
    title(['Parameter ', num2str(i)]);
end
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