human
$\mu$の事前分布に無情報事前分布を仮定する。
 ... Can you provide a the Python program you requested?
assistant
#Here is the Python program you requested.
class RWMH:
    def __init__(self, X):
        self.mu = 5
        self.x_var = np.mean(X)
        
    def prior_dist(self, t):
        ft = np.random.normal(0, 10000)
        return ft
        
    def prop_dist(self):
        self.mu = np.random.normal(self.mu, 0.001)
        return self.mu
    
    def accept(self, mu_new, mu):
        return min([1, self.prior_dist(mu_new)/self.prior_dist(mu)])
    
    def simulate(self):
        mu = np.zeros(11000)
        mu[0] = self.mu
        for i in range(1,11000):
            mu_new = self.prop_dist()
            u = np.random.uniform()
            if u <= self.accept(mu_new, mu[i-1]):
                mu[i] = mu_new
            else:
                mu[i] = mu[i-1]
            self.mu = mu[i] 
        return mu

rwmh = RWMH(X)

mu = rwmh.simulate()

plt.plot(mu)

plt.hist(mu)

plt.hist(mu[1000:])