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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def predict(self, X):
 """ Predictions with the model for all the MCMC samples. Returns posterior means and standard deviations at X. Note that this is different in GPy where the variances are given. """


        if X.ndim==1: X = X[None,:]
        ps = self.model.param_array.copy()
        means = []
        stds = []
        for s in self.hmc_samples:
            if self.model._fixes_ is None:
                self.model[:] = s
            else:
                self.model[self.model._fixes_] = s
            self.model._trigger_params_changed()
            m, v = self.model.predict(X)
            means.append(m)
            stds.append(np.sqrt(np.clip(v, 1e-10, np.inf)))
        self.model.param_array[:] = ps
        self.model._trigger_params_changed()
        return means, stds