Seaborn无Matplotlib添加多行绘图及Metropolis-Hastings代码无输出问题

Hey there! Let's break down why your code isn't producing plots and how to fix it, plus implement multi-line plotting using just Seaborn (no direct Matplotlib plt calls beyond the minimal display trigger, which Seaborn wraps anyway).

First: Finish the Metropolis-Hastings Function #

Your metropolis_hastings function is incomplete—you need to actually implement the sampling logic to generate the data we'll plot. Here's the full, working version:

import numpy as np
import scipy.stats as st
import seaborn as sns
import pandas as pd  # For easier data handling with Seaborn

mus = np.array([5, 5])
sigmas = np.array([[1, .9], [.9, 1]])

def circle(x, y): return (x-1)**2 + (y-2)**2 - 3**2
def pgauss(x, y): return st.multivariate_normal.pdf([x, y], mean=mus, cov=sigmas)

def metropolis_hastings(p, iter=1000):
    # Initialize starting point
    x, y = 0.0, 0.0
    samples = np.zeros((iter, 2))
    
    for i in range(iter):
        # Propose new point using normal distribution
        x_prop, y_prop = np.array([x, y]) + np.random.normal(size=2)
        # Calculate acceptance probability
        current_prob = p(x, y)
        prop_prob = p(x_prop, y_prop)
        accept_prob = min(1, prop_prob / current_prob)
        
        # Accept or reject the proposal
        if np.random.rand() < accept_prob:
            x, y = x_prop, y_prop
        samples[i] = [x, y]
    
    return samples

# Generate 5000 samples (more samples = better plot)
samples = metropolis_hastings(pgauss, iter=5000)

Second: Add Seaborn Plots (With Multi-Line Support) #

The reason you saw no output is you never called any plotting functions. Below are two ways to visualize your samples with multi-line elements, using only Seaborn's APIs:

Option 1: Joint Plot with Trajectory Lines #

This creates a scatter plot of your samples, plus adds trajectory lines for the first 1000 steps and mean reference lines:

# Create a joint plot of the samples
joint_plot = sns.jointplot(x=samples[:, 0], y=samples[:, 1], kind="scatter", alpha=0.3)

# Add x-trajectory line (first 1000 steps)
sns.lineplot(x=np.arange(1000), y=samples[:1000, 0], color="crimson", linewidth=0.8, ax=joint_plot.ax_joint)
# Add y-trajectory line (first 1000 steps)
sns.lineplot(x=np.arange(1000), y=samples[:1000, 1], color="navy", linewidth=0.8, ax=joint_plot.ax_joint)
# Add mean reference lines
sns.lineplot(x=[0, 1000], y=[mus[0], mus[0]], color="limegreen", linestyle="--", ax=joint_plot.ax_joint)
sns.lineplot(x=[mus[1], mus[1]], y=[0, 1000], color="limegreen", linestyle="--", ax=joint_plot.ax_joint)

# Trigger plot display (auto-shows in Jupyter, needed for some local environments)
sns.plt.show()

Option 2: Standalone Multi-Line Trajectory Plot #

If you want a dedicated plot showing how x and y values change over sampling steps:

# Convert samples to a DataFrame for Seaborn compatibility
sample_df = pd.DataFrame(samples[:1000], columns=["X Value", "Y Value"])
sample_df["Sampling Step"] = np.arange(1000)

# Melt the DataFrame to plot both x and y in one line plot
melted_df = sample_df.melt(id_vars="Sampling Step", var_name="Dimension", value_name="Sample Value")

# Create the multi-line plot with Seaborn
line_plot = sns.relplot(
    data=melted_df,
    x="Sampling Step",
    y="Sample Value",
    hue="Dimension",
    kind="line",
    linewidth=0.8
)
line_plot.set_axis_labels("Sampling Step", "Sample Value")
line_plot.fig.suptitle("Metropolis-Hastings Sampling Trajectory", y=1.02)

# Display the plot
sns.plt.show()

Key Notes #

• No plot output fix: You were missing both a completed sampling function and any calls to Seaborn's plotting methods. Once you generate the samples and call a Seaborn plot function, you'll see output.
• Seaborn-only multi-lines: We use Seaborn's lineplot and relplot to add multiple lines—no direct Matplotlib plt.plot() calls needed. The only Matplotlib-related call is sns.plt.show(), which is a Seaborn-wrapped shortcut to trigger display.

内容的提问来源于stack exchange，提问作者Bob