PyMC3和Arviz:使用arviz plot_hpd可视化多种条件下的最高后验密度

Question

我正在尝试用最高后验密度(hpd)来可视化多组的简单线性回归。但是，我在为每个条件应用hpd时遇到了一个问题。每当我运行这段代码时，我都会为每个条件提取相同的后验密度。我想要可视化与其条件相对应的后验密度。如何绘制每个组的hpd图？

编辑:问题已在PyMC3 discourse中解决

import pymc3 as pm
import numpy as np
import matplotlib.pyplot as plt
import arviz as az
import pandas as pd

# data

data = pd.read_csv('www_MCMC/MCMC/data.csv')
rsp = data['Mean Response'].values
rt = data['Mean Reaction Time'].values
idx = pd.Categorical(data['Structure'], categories=['No Background', 'Only Road', 'Only Dot Ground', 'Dot Terrain + Dot Ground', 'Space', 'Full Background']).codes
groups = len(np.unique(idx))

# model

with pm.Model() as rsp_rt:
        
    α = pm.Normal('α', mu=0, sd=10, shape=groups)
    β = pm.Normal('β', mu=0, sd=10, shape=groups)
    ϵ = pm.HalfCauchy('ϵ', 10)
    
    μ = pm.Deterministic('μ', α[idx] + β[idx] * rt)
    
    y_pred = pm.Normal('y_pred2', mu=μ, sd=ϵ, observed=rsp)
    
    trace_rsp_rt = pm.sample(cores=1) 
    
_, ax_rsp_rt = plt.subplots(2, 3, figsize=(10, 5), sharex=True, sharey=True, constrained_layout=True)
ax_rsp_rt = np.ravel(ax_rsp_rt)

for i in range(groups):
    
    alpha = trace_rsp_rt['α'][:, i].mean()
    beta = trace_rsp_rt['β'][:, i].mean()
    
    ax_rsp_rt[i].plot(rt, alpha + beta * rt, c='k', label= f'rsp = {alpha:.2f} + {beta:.2f} * rt')
    az.plot_hpd(rt, trace_rsp_rt['μ'], credible_interval=0.98, color='k', ax=ax_rsp_rt[i])
    ax_rsp_rt[i].set_title(f'$\mu_{i}$')
    ax_rsp_rt[i].set_xlabel(f'$x_{i}$')
    ax_rsp_rt[i].set_ylabel(f'$y_{i}$', labelpad=17, rotation=0)
    ax_rsp_rt[i].legend()
    plt.xlim(1.2, 1.8)
    plt.ylim(0.6, 1) 

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Answer 1

我已经在PyMC3 discourse上回答了这个问题，更详细的答案请参考那里。

为了完整性，我在这里也分享了部分答案：

有几个小的代码修改应该可以解决这个问题。但是，我建议使用this notebook中显示的ArviZ和xarray。

...

for i in range(groups):
    
    alpha = trace_rsp_rt['α'][:, i]
    beta = trace_rsp_rt['β'][:, i]
    mu = alpha + beta * rt  
    # there may be broadcasting issues requiring to use rt[None, :]
    # xarray would handle broadcasting automatically ass seen in the notebook
    
    ax_rsp_rt[i].plot(rt, mu.mean(), c='k', label= f'rsp = {alpha:.2f} + {beta:.2f} * rt')
    az.plot_hpd(rt, mu, credible_interval=0.98, color='k', ax=ax_rsp_rt[i])
    ax_rsp_rt[i].legend()
    # combining pyplot and object based commands can yield unexpected results
    ax.set_xlim(1.2, 1.8)  
    ax.set_ylim(0.6, 1)