Python贝叶斯分层模型专题|对环境健康、医学心梗患者、体育赛事数据空间异质性实证分析合集|附数据代码

# 数据清洗与整合
import pandas as pd

mn\_samples = raw\_data\[raw_data\['state'\] == 'MN'\].copy()
mn\_samples.columns = mn\_samples.columns.str.strip()
# 地理编码匹配
county\_info = pd.read\_csv("data/cty.dat")
mn\_county = county\_info\[county_info\['st'\] == 'MN'\].copy()
mn\_county\['geo\_code'\] = 1000 * mn\_county\['stfips'\] + mn\_county\['ctfips'\]
# 特征工程
mn\_samples = mn\_samples.merge(mn\_county\[\['geo\_code', 'Uppm'\]\], on='geo_code')
mn\_samples = mn\_samples.drop_duplicates(subset='idnum')
mn\_samples\['log\_radon'\] = np.log(mn_samples\['activity'\] + 0.1)

with pm.Model(coords=coords) as hierarchical_model:
 # 测量位置编码
 floor\_type = pm.MutableData("floor\_type", mn_samples\['floor'\].values)
 
# 超先验分布
 global\_intercept = pm.Normal("global\_intercept", mu=0, sigma=10)

# 县水平参数
 county\_intercept = pm.Normal("county\_intercept", 
m

# 误差项
 error\_std = pm.Exponential("error\_std", 1)

# 线性预测器
 predicted = county\_intercept\[mn\_samples\['county_code'\]\] + \
 county\_slope\[mn\_samples\['county\_code'\]\] * floor\_type
 
# 似然函数
 pm.Normal("obs\_likelihood", mu=predicted, sigma=error\_std, 
observed=mn\_samples\['log\_radon'\])

\\hat{\\alpha}\_j = \\frac{\\frac{n\_j}{\\sigma\_y^2} \\bar{y}\_j + \\frac{1}{\\sigma_\\alpha^2} \\bar{y}}{\\frac{n\_j}{\\sigma\_y^2} + \\frac{1}{\\sigma_\\alpha^2}}

posterior_means = trace.posterior.mean(dim=('chain', 'draw'))
high\_risk\_counties = posterior\_means.sortby('county\_intercept', ascending=False)

# 模型诊断示例
az.plot\_trace(trace, var\_names=\['global\_intercept', 'global\_slope'\])
az.plot\_forest(trace, var\_names=\['county_intercept'\], combined=True)

with pm.Model(coords=coords) as hierarchical_model:
 # 引入潜在变量
 z\_intercept = pm.Normal("z\_intercept", mu=0, sigma=1, dims='county')
 z\_slope = pm.Normal("z\_slope", mu=0, sigma=1, dims='county')
 
# 参数转换
 county\_intercept = global\_intercept + z\_intercept * intercept\_std
 county\_slope = global\_slope + z\_slope * slope\_std
 
# 其余结构保持不变

with pm.Modelcoord=coods) as hierarchical_model:
 # 县级协变量处理
 county\_uranium = np.lomn\_data\['ppm'\].values)
 
# 超先验分布
 gamma0 = pm.Normal("gama0mu=0, sigma=10)

# 协变量效应
 intercept\_mean = gamma0 + gamma1 * county\_uranium
 
# 县水平参数
 county\_ntecept pm.Norml("county\_itercept", 
mu=iercept_mean,, 
dims='couty')
 
# 其余结构保持不变

with pmMol() apm.Beta('death_ates, alpha2, be=2, shape=13)
 pm.Binomial('death\_bs, n=case\_counts, =deathates, or=deah_counts)

with pm.Mdel('death\_obs', n=sumase\_counts) p=death_rate, 
observed=m(death_couns))

with pmModel() as hierarcial_model:
 hyper\_alpha = pmGamm('yper\_pha, alpha4, beta=0.5)
 hyper\_bta  pm.Gamma('hyper\_beta', apha=4 beta=0.5)
 
hospita\_rtes = pm.eta(hosptalrats', hype\_alphahype_beta, shape=13)
 pm.Binomial('death\_obs', n=cse\_unts, =hospitarates, obsrv=death_counts)

with pm.Moel() as hierachical_model:
 z = pm.Normal('mu0, sigma=1, hape=13)
 hospital_rates = m.Beta(ospi.transforms.logit)

with pm.Modl() ex.Gamma'er_beta', alpha=4, beta=0.5)

rate\_mean = hypemath.sqr(rate\_merates', mu=rate_mean, 
sigma=rate_st

with pm.odel(indiviual'scorin_rate',alpha=, eta=1, shape=18)
 pm.Poisson'al\_o', mu=corin\_raobseved=gals_data)

with pm.Model() as poled_model:
 scoring\_rate = pm.Gamm(soringrat',ha=1, bum(goals\_data))

with pm.Model() as ierchical_model:
 hyper_alpha = pm.Exponenl('hypbeta', lam=1)

team\_rate = pm.amma'teamraamrae, bservd=gols\_data)

with pm.Mdel() as herhica_model:
 z = pm.Nrmal('z', mu=, sigma=1, shae=18)
 team\_rate = pm.mm('tem\_ate', hyper\_alpha, hyper\_beta, 
shape=18, transfrm=m.disrbions..log)

with pm.Model() aoenal(
rate\_mean = hper\_alpha / hye\_mean / hyper\_beta)
 em\_rate', mu=rate\_mean,
sigma=rate\_std * (1 + 0.2*ofensive\_stats), shape=18)