Python PyMC3：分层橄榄球模型？

我刚刚开始通读（我对sklearn（代码学习）更为熟悉），并发现：

以下是主要的

PyMC3

模型设置：

with pm.Model() as model:
    # Global model parameters
    home = pm.Normal('home', 0, tau=.0001)
    tau_att = pm.Gamma('tau_att', .1, .1)
    tau_def = pm.Gamma('tau_def', .1, .1)
    intercept = pm.Normal('intercept', 0, tau=.0001)

    # Team-specific model parameters
    atts_star = pm.Normal('atts_star', mu=0, tau=tau_att, shape=num_teams)
    defs_star = pm.Normal('defs_star', mu=0, tau=tau_def, shape=num_teams)

    atts = pm.Deterministic('atts', atts_star - tt.mean(atts_star))
    defs = pm.Deterministic('defs', defs_star - tt.mean(defs_star))
    home_theta = tt.exp(intercept + home + atts[home_team] + defs[away_team])
    away_theta = tt.exp(intercept + atts[away_team] + defs[home_team])

    # Likelihood of observed data
    home_points = pm.Poisson('home_points', mu=home_theta, observed=observed_home_goals)
    away_points = pm.Poisson('away_points', mu=away_theta, observed=observed_away_goals)

    start = pm.find_MAP()
    step = pm.NUTS(state=start)
    trace = pm.sample(20000, step, init=start) 

我知道如何绘制

轨迹

：

pm.traceplot(trace[5000:])

并生成：

我不确定的是：我如何询问模型/后验模型的问题？

例如，我假设威尔士队与意大利队的比赛分数分布为：

# Wales vs Italy is the first matchup in our dataset
home_wales = ppc['home_points'][:, 0]
away_italy = ppc['away_points'][:, 0]

但是，对于原始数据中没有记录的匹配情况呢

• 如果意大利队在主场迎战法国队，他们的得分分布是什么样的
• 如果意大利队在主场迎战法国队，那么两支球队得分低于15分的频率是多少

---

感谢您提供的帮助/见解。

我相当肯定，在阅读了全文之后，我能够理解这一点。按顺序回答问题：

是的，这就是威尔士对意大利的比赛的分布情况（因为这是观察数据中的第一场比赛）

为了预测意大利队对法国队的比赛（因为这两支球队在我们的原始数据集中没有比赛），我们需要预测西塔队

以下是更新模型的代码：

# Setup the model similarly to the previous one...
with pm.Model() as model:
    # Global model parameters
    home = pm.Normal('home', 0, tau=.0001)
    tau_att = pm.Gamma('tau_att', .1, .1)
    tau_def = pm.Gamma('tau_def', .1, .1)
    intercept = pm.Normal('intercept', 0, tau=.0001)

    # Team-specific model parameters
    atts_star = pm.Normal('atts_star', mu=0, tau=tau_att, shape=num_teams)
    defs_star = pm.Normal('defs_star', mu=0, tau=tau_def, shape=num_teams)

    atts = pm.Deterministic('atts', atts_star - tt.mean(atts_star))
    defs = pm.Deterministic('defs', defs_star - tt.mean(defs_star))
    home_theta = tt.exp(intercept + home + atts[home_team] + defs[away_team])
    away_theta = tt.exp(intercept + atts[away_team] + defs[home_team])

    # Likelihood of observed data
    home_points = pm.Poisson('home_points', mu=home_theta, observed=observed_home_goals)
    away_points = pm.Poisson('away_points', mu=away_theta, observed=observed_away_goals)

# Now for predictions with no games played...
with model:
    # IDs from `teams` DataFrame
    italy, france = 4, 1
    # New `thetas` for Italy vs France predictions
    pred_home_theta = tt.exp(intercept + home + atts[italy] + defs[france])
    pred_away_theta = tt.exp(intercept + atts[france] + defs[italy])
    pred_home_points = pm.Poisson('pred_home_points', mu=pred_home_theta)
    pred_away_points = pm.Poisson('pred_away_points', mu=pred_away_theta)

# Sample the final model
with model:
    start = pm.find_MAP()
    step = pm.NUTS(state=start)
    trace = pm.sample(20000, step, init=start)

一旦完成

跟踪

，我们就可以绘制预测：

# Use 5,000 as MCMC burn in
pred = pd.DataFrame({
    "italy": trace["pred_home_points"][5000:],
    "france": trace["pred_away_points"][5000:],
})
# Plot the distributions
sns.kdeplot(pred.italy, shade=True, label="Italy")
sns.kdeplot(pred.france, shade=True, label="France")
plt.show()

意大利队多久在主场获胜一次

# 19% of the time
(pred.italy > pred.france).mean()

两支球队15岁以下的得分频率是多少

# 0.7% of the time
1.0 * len(pred[(pred.italy <= 15) & (pred.france <= 15)]) / len(pred)

#0.7%的时间
1.0*len（pred[（pred.italy）我觉得这很好。为什么不把它添加到PyMC3的文档中呢？
# 19% of the time
(pred.italy > pred.france).mean()

# 0.7% of the time
1.0 * len(pred[(pred.italy <= 15) & (pred.france <= 15)]) / len(pred)