Python 用pymc3计算具有多重似然函数模型的WAIC

我尝试根据进球数预测足球比赛的结果，并使用以下模型：

with pm.Model() as model:
  # global model parameters
   h = pm.Normal('h', mu = mu, tau = tau)
   sd_a = pm.Gamma('sd_a', .1, .1) 
   sd_d = pm.Gamma('sd_d', .1, .1) 
   alpha = pm.Normal('alpha', mu=mu, tau = tau)

  # team-specific model parameters
   a_s = pm.Normal("a_s", mu=0, sd=sd_a, shape=n)
   d_s = pm.Normal("d_s", mu=0, sd=sd_d, shape=n)

   atts = pm.Deterministic('atts', a_s - tt.mean(a_s))
   defs = pm.Deterministic('defs', d_s - tt.mean(d_s))
   h_theta = tt.exp(alpha + h + atts[h_t] + defs[a_t])
   a_theta = tt.exp(alpha + atts[a_t] + defs[h_t])

  # likelihood of observed data
   h_goals = pm.Poisson('h_goals', mu=h_theta, observed=observed_h_goals)
   a_goals = pm.Poisson('a_goals', mu=a_theta, observed=observed_a_goals)

当我对模型进行采样时，跟踪图看起来很好

之后，当我要计算WAIC时：

waic=pm.waic（跟踪，模型）

我得到以下错误：

----> 1 waic = pm.waic(trace, model)

~\Anaconda3\envs\env\lib\site-packages\pymc3\stats_init_.py in wrapped(*args, **kwargs)
22 )
23 kwargs[new] = kwargs.pop(old)
—> 24 return func(*args, **kwargs)
25
26 return wrapped

~\Anaconda3\envs\env\lib\site-packages\arviz\stats\stats.py in waic(data, pointwise, scale)
1176 “”"
1177 inference_data = convert_to_inference_data(data)
-> 1178 log_likelihood = _get_log_likelihood(inference_data)
1179 scale = rcParams[“stats.ic_scale”] if scale is None else scale.lower()
1180

~\Anaconda3\envs\env\lib\site-packages\arviz\stats\stats_utils.py in get_log_likelihood(idata, var_name)
403 var_names.remove(“lp”)
404 if len(var_names) > 1:
–> 405 raise TypeError(
406 “Found several log likelihood arrays {}, var_name cannot be None”.format(var_names)
407 )

TypeError: Found several log likelihood arrays [‘h_goals’, ‘a_goals’], var_name cannot be None

---

当我在pymc3中有两个似然函数时，有没有办法计算WAIC并比较模型？（1：主队的进球数2：客队的进球数）

这是可能的，但需要确定您对预测的内容感兴趣，它可以是比赛结果，也可以是任一队的进球数（不是总数，每场比赛将提供2个预测结果）

有关完整和详细的答案，请访问

在这里，我将兴趣量是匹配结果的情况记录为摘要。ArviZ将自动检索2个逐点对数似然数组，我们必须以某种方式组合（例如，添加、连接、分组…）以获得单个数组。棘手的部分是知道每个数量对应的操作，必须根据每个模型进行评估。在此特定示例中，匹配结果的预测精度可通过以下方式计算：

dims = {
    "home_points": ["match"],
    "away_points": ["match"],
}
idata = az.from_pymc3(trace, dims=dims, model=model)

设置

match

dim对于告诉xarray如何对齐逐点对数似然数组非常重要，否则它们将无法以所需的方式广播和对齐

idata.sample_stats["log_likelihood"] = (
    idata.log_likelihood.home_points + idata.log_likelihood.away_points
)
az.waic(idata)
# Output
# Computed from 3000 by 60 log-likelihood matrix
#
#           Estimate       SE
# elpd_waic  -551.28    37.96
# p_waic       46.16        -
#
# There has been a warning during the calculation. Please check the results.

请注意，ArviZ>=0.7.0是必需的