如何在PyMC的Metropolis采样器中传入确定性变量？

我在调试《Probabilistic-Programming-and-Bayesian-Methods-for-Hackers》第2章末尾的代码（验证后验分布模拟数据与原始数据匹配），使用PyMC而非PyMC3，运行代码时出现报错。

原代码 #

N = 10000
with pm.Model() as model:
    beta = pm.Normal("beta", mu=0, tau=0.001, testval=0)
    alpha = pm.Normal("alpha", mu=0, tau=0.001, testval=0)
    p = pm.Deterministic("p", 1.0/(1. + tt.exp(beta*temperature + alpha)))
    observed = pm.Bernoulli("bernoulli_obs", p, observed=D)
    # pytensor.config.compute_test_value = "warn"

    simulated = pm.Bernoulli("bernoulli_sim", p,shape= p.shape )
    step = pm.Metropolis(vars=[p])
    trace = pm.sample(N, step=step)

报错信息 #

ValueError                                Traceback (most recent call last)
Cell In[32], line 10
      7 # pytensor.config.compute_test_value = "warn"
      9 simulated = pm.Bernoulli("bernoulli_sim", p,shape= p.shape )
---> 10 step = pm.Metropolis(vars=[p])
     11 trace = pm.sample(N, step=step)

File ~\.conda\envs\bayes_course\Lib\site-packages\pymc\step_methods\metropolis.py:168, in Metropolis.__init__(self, vars, S, proposal_dist, scaling, tune, tune_interval, model, mode, **kwargs)
    166     vars = model.value_vars
    167 else:
---> 168     vars = get_value_vars_from_user_vars(vars, model)
    170 initial_values_shape = [initial_values[v.name].shape for v in vars]
    171 if S is None:

File ~\.conda\envs\bayes_course\Lib\site-packages\pymc\util.py:480, in get_value_vars_from_user_vars(vars, model)
    477     notin = list(map(get_var_name, notin))
    478     # We mention random variables, even though the input may be a wrong value variable
    479     # because most users don't know about that duality
---> 480     raise ValueError(
    481         "The following variables are not random variables in the model: " + str(notin)
    482     )
    484 return value_vars

ValueError: The following variables are not random variables in the model: ['p']

解决方法 #

核心原因 #

p是通过pm.Deterministic定义的确定性变量，它的取值完全由alpha和beta计算而来，本身不是模型中的随机变量。Metropolis采样器只能对模型的随机变量（如alpha、beta）进行采样，无法直接作用于确定性变量。

修改步骤 #

1. 指定正确的采样变量：将step = pm.Metropolis(vars=[p])改为采样模型的随机变量alpha和beta：

   step = pm.Metropolis(vars=[alpha, beta])
   

   或者直接省略vars参数，PyMC会自动识别并采样所有随机变量：

   step = pm.Metropolis()
   

2. 保留确定性变量的记录：pm.Deterministic定义的p会自动被记录到采样后的trace中，后续可以通过trace["p"]获取其所有采样值，无需额外操作。

3. 可选：使用默认采样器：新版本PyMC推荐使用NUTS采样器（默认），如果你的数据适合（比如连续型参数），可以直接去掉step参数，让PyMC自动选择最优采样器：

   trace = pm.sample(N)
   

修改后的完整代码示例 #

N = 10000
with pm.Model() as model:
    beta = pm.Normal("beta", mu=0, tau=0.001, testval=0)
    alpha = pm.Normal("alpha", mu=0, tau=0.001, testval=0)
    p = pm.Deterministic("p", 1.0/(1. + tt.exp(beta*temperature + alpha)))
    observed = pm.Bernoulli("bernoulli_obs", p, observed=D)
    
    simulated = pm.Bernoulli("bernoulli_sim", p, shape=p.shape)
    # 采样随机变量alpha和beta，而非确定性变量p
    step = pm.Metropolis(vars=[alpha, beta])
    trace = pm.sample(N, step=step)

内容的提问来源于stack exchange，提问作者ranbir agarwal