在PyMC3中使用betabinomal

Question

我有一个二进制结果的计数表，我想用一个beta二项分布来估计$\alpha$和$\beta$参数，但是当我试图用其他情况下的方法拟合/采样模型分布时，会出现错误：

import pymc3 as pm
import pandas as pd

df = pd.read_csv('~/data.csv', low_memory=False)
df = df[df.Clicks >= 0]

C0=df.C.values
I0=df.N.values
N0 = C0 + I0

with pm.Model() as model:
    C=pm.constant(C0)
    I=pm.constant(I0)
    C1=pm.constant(C0 + 1)
    I1=pm.constant(I0 + 1)
    N=pm.constant(N0)
    alpha = pm.Exponential('alpha', 1/(C0.sum()+1))
    beta = pm.Exponential('beta', 1/(I0.sum()+1))
    obs = pm.BetaBinomial('obs', alpha, beta, N, observed=C0)


with model:
    advi_fit = pm.variational.advi(n=int(1e4))
    trace1 = pm.variational.sample_vp(advi_fit, draws=int(1e4))

pm.traceplot(trace1[::10])

with model:
    step = pm.NUTS()
    #step = pm.Metropolis() # <== same problem
    trace2 = pm.sample(int(1e3), step)

pm.traceplot(trace2[::10])

在这两种情况下，取样失败的原因是：

^{pr2}$

在advi情况下，完整堆栈跟踪为：

---

MissingInputError                         Traceback (most recent call last)
<ipython-input-46-8947c7c798e5> in <module>()
----> 1 import codecs, os;__pyfile = codecs.open('''/tmp/py7996Jip''', encoding='''utf-8''');__code = __pyfile.read().encode('''utf-8''');__pyfile.close();os.remove('''/tmp/py7996Jip''');exec(compile(__code, '''/home/dmahler/Scripts/adops-bayes2.py''', 'exec'));

/home/dmahler/Scripts/adops-bayes2.py in <module>()
     59     advi_fit = pm.variational.advi(n=int(J*6.4e4), learning_rate=1e-3/J, epsilon=1e-8, accurate_elbo=False)
     60     #advi_fit = pm.variational.advi_minibatch(minibatch_RVs=[alpha, beta, p], minibatch_tensors=[C,I,N])
---> 61     trace = pm.variational.sample_vp(advi_fit, draws=int(2e4))
     62 
     63 pm.traceplot(trace[::10])

/home/dmahler/Anaconda/lib/python2.7/site-packages/pymc3/variational/advi.pyc in sample_vp(vparams, draws, model, local_RVs, random_seed, hide_transformed)
    317 
    318     varnames = [str(var) for var in model.unobserved_RVs]
--> 319     trace = NDArray(model=model, vars=vars_sampled)
    320     trace.setup(draws=draws, chain=0)
    321 

/home/dmahler/Anaconda/lib/python2.7/site-packages/pymc3/backends/ndarray.pyc in __init__(self, name, model, vars)
     21     """
     22     def __init__(self, name=None, model=None, vars=None):
---> 23         super(NDArray, self).__init__(name, model, vars)
     24         self.draw_idx = 0
     25         self.draws = None

/home/dmahler/Anaconda/lib/python2.7/site-packages/pymc3/backends/base.pyc in __init__(self, name, model, vars)
     34         self.vars = vars
     35         self.varnames = [var.name for var in vars]
---> 36         self.fn = model.fastfn(vars)
     37 
     38 

/home/dmahler/Anaconda/lib/python2.7/site-packages/pymc3/model.pyc in fastfn(self, outs, mode, *args, **kwargs)
    374         Compiled Theano function as point function.
    375         """
--> 376         f = self.makefn(outs, mode, *args, **kwargs)
    377         return FastPointFunc(f)
    378 

/home/dmahler/Anaconda/lib/python2.7/site-packages/pymc3/memoize.pyc in memoizer(*args, **kwargs)
     12 
     13         if key not in cache:
---> 14             cache[key] = obj(*args, **kwargs)
     15 
     16         return cache[key]

/home/dmahler/Anaconda/lib/python2.7/site-packages/pymc3/model.pyc in makefn(self, outs, mode, *args, **kwargs)
    344                                on_unused_input='ignore',
    345                                accept_inplace=True,
--> 346                                mode=mode, *args, **kwargs)
    347 
    348     def fn(self, outs, mode=None, *args, **kwargs):

/home/dmahler/Anaconda/lib/python2.7/site-packages/theano/compile/function.pyc in function(inputs, outputs, mode, updates, givens, no_default_updates, accept_inplace, name, rebuild_strict, allow_input_downcast, profile, on_unused_input)
    318                    on_unused_input=on_unused_input,
    319                    profile=profile,
--> 320                    output_keys=output_keys)
    321     # We need to add the flag check_aliased inputs if we have any mutable or
    322     # borrowed used defined inputs

/home/dmahler/Anaconda/lib/python2.7/site-packages/theano/compile/pfunc.pyc in pfunc(params, outputs, mode, updates, givens, no_default_updates, accept_inplace, name, rebuild_strict, allow_input_downcast, profile, on_unused_input, output_keys)
    477                          accept_inplace=accept_inplace, name=name,
    478                          profile=profile, on_unused_input=on_unused_input,
--> 479                          output_keys=output_keys)
    480 
    481 

/home/dmahler/Anaconda/lib/python2.7/site-packages/theano/compile/function_module.pyc in orig_function(inputs, outputs, mode, accept_inplace, name, profile, on_unused_input, output_keys)
   1774                    profile=profile,
   1775                    on_unused_input=on_unused_input,
-> 1776                    output_keys=output_keys).create(
   1777             defaults)
   1778 

/home/dmahler/Anaconda/lib/python2.7/site-packages/theano/compile/function_module.pyc in __init__(self, inputs, outputs, mode, accept_inplace, function_builder, profile, on_unused_input, fgraph, output_keys)
   1426             # OUTPUT VARIABLES)
   1427             fgraph, additional_outputs = std_fgraph(inputs, outputs,
-> 1428                                                     accept_inplace)
   1429             fgraph.profile = profile
   1430         else:

/home/dmahler/Anaconda/lib/python2.7/site-packages/theano/compile/function_module.pyc in std_fgraph(input_specs, output_specs, accept_inplace)
    175 
    176     fgraph = gof.fg.FunctionGraph(orig_inputs, orig_outputs,
--> 177                                   update_mapping=update_mapping)
    178 
    179     for node in fgraph.apply_nodes:

/home/dmahler/Anaconda/lib/python2.7/site-packages/theano/gof/fg.pyc in __init__(self, inputs, outputs, features, clone, update_mapping)
    169 
    170         for output in outputs:
--> 171             self.__import_r__(output, reason="init")
    172         for i, output in enumerate(outputs):
    173             output.clients.append(('output', i))

/home/dmahler/Anaconda/lib/python2.7/site-packages/theano/gof/fg.pyc in __import_r__(self, variable, reason)
    358         # Imports the owners of the variables
    359         if variable.owner and variable.owner not in self.apply_nodes:
--> 360                 self.__import__(variable.owner, reason=reason)
    361         if (variable.owner is None and
    362                 not isinstance(variable, graph.Constant) and

/home/dmahler/Anaconda/lib/python2.7/site-packages/theano/gof/fg.pyc in __import__(self, apply_node, check, reason)
    472                             "for more information on this error."
    473                             % str(node)),
--> 474                             r)
    475 
    476         for node in new_nodes:

MissingInputError: ("An input of the graph, used to compute Elemwise{neg,no_inplace}(P_logodds_), was not provided and not given a value.Use the Theano flag exception_verbosity='high',for more information on this error.", P_logodds_)
> /home/dmahler/Anaconda/lib/python2.7/site-packages/theano/gof/fg.py(474)__import__()
    472                             "for more information on this error."
    473                             % str(node)),
--> 474                             r)
    475 
    476         for node in new_nodes:

在我意识到pymc3.BetaBinomial之前，我正在尝试使用单独的Beta和{}实例来实现相同的结果：

with pm.Model() as model:
    C=pm.constant(C0)
    I=pm.constant(I0)
    C1=pm.constant(C0 + 1)
    I1=pm.constant(I0 + 1)
    N=pm.constant(N0)
    alpha = pm.Exponential('alpha', 1/(C0.sum()+1))
    beta = pm.Exponential('beta', 1/(I0.sum()+1))
    p = pm.Beta('P', alpha, beta,  shape=K)
    b = pm.Binomial('B', N, p, observed=C0)

这是成功完成的，但不同的方法产生的结果截然不同。我认为这可能部分是由于先验和观测之间的间接性使得搜索空间更大。当我遇到BetaBinomial时，我想这会使搜索变得更容易，同时也是正确的选择。否则，我认为to模型在逻辑上应该是等价的。不幸的是，我不知道如何使batebinomial工作，我也无法在互联网上找到任何使用BetaBinomial的例子。在

• 如何使BetaBinomial模式工作？在
• 这些模型真的在逻辑上是等价的吗？在
• 有人能更好地猜测最初的层次结构版本的数值问题的原因吗？
  • 我怎么能修好它们？在

Answer 1

你的模型应该运行，你可以写这个

with pm.Model() as model:
    alpha = pm.Exponential('alpha', 1/(C0.sum()+1))
    beta = pm.Exponential('beta', 1/(I0.sum()+1))
    obs = pm.BetaBinomial('obs', alpha, beta, N0, observed=C0)

也就是说，（C，ic1，I1）在您的模型中定义了，但没有使用。不管怎样，这不是问题所在。您得到的错误是因为PyMC3需要一个变量P（就像在第二个模型中一样），但该变量没有定义。可能是您正在使用一个Jupyter笔记本，并且删除/注释了一个theano变量。再次尝试运行笔记本。在

从理论上讲，使用β和二项式或二项式可以得到相同的结果。从实际的角度来看。从BetaBinomial采样应该比从beta和二项式更快，因为部分工作已经在分析中完成了！在

假设一个正确的抽样，这两个模型应该提供相同的结果。要检查两个结果是否相等，请尝试增加样本数（并避免thinning）。同时比较模型之间和模型内的结果（差异应该大致相同）。如果不需要估计P变量（beta分布），那么使用BetaBinomial。在