PyMC3中的模型比较

我是PyMC3的新手，正在尝试实现Kruschke（2015）第12.2.2节（模型比较）中的分层模型。

我成功定义了完整模型，然后查看了后验参数值的差异（确定差异是否可以可信地称为零）。

我还试图明确地在本书中所示的模型中进行比较（定义完整模型和受限模型，并使用分类分布对它们进行采样）。

基本上，我尝试在PyMC3中实现以下JAGS模型定义。
http://nbviewer.jupyter.org/github/JWarmenhoven/DBDA-python/blob/master/Notebooks/Chapter%2012.ipynb
但我不知道如何使用模型索引来选择（伪）先验。有指针吗？

杂物：

model {
  for ( s in 1:nSubj ) {
    nCorrOfSubj[s] ~ dbin( theta[s] , nTrlOfSubj[s] )
    theta[s] ~ dbeta( aBeta[CondOfSubj[s]] , bBeta[CondOfSubj[s]] ) 
  }

  for ( j in 1:nCond ) {
    # Use omega[j] for model index 1, omega0 for model index 2:
    aBeta[j] <-       ( equals(mdlIdx,1)*omega[j] 
                      + equals(mdlIdx,2)*omega0  )   * (kappa[j]-2)+1
    bBeta[j] <- ( 1 - ( equals(mdlIdx,1)*omega[j] 
                      + equals(mdlIdx,2)*omega0  ) ) * (kappa[j]-2)+1
    omega[j] ~ dbeta( a[j,mdlIdx] , b[j,mdlIdx] )
  }

  omega0 ~ dbeta( a0[mdlIdx] , b0[mdlIdx] )
  for ( j in 1:nCond ) {
    kappa[j] <- kappaMinusTwo[j] + 2
    kappaMinusTwo[j] ~ dgamma( 2.618 , 0.0809 ) # mode 20 , sd 20
  }
  # Constants for prior and pseudoprior:
  aP <- 1
  bP <- 1
  # a0[model] and b0[model]
  a0[1] <- .48*500       # pseudo
  b0[1] <- (1-.48)*500   # pseudo 
  a0[2] <- aP            # true
  b0[2] <- bP            # true
  # a[condition,model] and b[condition,model]
  a[1,1] <- aP           # true
  a[2,1] <- aP           # true
  a[3,1] <- aP           # true
  a[4,1] <- aP           # true
  b[1,1] <- bP           # true
  b[2,1] <- bP           # true
  b[3,1] <- bP           # true
  b[4,1] <- bP           # true
  a[1,2] <- .40*125      # pseudo
  a[2,2] <- .50*125      # pseudo
  a[3,2] <- .51*125      # pseudo
  b[1,2] <- (1-.40)*125  # pseudo
  b[2,2] <- (1-.50)*125  # pseudo
  b[3,2] <- (1-.51)*125  # pseudo
  b[4,2] <- (1-.52)*125  # pseudo
  # Prior on model index:
  mdlIdx ~ dcat( modelProb[] )
  modelProb[1] <- .5
  modelProb[2] <- .5
}

PyMC3：

with pmc.Model() as model_1:
    # constants
    aP, bP = 1, 1

    # Pseudo- and true hyperpriors per model
    a0 = [.48*500, aP]      
    b0 = [(1-.48)*500, bP]  

    # Lower level pseudo- and true priors per model/condition combination
    a = np.c_[np.tile(aP, 4), [(.40*125), (.50*125), (.51*125), (.52*125)]]
    b = np.c_[np.tile(bP, 4), [(1-.40)*125, (1-.50)*125, (1-.51)*125, (1-.52)*125]]

    # Prior on model index [0,1]
    m_idx = pmc.Categorical('m_idx', np.asarray([.5, .5]))

    # Priors on concentration parameters
    kappa = pmc.Gamma('kappa', 2.618, 0.0809, shape=nCond)

    # omega0 
    omega0 = pmc.Beta('omega0', a0[m_idx], b0[m_idx])    

    # omega (condition specific)
    omega = pmc.Beta('omega', a[:,m_idx], b[:,m_idx], shape=nCond)

    # theta
    aBeta = pmc.switch(eq(m_idx, 0), omega0 * kappa[cond_idx]+1, omega[cond_idx] * kappa[cond_idx]+1)
    bBeta = pmc.switch(eq(m_idx, 0), (1-omega0) * kappa[cond_idx]+1, (1-omega[cond_idx]) * kappa[cond_idx]+1)

    theta = pmc.Beta('theta', aBeta[cond_idx], bBeta[cond_idx], shape=df.index.size)

    # Likelihood
    y = pmc.Binomial('y', n=df.nTrlOfSubj.values, p=theta, observed=df.nCorrOfSubj)    




Applied log-transform to kappa and added transformed kappa_log_ to model.

输出：

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-40-74e77ccc6ce9> in <module>()
      8 
      9     # omega0
---> 10     omega0 = pmc.Beta('omega0', a0[m_idx], b0[m_idx])
     11 
     12     # omega (condition specific)

TypeError: list indices must be integers or slices, not FreeRV

更新
校正伪优先级（缺少括号）后，结果看起来要好得多。但是，我不确定pmc.Beta（）函数是否可以将数组用作a和b的参数。http://nbviewer.jupyter.org/github/JWarmenhoven/DBDA-python/blob/master/Notebooks/Chapter%2012.ipynb