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从pymc2到PyMC3的CAR模型 – python程序员分享

本文介绍了从pymc2到PyMC3的CAR模型 – python程序员分享,有助于帮助完成毕业设计以及求职,是一篇很好的资料。

对技术面试,学习经验等有一些体会,在此分享。

我在PyMC3中仍然是菜鸟,所以这个问题可能让我很天真,但是我不知道如何在pymc3中翻译此pymc2代码。特别是我不清楚如何翻译R函数。

beta = pymc.Normal('beta', mu=0, tau=1.0e-4) s = pymc.Uniform('s', lower=0, upper=1.0e+4) tau = pymc.Lambda('tau', lambda s=s: s**(-2))  ### Intrinsic CAR @pymc.stochastic def R(tau=tau, value=np.zeros(N)):     # Calculate mu based on average of neighbors     mu = np.array([sum(W[i]*value[A[i]])/Wplus[i] for i in xrange(N)])      # Scale precision to the number of neighbors     taux = tau*Wplus     return pymc.normal_like(value, mu, taux)  @pymc.deterministic def M(beta=beta, R=R):     return [np.exp(beta + R[i]) for i in xrange(N)]  obsvd = pymc.Poisson("obsvd", mu=M, value=Y, observed=True) model = pymc.Model([s, beta, obsvd]) 

来自https://github.com/Youki/statistical-modeling-for-data-analysis-with-python/blob/945c13549a872d869e33bc48082c42efc022a07b/Chapter11/Chapter11.rst和http://glau.ca/?p=340的代码

你能帮助我吗?谢谢

参考方案

在PyMC3中,您可以使用Theano的扫描功能来实现CAR模型。他们的documentation中有一个示例代码。链接文档中有两种CAR实现。这是第一个 [Source]:

 from theano import scan floatX = "float32"  from pymc3.distributions import continuous from pymc3.distributions import distribution  class CAR(distribution.Continuous):     """     Conditional Autoregressive (CAR) distribution      Parameters     ----------     a : list of adjacency information     w : list of weight information     tau : precision at each location     """     def __init__(self, w, a, tau, *args, **kwargs):         super(CAR, self).__init__(*args, **kwargs)         self.a = a = tt.as_tensor_variable(a)         self.w = w = tt.as_tensor_variable(w)         self.tau = tau*tt.sum(w, axis=1)         self.mode = 0.      def get_mu(self, x):          def weigth_mu(w, a):             a1 = tt.cast(a, 'int32')             return tt.sum(w*x[a1])/tt.sum(w)          mu_w, _ = scan(fn=weigth_mu,                        sequences=[self.w, self.a])          return mu_w      def logp(self, x):         mu_w = self.get_mu(x)         tau = self.tau         return tt.sum(continuous.Normal.dist(mu=mu_w, tau=tau).logp(x))  with pm.Model() as model1:     # Vague prior on intercept     beta0 = pm.Normal('beta0', mu=0.0, tau=1.0e-5)     # Vague prior on covariate effect     beta1 = pm.Normal('beta1', mu=0.0, tau=1.0e-5)      # Random effects (hierarchial) prior     tau_h = pm.Gamma('tau_h', alpha=3.2761, beta=1.81)     # Spatial clustering prior     tau_c = pm.Gamma('tau_c', alpha=1.0, beta=1.0)      # Regional random effects     theta = pm.Normal('theta', mu=0.0, tau=tau_h, shape=N)     mu_phi = CAR('mu_phi', w=wmat, a=amat, tau=tau_c, shape=N)      # Zero-centre phi     phi = pm.Deterministic('phi', mu_phi-tt.mean(mu_phi))      # Mean model     mu = pm.Deterministic('mu', tt.exp(logE + beta0 + beta1*aff + theta + phi))      # Likelihood     Yi = pm.Poisson('Yi', mu=mu, observed=O)      # Marginal SD of heterogeniety effects     sd_h = pm.Deterministic('sd_h', tt.std(theta))     # Marginal SD of clustering (spatial) effects     sd_c = pm.Deterministic('sd_c', tt.std(phi))     # Proportion sptial variance     alpha = pm.Deterministic('alpha', sd_c/(sd_h+sd_c))      trace1 = pm.sample(1000, tune=500, cores=4,                        init='advi',                        nuts_kwargs={"target_accept":0.9,                                     "max_treedepth": 15})  

M函数在这里写为:

mu = pm.Deterministic('mu', tt.exp(logE + beta0 + beta1*aff + theta + phi)) 

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