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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