python - PyMC 最简单的线性模型

Question

假设我尝试使用以下数据估计一个简单的 y= m * x 问题的斜率:

x_data = np.array([0,1,2,3])
y_data = np.array([0,1,2,3])

显然斜率为1。但是，当我在 PyMC 中运行它时，我得到 10

slope  = pm.Uniform('slope',  lower=0, upper=20)

@pm.deterministic
def y_gen(value=y_data, x=x_data, slope=slope, observed=True):
  return slope * x

model = pm.Model([slope])
mcmc  = pm.MCMC(model)
mcmc.sample(100000, 5000)

# This returns 10
final_guess = mcmc.trace('slope')[:].mean()

但它应该是1!

注意:以上是PyMC2。

Answer 1

你需要定义一个可能性，试试这个:

import pymc as pm
import numpy as np

x_data = np.linspace(0,1,100)
y_data = np.linspace(0,1,100)

slope  = pm.Normal('slope',  mu=0, tau=10**-2)
tau    = pm.Uniform('tau', lower=0, upper=20)

@pm.deterministic
def y_gen(x=x_data, slope=slope):
  return slope * x

like = pm.Normal('likelihood', mu=y_gen, tau=tau, observed=True, value=y_data)

model = pm.Model([slope, y_gen, like, tau])
mcmc  = pm.MCMC(model)
mcmc.sample(100000, 5000)

# This returns 10
final_guess = mcmc.trace('slope')[:].mean()

它返回 10，因为您只是先从制服中抽样，而 10 是它的预期值。