我想从数据中估计一个简单线性函数的参数和一个伽马分布的噪声项。（注意：这是https://stats.stackexchange.com/questions/88676/regression-with-unidirectional-noise的后续问题，但经过简化且更具体化）。假设我的观察数据生成如下：
import numpy as np
np.random.seed(0)
size = 200
true_intercept = 1
true_slope = 2
# Generate observed data
x_ = np.linspace(0, 1, size)
true_regression_line = true_intercept + true_slope * x_ # y = a + b*x
noise_ = np.random.gamma(shape=1.0, scale=1.0, size=size)
y_ = true_regression_line + noise_
如下所示：
我尝试使用 pymc 估计这些参数，如下所示：
from pymc import Normal, Gamma, Uniform, Model, MAP
# Define priors
intercept = Normal('intercept', 0, tau=0.1)
slope = Normal('slope', 0, tau=0.1)
alpha = Uniform('alpha', 0, 2)
beta = Uniform('beta', 0, 2)
noise = Gamma('noise', alpha=alpha, beta=beta, size=size)
# Give likelihood > 0 to models where the regression line becomes larger than
# any of the datapoint
y = Normal('y', mu=intercept + slope * x_ + noise, tau=100,
observed=True, value=y_)
# Perform MAP fit of model
model = Model([alpha, beta, intercept, slope, noise])
map_ = MAP(model)
map_.fit()
但是，这给了我与真实值相去甚远的估计：
- 拦截：真：1.000，估计：3.281
- 斜率：真实：2.000，估计：-3.400
我做错了什么吗？