在 PyMC3 中采样多变量制服

Question

我想在使用 DensityDist 之前使用来自统一分布的自定义分布的样本。本着以下精神：

import theano.tensor as T
from pymc3 import DensityDist, Uniform, Model

with Model() as model:
    lim = 3
    x0 = Uniform('x0', -lim, lim)
    x1 = Uniform('x1', -lim, lim)

    x = T.concatenate([x0,x1])
    # Create custom densities
    star = DensityDist('star', lambda x: star(x[:,0],x[:,1]))

其中 star 是将二维笛卡尔点映射到非标准化对数似然函数的函数。这是我想使用 Metropolis-Hastings 采样的函数。

我尝试了多种变体，但 none 奏效了。当前代码失败：

ValueError: The index list is longer (size 2) than the number of dimensions of the tensor(namely 0). You are asking for a dimension of the tensor that does not exist! You might need to use dimshuffle to add extra dimension to your tensor.

感谢任何帮助！

Answer 1

x 的索引错误。它只是一维的，因此沿二维索引实际上行不通。

import theano.tensor as tt
from pymc3 import DensityDist, Uniform, Model

def star(x):
    return -0.5 * tt.exp(-tt.sum(x ** 2))
    # or if you need the components individually
    #return -0.5 * tt.exp(-x[0] ** 2 - x[1] ** 2)

with Model() as model:
    lim = 3
    x0 = Uniform('x0', -lim, lim)
    x1 = Uniform('x1', -lim, lim)

    x = T.stack([x0,x1])
    # Create custom densities
    star = DensityDist('star', star)

在 PyMC3 中采样多变量制服

sampling multivariate uniform in PyMC3

pymc

pymc3