PyMC-方差-协方差矩阵估计 [英] PyMC - variance-covariance matrix estimation

问题描述

我阅读了以下论文( http://www3.stat. sinica.edu.tw/statistica/oldpdf/A10n416.pdf )，他们将方差-协方差矩阵Σ建模为:

I read the following paper(http://www3.stat.sinica.edu.tw/statistica/oldpdf/A10n416.pdf) where they model the variance-covariance matrix Σ as:

Σ= diag(S)* R * diag(S)(本文方程1)

Σ = diag(S)*R*diag(S) (Equation 1 in the paper)

S是标准差的k×1向量，diag(S)是带有对角元素S的对角矩阵，R是k×k相关矩阵.

S is the k×1 vector of standard deviations, diag(S) is the diagonal matrix with diagonal elements S, and R is the k×k correlation matrix.

如何使用PyMC来实现呢?

How can I implement this using PyMC ?

这是我写的一些初始代码:

Here is some initial code I wrote:

import numpy as np
import pandas as pd
import pymc as pm

k=3
prior_mu=np.ones(k)
prior_var=np.eye(k)
prior_corr=np.eye(k)
prior_cov=prior_var*prior_corr*prior_var

post_mu = pm.Normal("returns",prior_mu,1,size=k)
post_var=pm.Lognormal("variance",np.diag(prior_var),1,size=k)
post_corr_inv=pm.Wishart("inv_corr",n_obs,np.linalg.inv(prior_corr))


post_cov_matrix_inv = ???

muVector=[10,5,-2]
varMatrix=np.diag([10,20,10])
corrMatrix=np.matrix([[1,.2,0],[.2,1,0],[0,0,1]])
cov_matrix=varMatrix*corrMatrix*varMatrix

n_obs=10000
x=np.random.multivariate_normal(muVector,cov_matrix,n_obs)
obs = pm.MvNormal( "observed returns", post_mu, post_cov_matrix_inv, observed = True, value = x )

model = pm.Model( [obs, post_mu, post_cov_matrix_inv] )
mcmc = pm.MCMC()

mcmc.sample( 5000, 2000, 3 )

谢谢

我认为可以使用以下方法做到这一点:

I think that can be done using the following:

@pm.deterministic
def post_cov_matrix_inv(post_sdev=post_sdev,post_corr_inv=post_corr_inv):
    return np.diag(post_sdev)*post_corr_inv*np.diag(post_sdev)

推荐答案

以下是迷失于此帖子的人的解决方案:

Here is the solution for the benefit of someone who stumbles onto this post:

p=3
prior_mu=np.ones(p)
prior_sdev=np.ones(p)
prior_corr_inv=np.eye(p)


muVector=[10,5,1]
sdevVector=[3,5,10]
corrMatrix=np.matrix([[1,0,-.1],[0,1,.5],[-.1,.5,1]])
cov_matrix=np.diag(sdevVector)*corrMatrix*np.diag(sdevVector)

n_obs=2000
x=np.random.multivariate_normal(muVector,cov_matrix,n_obs)

prior_cov=np.diag(prior_sdev)*np.linalg.inv(prior_corr_inv)*np.diag(prior_sdev)

post_mu = pm.Normal("returns",prior_mu,1,size=p)
post_sdev=pm.Lognormal("sdev",prior_sdev,1,size=p)
post_corr_inv=pm.Wishart("inv_corr",n_obs,prior_corr_inv)

#post_cov_matrix_inv = pm.Wishart("inv_cov_matrix",n_obs,np.linalg.inv(prior_cov))
@pm.deterministic
def post_cov_matrix_inv(post_sdev=post_sdev,post_corr_inv=post_corr_inv,nobs=n_obs):
    post_sdev_inv=(post_sdev)**-1
    return np.diag(post_sdev_inv)*cov2corr(post_corr_inv/nobs)*np.diag(post_sdev_inv)

obs = pm.MvNormal( "observed returns", post_mu, post_cov_matrix_inv, observed = True, value = x )

model = pm.Model( [obs, post_mu, post_sdev ,post_corr_inv])
mcmc = pm.MCMC(model)

mcmc.sample( 25000, 15000, 1,progress_bar=False )

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