PyMC - variance-covariance matrix estimation

问题:

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

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

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.

How can I implement this using PyMC ?

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 ) 

Thanks

[edit]

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) 

回答1:

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 ) 

文章来源: PyMC - variance-covariance matrix estimation