PyMC - 분산 공분산 행렬 추정

Question

I 읽어들이 같이 분산 공분산 행렬 Σ 모델링 다음 용지 (http://www3.stat.sinica.edu.tw/statistica/oldpdf/A10n416.pdf)

Σ = DIAG (S) * R * DIAG (S) (식 1 diag (S)는 대각선 요소 S를 갖는 대각선 행렬이고, R은 k × k 상관 행렬이다.

어떻게 PyMC를 사용하여 구현할 수 있습니까? 여기

는 몇 가지 초기 내가 쓴 코드 :

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) 

감사

[편집]

내가이 다음 사용하여 해당 수행 할 수 있다고 생각 : 여기

@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) 

Answer 1

입니다 이 게시물에 걸린 사람의 이익을위한 솔루션 :

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)