# Estimated covariance matrix

**URL:** <https://discourse.pymc.io/t/estimated-covariance-matrix/1212>\
**Category:** Questions\
**Created:** [May 13, 2018, 1:27pm UTC](https://discourse.pymc.io/t/estimated-covariance-matrix/1212 "2018-05-13T13:27:49Z")\
**Posts on this page:** 6\
**Page:** 1

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**Author:** ![Cabbagee](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/cabbagee/32/660_2.png) [@Cabbagee](https://discourse.pymc.io/u/Cabbagee)\
**Post date:** [May 13, 2018, 1:27pm UTC](https://discourse.pymc.io/t/estimated-covariance-matrix/1212/1 "2018-05-13T13:27:49Z")

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Pymc3 how to calculate the covariance matrix of the sample and compare it with the real covariance matrix to get the mean square error.

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**Author:** ![junpenglao](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/junpenglao/32/8_2.png) [@junpenglao](https://discourse.pymc.io/u/junpenglao)\
**Post date:** [May 13, 2018, 1:49pm UTC](https://discourse.pymc.io/t/estimated-covariance-matrix/1212/2 "2018-05-13T13:49:29Z")

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there is a `pm.trace_cov` function for that.

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<div class="post-metadata">

**Author:** ![Cabbagee](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/cabbagee/32/660_2.png) [@Cabbagee](https://discourse.pymc.io/u/Cabbagee)\
**Post date:** [May 14, 2018, 1:22am UTC](https://discourse.pymc.io/t/estimated-covariance-matrix/1212/3 "2018-05-14T01:22:19Z")

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Thank you for your help. I have another question: how to estimate the correlation matrix?

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<div class="post-metadata">

**Author:** ![junpenglao](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/junpenglao/32/8_2.png) [@junpenglao](https://discourse.pymc.io/u/junpenglao)\
**Post date:** [May 14, 2018, 4:40am UTC](https://discourse.pymc.io/t/estimated-covariance-matrix/1212/4 "2018-05-14T04:40:44Z")

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```python
sd = np.sqrt(np.diag(cov))
corr = np.diag(sd**-1).dot(cov.dot(np.diag(sd**-1)))

```

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<div class="post-metadata">

**Author:** ![Cabbagee](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/cabbagee/32/660_2.png) [@Cabbagee](https://discourse.pymc.io/u/Cabbagee)\
**Post date:** [May 15, 2018, 3:01am UTC](https://discourse.pymc.io/t/estimated-covariance-matrix/1212/5 "2018-05-15T03:01:07Z")

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Thank you,it works,  
now I want to train my model on multiple data sets, and calculate the mean square error of covariance matrix on each data set. Finally, I will take the average after adding these results together.so I wrote the following code

```
for i in range(M): # M data sets
    with pm.Model() as model:
        packed_l=pm.LKJCholeskyCov('packed_l',n=2,eta=2,sd_dist=pm.HalfCauchy.dist(2.5))
        L=pm.expand_packed_triangular(2,packed_l)
        Sigma=pm.Deterministic('Sigma',tt.dot(L,L.T))
        mu=pm.Normal('mu',0.,10,shape=2,testval=dataSet[i].mean(axis=0))
        obs=pm.MvNormal('obs',mu=mu,chol=L,observed=dataSet[i])
        trace = pm.sample(random_seed=seed,model=model,njobs=1)
    
    Sigma_post=trace['Sigma'].mean(axis=0) # Estimated covariance matrix

    MSE0=[]
    MSE0.append(1/(k**2)*np.sqrt(((Sigma_post-Sigma_real)**2).sum())) # mean square error
MSE=np.array(MSE0)
RMSE=np.sqrt((1/M)*MSE.sum())# Root mean square error
print(MSE.shape)
print(RMSE)

```

It should be `MSE.shape=(1,M)`, but the run results indicate that `MSE.shape=(1,)`,

I am very confused. Where is the mistake? Can you give me some advice?

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<div class="post-metadata">

**Author:** ![junpenglao](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/junpenglao/32/8_2.png) [@junpenglao](https://discourse.pymc.io/u/junpenglao)\
**Post date:** [May 15, 2018, 5:01am UTC](https://discourse.pymc.io/t/estimated-covariance-matrix/1212/6 "2018-05-15T05:01:10Z")

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You have

```python
    MSE0=[]

```

right above

```python
    MSE0.append(...)

```

which clears the MSE0 every time. You should put `MSE0=[]` outside of the for-loop.