# Traceplot Corresponding to a Lambda_hat Matrix

lambda_hat is matrix containing parameter of a Multiple Response Regression problem with Wishart Prior .

Hi,
it appears your chain is basically staying at the same location over whole sampling process. This means your model has some big problem, but it is impossible to say anything better without seeing the code. The strategies for investigation mentiond at Divergent transitions - a primer could also help you investigate (most apply to general modelling problems - even if you don’t really get divergent transitions).

Best of luck with your model!

@martinmodrak are you suggesting this for all elements of Lambda_hat or only the [1,1] and [1,3]?

Looking at the scales, you see that all changes in all `lambda_hat` are < 10^{-6}, so I think all are affected.

Did you look at the link I shread previously? Did you try some of the strategies or are you having problems applying them to your case?

The construction of `est_Sigma` is definitely suspicous. Why does `lambda_hat` enter the equation twice? Is the result even guaranteed to be a valid covariance matrix? Additionally, the `0.000001` multiplier is quite likely to induce sharp peaks in the geometry which will then prevent the sampler from moving around. What is the role of this multiplier?

Lambda_hat is not a covariance matrix, I have defined that in that way as I want the output to the Symmetric Positive Definite Matrix(it’s one of the desirable property for Lambda_hat).
The multiplier 0.000001 just reduces the extreme variance nothing else.(without that variance I am getting a line in traceplot for all the estimates.)

I am not sure I follow:

1. you define `lambda_hat` as `cov_matrix[K] lambda_hat;` so you definitely treat it as a covariance matrix
2. You use `est_Sigma` as a covariance matrix. And I admit my linear algebra is a bit rusty, so I might be missing something obvious but is `est_Sigma` guaranteed to be symmetric and positive semidefinite? A quick test in R shows that for general `omega_d`, it is not. Do you have guarantees on `omega_d` that ensure `est_Sigma` is valid covariance matrix?

I think this tells us that something is wrong with the model. What reasons you have to construct `est_Sigma` in this particular way? Since `lmabda_hat` has the same number of degrees of freedom as `est_Sigma`, would the model work if you fitted `est_Sigma` directly?

The model I am working on has the following properties-

1. lambda_hat is a Matrix consisting of Regression parameters and it needs to be Symmetric and as well Positive Definite.
2)est_Sigma=2lambda_hatomega_d*lambda_hat , is a desired result for the model, where omega_d is also a variance covarince matrix.
I was as well thinking of relaxing the constraint regarding est_Sigma, can you suggest me some thing regarding it?
I myself was thinking of at t=T taking est_Sigma=variance(observations on y upto time t=T).

That’s hard to say without knowing what the model means. One thing I would expect to help would be to move `est_Sigma` to parametes, so you’d have:

``````parameters {
cov_matrix[K] est_Sigma;
}
``````

And fit `est_Sigma` directly. You then should be able to reconstruct `lambda_hat` from `est_Sigma` and `omega`.