Kind regards,
I am building a model in which each observation is a matrix, i want to model it using the matrix normal distribution as define in:
Thanks.
No. Use the third equation on the wikipedia page that you linked to generate it yourself. You’ll have to specify priors for both the row and column covariance matrices – LKJ priors for correlations and [whatever you want] for volatilities will do nicely – then Kronecker product them together to get the overall covariance matrix for the multivariate normal. A prior for the mean is [whatever you want], just in vector form. After you draw from MultivariateNormal, reshape into the matrix shape you want. Does that make sense?
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Have been reading up a bit on this.
For modeling a point cloud in 3D, of shape (num_points,3)
- Glanz, H., & Carvalho, L. (2013). An Expectation-Maximization Algorithm for the Matrix Normal Distribution, 1–11.
- Moreta, L. S., Al-Sibahi, A. S., Theobald, D., Bullock, W., Rommes, B. N., Manoukian, A., & Hamelryck, T. (2019). A Probabilistic Programming Approach to Protein Structure Superposition. 2019 IEEE Conference on Computational Intelligence in Bioinformatics and Computational Biology, CIBCB 2019 . A Probabilistic Programming Approach to Protein Structure Superposition | IEEE Conference Publication | IEEE Xplore
Can you tell me more about a KJL prior for the covariance matrix?