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Independence properties for tree beta models
Yoshihiro Gyotoku, Makiko Sasada, Jacek Wesołowski
This paper is devoted to introduce new probabilistic tree-based models complementing already known Matsumoto-Yor and Hamza-Vallois tree models with two tree beta-type models.
GIG random matrices and a Yang-Baxter extension of the Matsumoto-Yor property
Gérard Letac, Mauro Piccioni, Jacek Wesołowski
Sasada and Uozumi, \cite{SasUoz2024}, identified independence preserving quadrirational parametric Yang-Baxter maps, see \eqref{YBEQ}, on . In particular, the m…
Expected number of jumps and the number of active particles in TASEP
Paweł Hitczenko, Jacek Wesołowski
For a TASEP on with the step initial condition we identify limits as of the expected total number of jumps until time and the expected number of acti…
Probability laws associated to the independence preserving quadrirational Yang-Baxter maps -- the ultimate case
Bartosz Kołodziejek, Gérard Letac, Mauro Piccioni +1
A map is said to be independence preserving (IP) if there exists a pair of independent random variables v…
Reversible Markov kernels and involutions on product spaces
Mauro Piccioni, Jacek Wesołowski
In this paper the relations between independence preserving (IP) involutions and reversible Markov kernels are investigated. We introduce an involutive augmentation H = (f, g_f) of…
Graphical Negative Multinomial and Multinomial Models with Dirichlet-type priors
Iza Danielewska, Bartosz Kołodziejek, Jacek Wesołowski +1
Bayesian statistical graphical models are typically classified as either continuous and parametric (Gaussian, parameterized by the graph-dependent precision matrix with Wishart-typ…