Relabelling in Bayesian mixture models by pivotal units

A simple procedure based on relabelling to deal with label switching when exploring complex posterior distributions by MCMC algorithms is proposed. Although it cannot be generalized to any situation, it may be handy in many applications because of its simplicity and low computational burden. A possible area where it proves to be useful is when deriving a sample for the posterior distribution arising from finite mixture models when no simple or rational ordering between the components is available

A Graphical copula-based tool for detecting tail dependence

In many practical applications, the selection of copulas with a specific tail behaviour may allow to estimate properly the region of the distribution that is needed at most, especially in risk management procedures. Here, a graphical tool related to copulas is presented in order to assist the decision maker in the selection of an appropriate model for the problem at hand. Such a tool provides valuable indications for a preliminary overview of the tail features of different copulas which may help in the choice of a parametric model. Its use will be illustrated under various dependency scenarios

Maxima Units Search (MUS) algorithm: methodology and applications

4An algorithm for extracting identity submatrices of small rank and pivotal units from large and sparse matrices is proposed. The procedure has already been satisfactorily applied for solving the label switching problem in Bayesian mixture models. Here we introduce it on its own and explore possible applications in different contexts.reservedmixedEgidi, Leonardo; Pappadà, Roberta; Pauli, Francesco; Torelli, NicolaEgidi, Leonardo; Pappada', Roberta; Pauli, Francesco; Torelli, Nicol

Copulas, diagonals, and tail dependence

We present some known and novel aspects about bivariate copulas with prescribed diagonal section by highlighting their use in the description of the tail dependence. Moreover, we present the tail concentration function (which depends on the diagonal section of a copula) as a tool to give a description of tail dependence at finite scale. The tail concentration function is hence used to introduce a graphical tool that can help to distinguish different families of copulas in the copula test space. Moreover, it serves as a basis to determine the grouping structure of different financial time series by taking into account their pairwise tail behavior