Concordance correlation coefficients estimated by modified variance components and generalized estimating equations for longitudinal overdispersed Poisson data

For longitudinal overdispersed Poisson data sets, estimators of the intra-, inter-, and total concordance correlation coefficient through variance components have been proposed. However, biased estimators of quadratic forms are used in concordance correlation coefficient estimation. In addition, the generalized estimating equations approach has been used in estimating agreement for longitudinal normal data and not for longitudinal overdispersed Poisson data. Therefore, this paper proposes a modified variance component approach to develop the unbiased estimators of the concordance correlation coefficient for longitudinal overdispersed Poisson data. Further, the indices of intra-, inter-, and total agreement through generalized estimating equations are also developed considering the correlation structure of longitudinal count repeated measurements. Simulation studies are conducted to compare the performance of the modified variance component and generalized estimating equation approaches for longitudinal Poisson and overdispersed Poisson data sets. An application of corticospinal diffusion tensor tractography study is used for illustration. In conclusion, the modified variance component approach performs outstandingly well with small mean square errors and nominal 95% coverage rates. The generalized estimating equation approach provides in model assumption flexibility of correlation structures for repeated measurements to produce satisfactory concordance correlation coefficient estimation results.

Low-Pass Filtering Method for Poisson Data Time Series

Problems of digital processing of Poisson-distributed data time series from various counters of radiation particles, photons, slow neutrons etc. are relevant for experimental physics and measuring technology. A low-pass filtering method for normalized Poisson-distributed data time series is proposed. A digital quasi-Gaussian filter is designed, with a finite impulse response and non-negative weights. The quasi-Gaussian filter synthesis is implemented using the technology of stochastic global minimization and modification of the annealing simulation algorithm. The results of testing the filtering method and the quasi-Gaussian filter on model and experimental normalized Poisson data from the URAGAN muon hodoscope, that have confirmed their effectiveness, are presented.

Analysis of Change Points With Bayes Factor, Thresholds, and CUSUM

In this work, an analysis of change points is made with the Bayes factor, thresholds, and cumulative sum (CUSUM) statistics methods. For the analysis of change points with the Bayes factor, Poisson data were simulated; the threshold method was worked with a regression and data of the National Institute of Statistics, Geography and Informatics (INEGI) of Mexico and coronavirus were used for the CUSUM.

Poisson-geometric Analogues of Kitaev Models

We define Poisson-geometric analogues of Kitaev’s lattice models. They are obtained from a Kitaev model on an embedded graph $$\Gamma $$ Γ by replacing its Hopf algebraic data with Poisson data for a Poisson-Lie group G. Each edge is assigned a copy of the Heisenberg double $${\mathcal {H}}(G)$$ H ( G ) . Each vertex (face) of $$\Gamma $$ Γ defines a Poisson action of G (of $$G^*$$ G ∗ ) on the product of these Heisenberg doubles. The actions for a vertex and adjacent face form a Poisson action of the double Poisson-Lie group D(G). We define Poisson counterparts of vertex and face operators and relate them via the Poisson bracket to the vector fields generating the actions of D(G). We construct an isomorphism of Poisson D(G)-spaces between this Poisson-geometrical Kitaev model and Fock and Rosly’s Poisson structure for the graph $$\Gamma $$ Γ and the Poisson-Lie group D(G). This decouples the latter and represents it as a product of Heisenberg doubles. It also relates the Poisson-geometrical Kitaev model to the symplectic structure on the moduli space of flat D(G)-bundles on an oriented surface with boundary constructed from $$\Gamma $$ Γ .