Longitudinal data with ordinal outcomes commonly arise in clinical and social studies, where the purpose of interest is usually quantile curves rather than a simple reference range. In this paper we consider Bayesian nonlinear quantile regression for longitudinal ordinal data through a latent variable. An efficient Metropolis–Hastings within Gibbs algorithm was developed for model fitting. Simulation studies and a real data example are conducted to assess the performance of the proposed method. Results show that the proposed approach performs well.

This article proposes some related issues to classification problem by Bayesian method for two populations. They are relationships between Bayes error (BE) and other measures and the results for determining the BE. In addition, we propose three methods to find the prior probabilities that can make to reduce BE. The calculation of these methods can be performed conveniently and efficiently by the MATLAB procedures. The new approaches are tested by the numerical examples including synthetic and benchmark data and applied in medicine and economics. These examples also show the advantages of the proposed methods in comparison with existing methods.

This paper focuses on optimal control of nonlinear stochastic delay system constructed through Teugels martingales associated with Lévy processes and standard Brownian motion, in which finite horizon is extended to infinite horizon. In order to describe the interacting many-body system, the expectation values of state processes are added to the concerned system. Further, sufficient and necessary conditions are established under convexity assumptions of the control domain. Finally, an example is given to demonstrate the application of the theory.

In this paper, the author examines the two methods that people used to systematically construct isospectral non-isometric Riemannian manifolds, the Sunada–Pesce–Sutton method and the torus action method, and shows that both methods can be used to produce equivariantly isospectral non-isometric Riemannian G-manifolds. The author also shows that the Milnor’s isospectral pair is not equivariantly isospectral.

In this paper, we establish a generalized Hitchin–Kobayashi correspondence between the $\tau $$-semi-stability and the existence of approximate $\tau $$-Hermitian–Einstein structure on holomorphic pair $(E,\phi )$$ over the compact Gauduchon manifold.

We give a combinatorial characterization of upward planar graphs in terms of upward planar orders, which are special linear extensions of edge posets.