Fupeng Sun

We study an all-pay contest where players with low abilities are filtered prior to the round of competing for prizes. These are often practiced due to limited resources or to enhance the competitiveness of the contest. We consider a setting where the designer admits a certain number of top players into the contest. The players admitted into the contest update their beliefs about their opponents based on the signal that their abilities are among the top. We find that their posterior beliefs, even with IID priors, are correlated and depend on players' private abilities, representing a unique feature of this game. We explicitly characterize the symmetric and unique Bayesian equilibrium strategy. We find that each admitted player's equilibrium effort is in general \emph{not} monotone with the number of admitted players. Despite this non-monotonicity, surprisingly, \emph{all} players exert their highest efforts when all players are admitted. This result holds generally --- it is true under any ranking-based prize structure, ability distribution, and cost function. We also discuss a two-stage extension where players with top first-stage efforts can proceed to the second stage competing for prizes.

Electrocardiograms (ECG) analysis is one of the most important ways to diagnose heart disease. This paper proposes an efficient ECG classification method based on Wasserstein scalar curvature to comprehend the connection between heart disease and the mathematical characteristics of ECG. The newly proposed method converts an ECG into a point cloud on the family of Gaussian distribution, where the pathological characteristics of ECG will be extracted by the Wasserstein geometric structure of the statistical manifold. Technically, this paper defines the histogram dispersion of Wasserstein scalar curvature, which can accurately describe the divergence between different heart diseases. By combining medical experience with mathematical ideas from geometry and data science, this paper provides a feasible algorithm for the new method, and the theoretical analysis of the algorithm is carried out. Digital experiments on the classical database with large samples show the new algorithm's accuracy and efficiency when dealing with the classification of heart disease.

Preprint version (June 2022)

Bayesian methods have been rapidly developed due to the important role of explicable causality in practical problems. We develope geometric approaches to Bayesian inference of Pareto models, and give an application to the analysis of sea clutter. {\color{green}{For Pareto two-parameter model}}, we show the non-existence of $\alpha$-parallel prior in general, hence we adopt Jeffreys prior to deal with the Bayesian inference. Considering geodesic distance as the loss function, an estimation in the sense of minimal mean geodesic distance is obtained. Meanwhile, by involving Al-Bayyati's loss function we gain a new class of Bayesian estimations. In the simulation, for sea clutter, we adopt Pareto model to acquire various types of parameter estimations and the posterior prediction results. Simulation results show the advantages of the Bayesian estimations proposed and the posterior prediction.

Classification and prediction of heart disease is a significant problem to realize medical treatment and life protection. In this paper, persistent homology is involved to analyze electrocardiograms and a novel heart disease classification method is proposed. Each electrocardiogram becomes a point cloud by sliding windows and fast Fourier transform embedding. The obtained point cloud reveals periodicity and stability characteristics of electrocardiograms. By persistent homology, three features including normalized persistent entropy, maximum life of time and maximum life of Betty number are extracted. These features show the structural differences between different types of electrocardiograms and display encouraging potentiality in classification of heart disease.

Preprint version

In this paper, we introduce the adaptive Wasserstein curvature denoising (AWCD), an original processing approach for point cloud data. By collecting curvatures information from Wasserstein distance, AWCD consider more precise structures of data and preserves stability and effectiveness even for data with noise in high density. This paper contains some theoretical analysis about the Wasserstein curvature and the complete algorithm of AWCD. In addition, we design digital experiments to show the denoising effect of AWCD. According to comparison results, we present the advantages of AWCD against traditional algorithms.

Preprint version

Considering the difference of local statistical properties between data points,and combining with K-means algorithm,a novel clustering algorithm based on statistical manifold was proposed. By calculating the mean and covariance of the neighborhood of the data points,the original data point cloud was mapped to the normal distribution family manifold to form the parameter point cloud. Different measurement structures were constructed on the normal distribution family manifold,and K-means method was applied to cluster the parameter point cloud,so as to classify the corresponding original data. To verify the effect in the point cloud denoising,the algorithms based on different difference function were used to denoise the point cloud with high density noise,and simulation analysis was carried out. The simulation results show that the algorithm using KL divergence as difference function can get a better denoising effect,verifying the potential of the algorithm in denoising application.