Compound sequential change-point detection in parallel data streams

We consider sequential change-point detection in parallel data streams, where each stream has its own change point. Once a change is detected in a data stream, this stream is deactivated permanently. The goal is to maximize the normal operation of the pre-change streams, while controlling the proportion of post-change streams among the active streams at all time points. Taking a Bayesian formulation, we develop a compound decision framework for this problem. A procedure is proposed that is uniformly optimal among all sequential procedures which control the expected proportion of post-change streams at all time points. We also investigate the asymptotic behavior of the proposed method when the number of data streams grows large. Numerical examples are provided to illustrate the use and performance of the proposed method

Determining the number of factors in high-dimensional generalized latent factor models

As a generalization of the classical linear factor model, generalized latent factor models are useful for analysing multivariate data of different types, including binary choices and counts. This paper proposes an information criterion to determine the number of factors in generalized latent factor models. The consistency of the proposed information criterion is established under a high-dimensional setting, where both the sample size and the number of manifest variables grow to infinity, and data may have many missing values. An error bound is established for the parameter estimates, which plays an important role in establishing the consistency of the proposed information criterion. This error bound improves several existing results and may be of independent theoretical interest. We evaluate the proposed method by a simulation study and an application to Eysenck’s personality questionnaire

Spatial variation in aragonite saturation state and the influencing factors in Jiaozhou Bay, China

Both natural processes and human activities affect seawater calcium carbonate saturation state (Ωarag), while the mechanisms are still far from being clearly understood. This study analysed the seawater surface Ωarag during summer and winter in Jiaozhou Bay (JZB), China, based on two cruises observations performed in January and June 2017. The ranges of Ωarag values were 1.55~2.92 in summer and 1.62~2.15 in winter. Regression analyses were conducted to identify the drivers of the change of Ωarag distribution, and then the relative contributions of temperature, mixing processes and biological processes to the spatial differences in Ωarag were evaluated by introducing the difference between total alkalinity (TA) and dissolved inorganic carbon (DIC) as a proxy for Ωarag. The results showed that biological processes were the main factor affecting the spatial differences in Ωarag, with relative contributions of 70% in summer and 50% in winter. The contributions of temperature (25% in summer and 20% in winter) and the mixing processes (5% in summer and 30% in winter) were lower. The increasing urbanization in offshore areas can further worsen acidification, therefore environmental protection in both offshore and onshore is needed

Asymptotically optimal sequential design for rank aggregation

A sequential design problem for rank aggregation is commonly encountered in psychology, politics, marketing, sports, etc. In this problem, a decision maker is responsible for ranking K items by sequentially collecting noisy pairwise comparisons from judges. The decision maker needs to choose a pair of items for comparison in each step, decide when to stop data collection, and make a final decision after stopping based on a sequential flow of information. Because of the complex ranking structure, existing sequential analysis methods are not suitable. In this paper, we formulate the problem under a Bayesian decision framework and propose sequential procedures that are asymptotically optimal. These procedures achieve asymptotic optimality by seeking a balance between exploration (i.e., finding the most indistinguishable pair of items) and exploitation (i.e., comparing the most indistinguishable pair based on the current information). New analytical tools are developed for proving the asymptotic results, combining advanced change of measure techniques for handling the level crossing of likelihood ratios and classic large deviation results for martingales, which are of separate theoretical interest in solving complex sequential design problems. A mirror-descent algorithm is developed for the computation of the proposed sequential procedures