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Data sets with missing values bring great challenges to k-means clustering (KMC). At present, most studies focus on KMC data with low missing ratio while few studies on KMC data with high missing ratio. The current imputation methods have the following problems when dealing with the KMC data: (1) the error between imputation value and original true value is large, which leads to the poor imputation precision; (2) the imputation results have a great influence on the clustering results, which reduce the accuracies of the clustering results. We propose a novel imputation method, to deal with the problems, called as trimmed scores regression (TSR), which obtains an imputation estimator from a regression equation with a trimmed score matrix, and a novel cluster with k-means method. Compared with other imputation methods in numerical analysis, the TSR method exhibits better performance.

List of the previously identified 100 independent prostate cancer susceptibility SNPs.

Plot of the first two principal components for the 7,920 participants in the iCOGS dataset.

Background: We have developed a genome-wide association study analysis method called DEPTH (DEPendency of association on the number of Top Hits) to identify genomic regions potentially associated with disease by considering overlapping groups of contiguous markers (e.g., SNPs) across the genome. DEPTH is a machine learning algorithm for feature ranking of ultra-high dimensional datasets, built from well-established statistical tools such as bootstrapping, penalized regression, and decision trees. Unlike marginal regression, which considers each SNP individually, the key idea behind DEPTH is to rank groups of SNPs in terms of their joint strength of association with the outcome. Our aim was to compare the performance of DEPTH with that of standard logistic regression analysis.Methods: We selected 1,854 prostate cancer cases and 1,894 controls from the UK for whom 541,129 SNPs were measured using the Illumina Infinium HumanHap550 array. Confirmation was sought using 4,152 cases and 2,874 controls, ascertained from the UK and Australia, for whom 211,155 SNPs were measured using the iCOGS Illumina Infinium array.Results: From the DEPTH analysis, we identified 14 regions associated with prostate cancer risk that had been reported previously, five of which would not have been identified by conventional logistic regression. We also identified 112 novel putative susceptibility regions.Conclusions: DEPTH can reveal new risk-associated regions that would not have been identified using a conventional logistic regression analysis of individual SNPs.Impact: This study demonstrates that the DEPTH algorithm could identify additional genetic susceptibility regions that merit further investigation. Cancer Epidemiol Biomarkers Prev; 25(12); 1619–24. ©2016 AACR.

Technical details of the DEPTH procedure.

Time series data having low signal-to-noise ratio, non-stationarity and non-linearity are commonly seen in high-frequency stock trading, where the objective is to increase the likelihood of profit by taking advantage of tiny discrepancies in prices and trading on them quickly and in huge quantities. For this purpose, it is essential to apply a trading method that is capable of fast and accurate prediction from such time series data. In this paper, we develop an online time series forecasting method for high-frequency trading (HFT) by integrating three neural network deep learning models, i.e., Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU) and Transformer; and we abbreviate the new method to online LGT or O-LGT. The key innovation underlying our method is its efficient storage management, which enables super-fast computing. Specifically, when computing the forecast for the immediate future time, we use only the output calculated from the previous trading data (rather than the previous trading data themselves) together with the current trading data. Thus, the computing involves updating only the current data into the process. We evaluate the performance of O-LGT by analyzing the high-frequency Limit Order Book (LOB) data from the China market. It shows that our model in most cases achieves similar speed with much higher accuracy than the conventional fast supervised learning models for HFT. However, with a slight sacrifice in accuracy, O-LGT is approximately 40 times faster than the existing high-accuracy neural network models for the LOB data in China market.

This study aims to develop a general framework for predicting the duration of the Turning Period (or Turning Phase) for the COVID-19 outbreak in China that started in late December 2019 from Wuhan. A new concept called the Term Structure for Turning Period (instead of Turning Point) is used for this study, and the framework, implemented into an individual SEIR (iSEIR) model, has enabled a timely prediction of the turning period when applied to Wuhan's COVID-19 epidemic, and provided the opportunity for relevant authorities to take appropriate and timely actions to successfully control the epidemic. By using the observed daily COVID-19 cases in Wuhan from January 23, 2020 to February 6 (and February 10), 2020 as inputs to the framework it allowed us to generate the trajectory of COVID-19 dynamics and to predict that the Turning Period of COVID-19 outbreak in Wuhan would arrive within one week after February 14. This prediction turned out to be timely and accurate, which has provided adequate time for the government, hospitals and related sectors and services to meet peak demand and to prepare aftermath planning. We want to emphasize that emergency risk management entails the implementation of an emergency plan, where timing the Turning Period is key to express a clear timeline for effective actions. Our study confirms the observed effectiveness of Wuhan's Lockdown and Isolation control program imposed since January 23, 2020 to the middle of March, 2020 and resulted in swiftly flattened epidemic curve, and Wuhan's success offers an exemplary lesson for the world to learn in combating COVID-19 pandemic.

Finding associations between genetic markers and a phenotypic trait such as coronary artery disease (CAD) is of primary interest in genome-wide association studies (GWAS). A major challenge in GWAS is the involved genomic data often contain large number of genetic markers and the underlying genotype-phenotype relationship is mostly complex. Current statistical and machine learning methods lack the power to tackle this challenge with effectiveness and efficiency. In this paper we develop a stochastic search method to mine the genotype-phenotype associations from GWAS data. The new method generalizes the well-established association rule mining (ARM) framework for searching for the most important genotype-phenotype association rules, where we develop a multinomial Gibbs sampling algorithm and use it together with the Apriori algorithm to overcome the overwhelming computing complexity in ARM in GWAS. Three simulation studies based on synthetic data are used to assess the performance of our developed method, delivering the anticipated results. Finally, we illustrate the use of the developed method through a case study of CAD GWAS.

In recent years, big datasets are often split into several subsets due to the storage requirements. We propose a parallel group Bayesian method for statistical inference in sparse big data. This method improves the existing methods in two aspects: the total datasets are also split into a data subset sequence and the parameter vector is divided into several sub-vectors. Besides, we add a weight sequence to optimize the sub-estimators when each of them has a different covariance matrix. We obtain several theoretical properties of the estimator. The results of numerical simulations show that our method is consistent with the theoretical results and is more effective than classic Markov chain Monte Carlo methods.

This research develops a scalable computing method based on quasi-Newton algorithm for several estimation problems in dynamic generalised linear models (DGLMs). The new method is developed by applying the principle of maximising a pointwise penalised quasi-likelihood (PPQ) for a DGLM for observed data often of massive size. Statistical and computational challenges involved in this development have been effectively tackled by exploiting the specific block structure and sparsity involved in the underlying projection matrix. The obtained maximum PPQ estimator of the state vector in the DGLM has been shown to be consistent and asymptotically normal under regularity conditions. Numerical studies and real data applications are conducted to assess the performance of the developed method.

Distributed interval estimation in linear regression may be computationally infeasible in the presence of big data that are normally stored in different computer servers or in cloud. The existing challenge represents the results from the distributed estimation may still contain redundant information about the population characteristics of the data. To tackle this computing challenge, we develop an optimization procedure to select the best subset from the collection of data subsets, based on which we perform interval estimation in the context of linear regression. The procedure is derived based on minimizing the length of the final interval estimator and maximizing the information remained in the selected data subset, thus is named as the LIC criterion. Theoretical performance of the LIC criterion is studied in this paper together with a simulation study and real data analysis.

High-dimensional, non-stationary vector time-series data are often seen in ground motion monitoring of geo-hazard events, e.g., landslides. For timely and reliable forecasts from such data, we developed a new statistical approach based on two advanced econometric methods, i.e., error-correction cointegration (ECC) and vector autoregression (VAR), and a newly developed dimension reduction technique named empirical dynamic quantiles (EDQ). Our ECC–VAR–EDQ method was born by analyzing a big landslide dataset, comprising interferometric synthetic-aperture radar (InSAR) measurements of ground displacement that were observed at 5090 time states and 1803 locations on a slope. The aim was to develop an early warning system for reliably forecasting any impending slope failure whenever a precursory slope deformation is on the horizon. Specifically, we first reduced the spatial dimension of the observed landslide data by representing them as a small set of EDQ series with negligible loss of information. We then used the ECC–VAR model to optimally fit these EDQ series, from which forecasts of future ground motion can be efficiently computed. Moreover, our method is able to assess the future landslide risk by computing the relevant probability of ground motion to exceed a red-alert threshold level at each future time state and location. Applying the ECC–VAR–EDQ method to the motivating landslide data gives a prediction of the incoming slope failure more than 8 days in advance.

Uncovering hidden change-points in an observed signal sequence is challenging both mathematically and computationally. We tackle this by developing an innovative methodology based on Markov chain Monte Carlo and statistical information theory. It consists of an empirical Bayesian information criterion (emBIC) to assess the fitness and virtue of candidate configurations of change-points, and a stochastic search algorithm induced from Gibbs sampling to find the optimal change-points configuration. Our emBIC is derived by treating the unknown change-point locations as latent data rather than parameters as is in traditional BIC, resulting in significant improvement over the latter which is known to mostly over-detect change-points. The use of the Gibbs sampler induced search enables one to quickly find the optimal change-points configuration with high probability and without going through computationally infeasible enumeration. We also integrate the Gibbs sampler induced search with a current BIC-based change-points sequential testing method, significantly improving the method’s performance and computing feasibility. We further develop two comprehensive 3-step computing procedures to implement the proposed methodology for practical use. Finally, simulation studies and real examples analyzing business and genetic data are presented to illustrate and assess the procedures.

Satellite imagery provides estimates for the amount of precipitation that has occurred in a region, these estimates are then used in models for predicting future precipitation trends. As these satellite images only provide an estimate for the amount of precipitation that has occurred, it is important that they be accurate estimates. If we assume that a rain gauge correctly measures the amount of precipitation that has occurred in some location over a specified time interval, then we can compare the satellite precipitation estimate to the gauge measurement for the same time interval. By expressing the relationship between the gauge measurement and the satellite precipitation estimate for the same time interval as a linear equation we can then spatially map the coefficients of this linear relationship to inspect the spatial trends of the regression coefficients. We then model the coefficients of the linear equations of each location by a spatial linear model and then use this model to predict the coefficients in location where there are no rain gauges available.

Based on a new concept called “Turning Period”, the goal of this report is to show how we can conduct the prediction for the outlook in the different stages for the battle with outbreak of COVID-19 currently in US, in particular, to identify when each of top 15 states in USA (basically on their populations) is going to enter into the stage that the outbreak of COVID-19 is under the control by the criteria such as daily change of new patients is less than 10% smoothly. Indeed, based on the data of April 10, 2020 with the numerical analysis, we are able to classify 15 states of US into the following four different categories for the Prevention and Control of Infectious Diseases Today and the main conclusion are:First, staring around April 14, 20202, three states which are Washington State, Louisiana and Indiana are entering the stage that the outbreak of COVID-19 is under the control, which means daily change of new patients is less than 10% and the gamma is less than zero in general.Second, staring aroundApril15, 20202, two states which are New Jersey, and New York are entering the stage that the outbreak of COVID-19 is under the control, which means daily change of new patients is less than 10% and the gamma is less than zero in general.Third, staring aroundApril16, 20202, seven states which are California, Florida, Georgia (GA), Illinois, Maryland, Indiana, Michigan, and Pennsylvania are entering the stage that the outbreak of COVID-19 is under the control, which means daily change of new patients is less than 10% and the gamma is less than zero in general.Fourth, staring aroundApril17, 20202, three states which are Texas, Massachusetts, and Connecticut are entering the stage that the outbreak of COVID-19 is under the control, which means daily change of new patients is less than 10% and the gamma is less than zero in general.Finally, we want to reinforce that emergency risk management is always associated with the implementation of an emergency plan. The identification of the Turning Time Period is key to emergency planning as it provides a timeline for effective actions and solutions to combat a pandemic by reducing as much unexpected risk as soon as possible.

The goal of this study is to establish a general framework for predicting the so-called critical “Turning Period” in an infectious disease epidemic such as the COVID-19 outbreak in China early this year. This framework enabled a timely prediction of the turning period when applied to Wuhan COVID-19 epidemic and informed the relevant authority for taking appropriate and timely actions to control the epidemic. It is expected to provide insightful information on turning period for the world’s current battle against the COVID-19 pandemic.The underlying mathematical model in our framework is the individual Susceptible-Exposed-Infective-Removed (iSEIR) model, which is a set of differential equations extending the classic SEIR model. We used the observed daily cases of COVID-19 in Wuhan from February 6 to 10, 2020 as the input to the iSEIR model and were able to generate the trajectory of COVID-19 cases dynamics for the following days at midnight of February 10 based on the updated model, from which we predicted that the turning period of CIVID-19 outbreak in Wuhan would arrive within one week after February 14. This prediction turned to be timely and accurate, providing adequate time for the government, hospitals, essential industry sectors and services to meet peak demands and to prepare aftermath planning.Our study also supports the observed effectiveness on flatting the epidemic curve by decisively imposing the “Lockdown and Isolation Control Program” in Wuhan since January 23, 2020. The Wuhan experience provides an exemplary lesson for the whole world to learn in combating COVID-19.

Based on a new concept called “ Turning Period”, the goal of this report is to show how we can conduct the prediction for the outlook in the different stages for the battle with outbreak of COVID-19 currently worldwide. Indeed, based on the data of April 9, 2020 with the numerical analysis, we are able to classify 13 countries in Europe fighting with COVID-19 into three different categories stages for the Prevention and Control of Infectious Diseases Worldwide Today. We want to reinforce that emergency risk management is always associated with the implementation of an emergency plan. The identification of the Turning Time Period is key to emergency planning as it provides a timeline for effective actions and solutions to combat a pandemic by reducing as much unexpected risk as soon as possible.

The goal of this study is to establish a general framework for predicting the so-called critical Turning Period in an infectious disease epidemic such as the COVID-19 outbreak in China early this year. This framework enabled a timely prediction of the turning period when applied to Wuhan COVID-19 epidemic and informed the relevant authority for taking appropriate and timely actions to control the epidemic. It is expected to provide insightful information on turning period for the world's current battle against the COVID-19 pandemic. The underlying mathematical model in our framework is the individual Susceptible-Exposed- Infective-Removed (iSEIR) model, which is a set of differential equations extending the classic SEIR model. We used the observed daily cases of COVID-19 in Wuhan from February 6 to 10, 2020 as the input to the iSEIR model and were able to generate the trajectory of COVID-19 cases dynamics for the following days at midnight of February 10 based on the updated model, from which we predicted that the turning period of CIVID-19 outbreak in Wuhan would arrive within one week after February 14. This prediction turned to be timely and accurate, providing adequate time for the government, hospitals, essential industry sectors and services to meet peak demands and to prepare aftermath planning. Our study also supports the observed effectiveness on flatting the epidemic curve by decisively imposing the Lockdown and Isolation Control Program in Wuhan since January 23, 2020. The Wuhan experience provides an exemplary lesson for the whole world to learn in combating COVID-19., Comment: 24 paages, 9 figures, 10 tables

Variable selection for short-term forecasting (up to 72 h) of tropical cyclone (TC) genesis has been investigated. IBTrACS data (1979–2014) are used to identify the genesis time and position of over 2500 TCs between 30°N and 30°S. Tracks are extended using a tropical cloud cluster (TCC) dataset, which is also used to identify over 28 000 nondeveloping TCCs. Subsequently, corresponding local environment states at various atmospheric pressure levels are retrieved from ERA-Interim data. An initial selection of potentially favorable variables for TC genesis is made based on mutual information, which forms the set of nodes for graphical model structure learning using the Peter–Clark (PC) algorithm. Structure learning identifies the variables with the strongest influence on TC genesis, while taking into account the interrelationship with other variables. Variables are ranked based on the maximum observed p value in all (conditional) independence tests of the variable with the TC genesis node. The results indicate that potential vorticity (600 hPa), relative vorticity (925 hPa), and (vector) vertical wind shear (200–700 hPa) are the highest ranked variables for forecasting up to 72 h. These are followed by the basin and zonal wind speed (200 hPa), and for very short lead-time divergence (925 hPa), air temperature (300 hPa), and average vertical velocity. Predictive modeling with logistic regression confirms the superior performance of the top-ranked variables. The presented variable ranking (methodology) can be used as a building block for the creation of genesis indices or predictive models in the future.

A tropical cyclone (TC) making landfall at a populated coastal area can cause both loss of life and damage to infrastructure and the natural environment. Wind field models which accurately describe the spatial distribution of TC wind speeds can assist in reducing some of these risks, by identifying the most dangerous locations with respect to damaging winds. Existing models either have limitations in describing the skewness of the wind field or do not have the flexibility to incorporate multiple wind observations. We developed a new mathematical model to represent the temporal-spatial distribution of near-surface wind speeds in a TC over an open ocean that captures asymmetries in both the eyewall and tail of the wind profile. The model formulation is flexible, with options for a generic fit or inclusion of extra observations to achieve a fit with higher accuracy and has tuning parameters for calibration to wind observations. Utilising several covariates that could be obtained from satellite remote sensing data, we derive anchor points that the wind profile should pass through. Next, polar coordinate based cubic splines that minimise modified discontinuity energy and preserve specified shape constraints are used to model the wind speeds profile, which is formulated as solving several linear programming problems. Appropriate formulation adjustments are made for clockwise and counterclockwise rotations of air around a TC centre in the Southern and Northern Hemispheres, respectively. Model performance of the generic fit is tested using near-surface wind observations at automatic weather stations. Comparison with an earlier developed wind model shows that the spline model produces more accurate wind estimates near the radius of maximum winds. Although the spline model describes TC wind speeds over water well, a limitation is its inability to capture reduction in wind speeds caused by terrain friction. Overall, the spline model can be used successfully to describe TC wind speeds over waters.

Statistical inference for dynamic generalized linear models (DGLMs) is challenging due to the time varying nature of the unknown parameters in these models. In this paper, we focus on the covariance matrix and the transfer function, the two key components in DGLMs. We first establish some convergence results for the covariance matrix estimation. We then provide an in-depth study of the transfer function on its stability and Fourier transformation, which is necessary for parameter estimation in DGLMs. Implications of our results on estimation in DGLMs are illustrated in the paper through a simulation study and a real data example. Our understanding on DGLMs has substantially improved though this study.

We develop a new stochastic spatio-temporal cointegration (SSTC) framework to model spatial and temporal dependence dynamics in high-dimensional non-stationary spatio-temporal data of geological hazards. Such data, often collected from real-time remote sensing, are common in complex geophysical systems such as landslides, earthquakes and volcano eruptions. Our framework employs cointegrated vector autoregression to characterize the spatial–temporal dependence dynamics with error-correction. The framework is justified both statistically and by the domain mechanism underlying the data. By applying the SSTC method to only a small number of empirical dynamic quantile series that summarize the original large-scale data, we have achieved computational scalability with insignificant loss of spatio-temporal dynamic information. In this paper, we focus on deriving the SSTC framework and estimating the best SSTC model(s) by the maximum quasi-likelihood principle. We demonstrate the forecasting efficacy by applying our SSTC framework to radar data comprising displacement measurements recorded at 1803 locations and 5090 time states over 21.5 days. Broadly, our results provide new insights on modeling, dimension-reduction, estimation and prediction in large-scale and non-stationary, spatio-temporal data analytics. Regarding landslide forecasting, this study delivers much-needed results for timely predictions of dynamics of an impending landslide from big and dense spatio-temporal data.

Consistency and run-time are important questions in performing multiple linear regression models. In response, we introduce a new parallel maximum likelihood estimator for multiple linear models. We first provide an equivalent condition between the method and the generalized least squares estimator. We also consider the rank of projections and the eigenvalue. We then present consistency when a stable solution exists. In this paper, we describe several consistency theorems and perform experiments on consistency, outlier, and scalability. Finally, we fit the proposed method onto bankruptcy data.

In this paper we develop a non-conventional statistical test for the change-point in a mean model by making use of an almost-sure (a.s.) convergence (or strong convergence) result that we obtain, in respect of the difference between the sums of squared residuals under the null and alternative hypotheses. We prove that both types of error probabilities of the new test converge to zero almost surely when the sample size goes to infinity. This result does not hold for any conventional statistical test where the type I error probability, i.e. the significance level or the size, is prescribed at a low but non-zero level (e.g. 0.05). The test developed is easy to use in practice, and is ready to be generalised to other change-point models provided that the relevant almost-sure convergence results are available. We also provide a simulation study in the paper to compare the new and conventional tests under different data scenarios. The results obtained are consistent with our asymptotic study. In addition we provide least squares estimators of those parameters used in the change-point test together with their almost-sure convergence properties. © 2013 Australian Statistical Publishing Association Inc.Pty Ltd..

Background: We have developed a genome-wide association study analysis method called DEPTH (DEPendency of association on the number of Top Hits) to identify genomic regions potentially associated with disease by considering overlapping groups of contiguous markers (e.g., SNPs) across the genome. DEPTH is a machine learning algorithm for feature ranking of ultra-high dimensional datasets, built from well-established statistical tools such as bootstrapping, penalized regression, and decision trees. Unlike marginal regression, which considers each SNP individually, the key idea behind DEPTH is to rank groups of SNPs in terms of their joint strength of association with the outcome. Our aim was to compare the performance of DEPTH with that of standard logistic regression analysis. Methods: We selected 1,854 prostate cancer cases and 1,894 controls from the UK for whom 541,129 SNPs were measured using the Illumina Infinium HumanHap550 array. Confirmation was sought using 4,152 cases and 2,874 controls, ascertained from the UK and Australia, for whom 211,155 SNPs were measured using the iCOGS Illumina Infinium array. Results: From the DEPTH analysis, we identified 14 regions associated with prostate cancer risk that had been reported previously, five of which would not have been identified by conventional logistic regression. We also identified 112 novel putative susceptibility regions. Conclusions: DEPTH can reveal new risk-associated regions that would not have been identified using a conventional logistic regression analysis of individual SNPs. Impact: This study demonstrates that the DEPTH algorithm could identify additional genetic susceptibility regions that merit further investigation. Cancer Epidemiol Biomarkers Prev; 25(12); 1619–24. ©2016 AACR.

The Bayesian horseshoe estimator is known for its robustness when handling noisy and sparse big data problems. This paper presents two extensions of the regular Bayesian horseshoe: (i) the grouped Bayesian horseshoe and (ii) the hierarchical Bayesian grouped horseshoe. The advantages of the proposed methods are their flexibility in handling grouped variables through extra shrinkage parameters at the group and within-group levels. We apply the proposed methods to the important class of additive models where group structures naturally exist, and we demonstrate that the grouped hierarchical Bayesian horseshoe has promising performance on both simulated and real data.

Testing the association between a phenotype and many genetic variants from case-control data is essential in genome-wide association study (GWAS). This is a challenging task as many such variants are correlated or non-informative. Similarities exist in testing the population difference between two groups of high dimensional data with intractable full likelihood function. Testing may be tackled by a maximum composite likelihood (MCL) not entailing the full likelihood, but current MCL tests are subject to power loss for involving non-informative or redundant sub-likelihoods. In this paper, we develop a forward search and test method for simultaneous powerful group difference testing and informative sub-likelihoods composition. Our method constructs a sequence of Wald-type test statistics by including only informative sub-likelihoods progressively so as to improve the test power under local sparsity alternatives. Numerical studies show that it achieves considerable improvement over the available tests as the modeling complexity grows. Our method is further validated by testing the motivating GWAS data on breast cancer with interesting results obtained., Comment: 31 pages, 5 figures

Regression clustering is a mixture of unsupervised and supervised statistical learning and data mining method which is found in a wide range of applications including artificial intelligence and neuroscience. It performs unsupervised learning when it clusters the data according to their respective unobserved regression hyperplanes. The method also performs supervised learning when it fits regression hyperplanes to the corresponding data clusters. Applying regression clustering in practice requires means of determining the underlying number of clusters in the data, finding the cluster label of each data point, and estimating the regression coefficients of the model. In this paper, we review the estimation and selection issues in regression clustering with regard to the least squares and robust statistical methods. We also provide a model selection based technique to determine the number of regression clusters underlying the data. We further develop a computing procedure for regression clustering estimation and selection. Finally, simulation studies are presented for assessing the procedure, together with analyzing a real data set on RGB cell marking in neuroscience to illustrate and interpret the method.

We propose a dynamic model for the evolution of an open animal population that is subject to an environmental catastrophe. The model incorporates a capture-recapture experiment often conducted for studying wildlife population, and enables inferences on the population size and possible effect of the catastrophe. A Bayesian approach is used to model unobserved quantities in the problem as latent variables and Markov chain Monte Carlo (MCMC) is used for posterior computation. Because the particular interrelationship between observed and latent variables negates the feasibility of standard MCMC methods, we propose a hybrid Monte Carlo approach that integrates a Gibbs sampler with the strategies of sequential importance sampling (SIS) and acceptance-rejection (AR) sampling for model estimation. We develop results on how to construct effective proposal densities for the SIS scheme. The approach is illustrated through a simulation study, and is applied to data from a mountain pygmy possum (Burramys Parvus) population that was affected by a bushfire.

A setwise Gibbs sampler (SGS) method is developed to simulate stationary distributions and performance measures of network occupancy of Baskett-Chandy-Muntz-Palacios (BCMP) telecommunication models. It overcomes the simulation difficulty encountered in applying the standard Gibbs sampler to closed BCMP networks with constant occupancy constraints. We show Markov chains induced by SGS converge to the target stationary distributions. This article also investigates the filtered Gibbs sampler (FGS) as an efficient method for estimating various network performance measures. It shows that FGS's efficiency is considerable, but may be improperly overestimated. A more conservative performance estimator is then presented.

This paper studies the problem of estimating the number of clusters in the context of logistic regression clustering. The classification likelihood approach is employed to tackle this problem. A model-selection based criterion for selecting the number of logistic curves is proposed and its asymptotic property is also considered. The small sample performance of the proposed criterion is studied by Monto Carlo simulation. In addition, a real data example is presented.