大学生数学成绩影响因素的实证分析

伴随着近几年高校的扩大招生,部分大学生的数学成绩显著下降。用统计学软件SPSS 13.0对哈尔滨工程大学部分学生的高等数学成绩及其相关因素进行统计分析,考察学生的高考数学成绩、性别、生源所在地等因素对其大学数学成绩的影响。在给出了一些切实可行的对策和建议的同时,指出培养大学生学习的主动性和研究探索精神,已经成为当今高校教师和教育工作者培养高素质人才和提高教学水平的关键。     

Statistics in the elementary school

This paper discusses the role of statistics within an interdisciplinary program on real problem solving in elementary schools (through grade 8). We first describe some general features of the USMES (Unified Science and Mathematics for Elementary Schools) curriculum and some situations where the application of statistical principles and techniques can enter the program. Then we present our ideas concerning the kinds of statistical methods that are appropriate in this environment, and we discuss the use of this material with both elementary school students and elementary     

Nonparametric Inference for a Partially Observed Compartmental Process

Methods of nonparametric inference are proposed for a process with two transient and three absorbing states. It is assumed that the time of transitions between the transient states are unobservable. One area of applications is in epidemiology where the transient states correspond to healthy and ill, while the absorbing states correspond to types of death. It is the onset of illness which is not observable. An estimate is given for a cumulative hazard rate between the transient states, the exit hazard rates are estimated at a specific point in time and a statistic for comparing exit rates from the transient states is given.     

ESTIMATING COMPONENTS IN FINITE MIXTURES AND HIDDEN MARKOV MODELS

When the unobservable Markov chain in a hidden Markov model is stationary the marginal distribution of the observations is a finite mixture with the number of terms equal to the number of the states of the Markov chain. This suggests the number of states of the unobservable Markov chain can be estimated by determining the number of mixture components in the marginal distribution. This paper presents new methods for estimating the number of states in a hidden Markov model, and coincidentally the unknown number of components in a finite mixture, based on penalized quasi‐likelihood and generalized quasi‐likelihood ratio methods constructed from the marginal distribution. The procedures advocated are simple to calculate, and results obtained in empirical applications indicate that they are as effective as current available methods based on the full likelihood. Under fairly general regularity conditions, the methods proposed generate strongly consistent estimates of the unknown number of states or components.     

Modelling change in cognitive understanding with finite mixtures

Psychological theories often posit the existence of several different states. Individuals are viewed as belonging to one of the states at a given age, but with development pass to another state. A main problem in evaluating such theories is representing the transition from one state to another over age. A stochastic transition framework is proposed which should be useful in many different settings. The model is illustrated with data from a cognitive development task.     

适应经济发展的高校学科结构优化模型

文章利用1994~2003年的分学科高校在校生资料,进行一阶差分,用净增人数建立灰色动态模型,对2008年和2010年的在校生进行中期预测。并把分学科在校生与人均GDP的关联度作为灰色线性规划的贡献率灰数,优化出各学科在校生的结构。结果显示,需要适度减缓哲学、历史学、法学、经济学的发展速度,增加教育学、工学、医学的培养人数。     

Mixture models, latent variables and partitioned importance sampling

Gibbs sampling has had great success in the analysis of mixture models. In particular, the “latent variable” formulation of the mixture model greatly reduces computational complexity. However, one failing of this approach is the possible existence of almost-absorbing states, called trapping states, as it may require an enormous number of iterations to escape from these states. Here we examine an alternative approach to estimation in mixture models, one based on a Rao–Blackwellization argument applied to a latent-variable-based estimator. From this derivation we construct an alternative Monte Carlo sampling scheme that avoids trapping states.     

Estimation in a model for a semi-Markov process with covariates under right-censoring

A semi-Markov model with covariates is proposed for a multi-state process with a finite number of states such that the transition probabilities between the states and the distribution functions of the duration times between the occurrence of two states depend on a discrete covariate. The hazard rates for the time elapsed between two successive states depend on the covariate through a proportional hazards model involving a set of regression parameters, while the transition probabilities depend on the covariate in an unspecified way. We propose estimators for these parameters and for the cumulative hazard functions of the sojourn times. A difficulty comes from the fact that when a sojourn time in a state is right-censored, the next state is unknown. We prove that our estimators are consistent and asymptotically Gaussian under the model constraints.     

Monitoring contemporary student flows and characteristics: secondary analyses using the Labour Force Survey and the General Household Survey

This paper examines trends in the participation in higher education by disadvantaged social groups over the recent period of higher education expansion and reform. It has been suggested that disadvantaged groups can recoup by participation at mature ages and this question is examined. The data sources used are the Labour Force Survey (1986–1995), which yielded 13384 students (6747 men and 6637 women) and the General Household Survey (1984–1992) which yielded 1936 students (982 men and 954 women). From a perspective of equal opportunities, the relative participation of young people from manual and non-manual origins does not appear to have changed over the period considered, but there is some evidence of increased relative participation by people from manual class origins as mature students. Mature students from such origins were older than those from non-manual class origins, as were mature women than mature men, with consequences for employability. From a perspective of lifelong learning, the recent expansion has been successful, with more entrants from the unemployed. Considerable percentages of women also enter from full-time housework, and increasing percentages from manual work. However, as in the past, many entrants had been successful in becoming employed before entry, some being seconded by employers. Despite these changes, the greatest absolute take-up has been from middle class youth. Early employment outcomes were examined and suggest some discrimination against mature students. It is possible that the increased cost of higher education, in the context of an expanded labour market of graduates, may deter some mature students.     

Graduate Statistics Service Courses

This article describes our experience in, and recommendations for, teaching introductory statistics service courses to graduate students. Drawing on the student's research orientation, the instructor can present statistics as a valuable component of the scientific method, using examples from the student's particular discipline(s). Statistically qualified course instructors may be affiliated with statistics or other departments, and the course may be offered within any department. Course goals can range from training students to function independently as statistical analysts in future research to training students to consult a qualified statistician about design and analysis issues.     

VARIATIONAL BAYESIAN ANALYSIS FOR HIDDEN MARKOV MODELS

The variational approach to Bayesian inference enables simultaneous estimation of model parameters and model complexity. An interesting feature of this approach is that it also leads to an automatic choice of model complexity. Empirical results from the analysis of hidden Markov models with Gaussian observation densities illustrate this. If the variational algorithm is initialized with a large number of hidden states, redundant states are eliminated as the method converges to a solution, thereby leading to a selection of the number of hidden states. In addition, through the use of a variational approximation, the deviance information criterion for Bayesian model selection can be extended to the hidden Markov model framework. Calculation of the deviance information criterion provides a further tool for model selection, which can be used in conjunction with the variational approach.     

The effects of census undercount adjustment on congressional apportionment

"This article shows that undercount adjustment [of the 1990 U.S. census] will probably reallocate one [in] three House seats across the states. The adjustment's impact may depend on the method used and the assumptions underlying undercount estimates. Using regression analysis to reduce sampling error in undercount estimates from dual-systems analysis, however, eliminates sensitivity to all but the most extreme changes in assumptions. Generally, adjustment will more likely affect large states than small ones, and large states with proportionately many urban Black and Hispanic residents will likely gain seats at the expense of large states with few such residents."     

A Bayesian HMM with random effects and an unknown number of states for DNA copy number analysis

Hidden Markov models (HMMs) have been shown to be a flexible tool for modelling complex biological processes. However, choosing the number of hidden states remains an open question and the inclusion of random effects also deserves more research, as it is a recent addition to the fixed-effect HMM in many application fields. We present a Bayesian mixed HMM with an unknown number of hidden states and fixed covariates. The model is fitted using reversible-jump Markov chain Monte Carlo, avoiding the need to select the number of hidden states. We show through simulations that the estimations produced are more precise than those from a fixed-effect HMM and illustrate its practical application to the analysis of DNA copy number data, a field where HMMs are widely used.     

Class Size and Educational Policy: Who Benefits from Smaller Classes?

ABSTRACT

The impact of class size on student achievement remains an open question despite hundreds of empirical studies and the perception among parents, teachers, and policymakers that larger classes are a significant detriment to student development. This study sheds new light on this ambiguity by utilizing nonparametric tests for stochastic dominance to analyze unconditional and conditional test score distributions across students facing different class sizes. Analyzing the conditional distributions of test scores (purged of observables using class-size specific returns), we find that there is little causal effect of marginal reductions in class size on test scores within the range of 20 or more students. However, reductions in class size from above 20 students to below 20 students, as well as marginal reductions in classes with fewer than 20 students, increase test scores for students below the median, but decrease test scores above the median. This nonuniform impact of class size suggests that compensatory school policies, whereby lower-performing students are placed in smaller classes and higher-performing students are placed in larger classes, improves the academic achievement of not just the lower-performing students but also the higher-performing students.     

A network analysis of student mobility patterns from high school to master’s

Human migration involves the movement of people from one place to another. An example of undirected migration is Italian student mobility where students move from the South to the Center-North. This kind of mobility has become of general interest, and this work explores student mobility from Sicily towards universities outside the island. The data used in this paper regards six cohorts of students, from 2008/09 to 2013/14. In particular, our goal is to study the 3-step migration path: the area of origin (Sicilian provinces), the regional university for the bachelor’s degree, and the regional university for the master’s. Our analysis is conducted by building a multipartite network with four sets of nodes: students; Sicilian provinces; bachelor region of studies; and the master region of studies. By projecting the students’ set onto the others, we obtain a tripartite network where the number of students represents the link weight. Results show that the big Sicilian cities—Palermo, Catania, and Messina—have different preferential paths compared to small Sicilian cities. Furthermore, the results reveal preferential paths of 3-step mobility that only, in part, reflect a south-north orientation in the transition from the region of study for the bachelor degree to that for the master’s.

     

Assessing influential trade effects via high-frequency market reactions

In the literature, traders are often classified into informed and uninformed and the trades from informed traders have market impacts. We investigate these trades by first establishing a scheme to identify the influential trades from the ordinary trades under certain criteria. The differential properties between these two types of trades are examined via the four transaction states classified by the trade price, trade volume, quotes, and quoted depth. Marginal distribution of the four states and the transition probability between different states are shown to be distinct for informed trades and ordinary liquidity trades. Furthermore, four market reaction factors are introduced and logistic regression models of the influential trades are established based on these four factors. Empirical study on the high-frequency transaction data from the NYSE TAQ database show supportive evidence for high correct classification rates of the logistic regression models.     

Inventory model for convertible item with deterioration

Abstract

In this article, we developed a model for a convertible item (or product) where initial form of the item converts into another product by consuming conversion cost and time both. After duration, it converts again into a new product of a different nature. It is a sequential-type conversion from initial into two other products over states. The demand pattern and deterioration rate differ at each converted state. An inventory model is developed for such a kind of sequential convertible item. Expressions for total cost and other related costs (as per states) are derived and optimal time to convert the product in different states are calculated under model assumptions. A numerical example is incorporated in support of the theoretical findings and it validates the strength of the model.     

Testing for intercept‐scale switch in linear autoregression

Autoregressive models with switching regime are a frequently used class of nonlinear time series models, which are popular in finance, engineering, and other fields. We consider linear switching autoregressions in which the intercept and variance possibly switch simultaneously, while the autoregressive parameters are structural and hence the same in all states, and we propose quasi‐likelihood‐based tests for a regime switch in this class of models. Our motivation is from financial time series, where one expects states with high volatility and low mean together with states with low volatility and higher mean. We investigate the performance of our tests in a simulation study, and give an application to a series of IBM monthly stock returns. The Canadian Journal of Statistics 40: 427–446; 2012 © 2012 Statistical Society of Canada     

A grouped beta process model for multivariate resting‐state EEG microstate analysis on twins

EEG microstate analysis investigates the collection of distinct temporal blocks that characterize the electrical activity of the brain. Brain activity within each microstate is stable, but activity switches rapidly between different microstates in a nonrandom way. We propose a Bayesian nonparametric model that concurrently estimates the number of microstates and their underlying behaviour. We use a Markov switching vector autoregressive (VAR) framework, where a hidden Markov model (HMM) controls the nonrandom state switching dynamics of the EEG activity and a VAR model defines the behaviour of all time points within a given state. We analyze the resting‐state EEG data from twin pairs collected through the Minnesota Twin Family Study, consisting of 70 epochs per participant, where each epoch corresponds to 2 s of EEG data. We fit our model at the twin pair level, sharing information within epochs from the same participant and within epochs from the same twin pair. We capture within twin‐pair similarity, using an Indian buffet process, to consider an infinite library of microstates, allowing each participant to select a finite number of states from this library. The state spaces of highly similar twins may completely overlap while dissimilar twins could select distinct state spaces. In this way, our Bayesian nonparametric model defines a sparse set of states that describe the EEG data. All epochs from a single participant use the same set of states and are assumed to adhere to the same state switching dynamics in the HMM model, enforcing within‐participant similarity.