Learning from a lot: Empirical Bayes for high‐dimensional model‐based prediction

Empirical Bayes is a versatile approach to “learn from a lot” in two ways: first, from a large number of variables and, second, from a potentially large amount of prior information, for example, stored in public repositories. We review applications of a variety of empirical Bayes methods to several well‐known model‐based prediction methods, including penalized regression, linear discriminant analysis, and Bayesian models with sparse or dense priors. We discuss “formal” empirical Bayes methods that maximize the marginal likelihood but also more informal approaches based on other data summaries. We contrast empirical Bayes to cross‐validation and full Bayes and discuss hybrid approaches. To study the relation between the quality of an empirical Bayes estimator and p, the number of variables, we consider a simple empirical Bayes estimator in a linear model setting. We argue that empirical Bayes is particularly useful when the prior contains multiple parameters, which model a priori information on variables termed “co‐data”. In particular, we present two novel examples that allow for co‐data: first, a Bayesian spike‐and‐slab setting that facilitates inclusion of multiple co‐data sources and types and, second, a hybrid empirical Bayes–full Bayes ridge regression approach for estimation of the posterior predictive interval.     

Inference and optimal design of multiple constant-stress testing for generalized half-normal distribution under type-II progressive censoring

The generalized half-normal (GHN) distribution and progressive type-II censoring are considered in this article for studying some statistical inferences of constant-stress accelerated life testing. The EM algorithm is considered to calculate the maximum likelihood estimates. Fisher information matrix is formed depending on the missing information law and it is utilized for structuring the asymptomatic confidence intervals. Further, interval estimation is discussed through bootstrap intervals. The Tierney and Kadane method, importance sampling procedure and Metropolis-Hastings algorithm are utilized to compute Bayesian estimates. Furthermore, predictive estimates for censored data and the related prediction intervals are obtained. We consider three optimality criteria to find out the optimal stress level. A real data set is used to illustrate the importance of GHN distribution as an alternative lifetime model for well-known distributions. Finally, a simulation study is provided with discussion.     

重庆市都市区人中就业现状及变化趋势

都市区作为重庆经济的核心区域,随着经济的快速发展以及城市化进程的加快,正对人口产生巨大的聚集效应,而人口就业将成为一个十分突出的问题。因此,准确把握劳动力供求变动趋势十分重要。为此通过模型运算,对2000-2020年的都市区劳动年龄人口和劳动力的供求变动趋势进行了预测分析。     

中国上市公司财务预警实证研究

在对国外公司财务预警经典研究成果进行回顾和总结的基础上,运用多元判别分析方法（MDA）和逐步判别分析（Stepdisc）等方法逐层推进构造预测模型,以经济实用为选择标准,最终建立一个预测准确率最高、变量最少的适合中国实际情况的财务危机预测模型。     

Towards Enhancement of the Economy of a Thermal Power Generating System through Prediction of Plant Efficiency

The plant ‘Heat Rate’ (HR) is a measure of overall efficiency of a thermal power generating system. It depends on a large number of factors, some of which are non-measurable, while data relating to others are seldom available and recorded. However, coal quality (expressed in terms of ‘effective heat value’ (EHV) as kcal/kg) transpires to be one of the important factors that influences HR values and data on EHV are available in any thermal power generating system. In the present work, we propose a prediction interval of the HR values on the basis of only EHV, keeping in mind that coal quality is one of the important (but not the only) factors that have a pronounced effect on the combustion process and hence on HR. The underlying theory borrows the idea of providing simultaneous confidence interval (SCI) to the coefficients of a p-th p(≥1) order autoregressive model (AR(p)). The theory has been substantiated with the help of real life data from a power utility (after suitable base and scale transformation of the data to maintain the confidentiality of the classified document). Scope for formulating strategies to enhance the economy of a thermal power generating system has also been explored.     

Statistical Analyses and Modelling of the Mixing Process of Euro Coins in Germany and Europe

This paper reports on the mixing of Euro coins from different countries of origin in Europe, which started on 1 January 2002. There is an interesting conclusion: that the mobility of small and large denominations is different. The long‐term behaviour of the mixing process is studied using a simple deterministic model and data from Germany, France and the Netherlands. The analysis leads to predictions about the future progress of the mixing process.     

Statistik für bivariate gemischte Poisson–Prozesse am Beispiel der Kraftfahrthaftpflichtversicherung

Zusammenfassung: In diesem Artikel wird der Weg von einem univariaten gemischten Poisson–Prozess, der in vielen Bereichen zum Z?hlen von Ereignissen benutzt wird, zu einem bivariaten gemischten Poisson–Prozess aufgezeigt. Dazu werden einige Eigenschaften des bivariaten Prozesses angegeben. Im zweiten Teil der Arbeit wird gezeigt, wie mit Hilfe dieses Prozesses der übergang von einem herk?mmlichen Bonus–Malus–System in der Kraftfahrthaftpflichtversicherung zu einem Bonus–Malus–System mit Berücksichtigung der Schadenart beschritten werden kann. Dazu wird zuerst eine Modellprüfung der gegebenen Daten vorgenommen und sodann werden für verschiedene mischende Verteilungen die Verteilungsparameter gesch?tzt und Nettopr?mien angegeben sowie die Prognosegenauigkeit getestet.

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Summary: In this paper we show that the model of the bivariate mixed Poisson process arises in a natural way from the univariate mixed Poisson process, which is used in several areas for counting certain events. Furthermore we state some properties of the bivariate process. In the second part of the paper we illustrate how by means of the bivariate mixed Poisson process a bonus–malus system handling different types of accidents can be derived from the classical bonus–malus system in third–party liability insurance. To this end we first check the model on the given data and then estimate distribution parameters and compute net premiums for different mixing distributions as well as test the prediction probabilities.

* Vortrag am Dresdner Forum zur Versicherungsmathematik: Tarifierung in Erst- und Rückversicherung am 25. Juni 2004. Für die Unterstützung zu dieser Arbeit m?chte der Autor Lothar Partzsch, Klaus D. Schmidt (beide Dresden) und Friedemann Spies (München) recht herzlich danken.     

解码理论在日语听力理解中的运用

在日语学习中,因受语言环境和学习方法的限制,听力被认为是提高日语水平和成绩的一大难关。作者遵循听觉系统中听力的解码理论,以一年一度的国际日本语能力测试题为例,提出并具体分析了提高日语听力的三种模式———预测法、捕捉法和贯穿法,并指出运用这些技巧时应注意的几个问题。期望学习者能克服心理障碍,讲究科学的方法,把这些模式积极运用到平时的训练和测试中去,以此来提高日语听力水平和成绩。     

福建经济若干统计特征及发展趋势

选取福建省．1983年以来经济部分指标进行了统计分析。描述了一些指标的变化规律,划分了经济发展的阶段,采用新方法预测了2006年和2007年的经济指标,进而得出若干启示和分析结论。     

旅游城镇化与社会治理协同发展时空格局及趋势预测——以张家界市为例

利用耦合模型、重心-标准差椭圆及障碍度等方法,分析2009—2020年张家界市旅游城镇化与社会治理协同发展关系及时空格局,构建修正后的灰色马尔科夫模型,对未来十年旅游城镇化与社会治理耦合协调度进行精准预测。结果表明：（1）2009—2020年张家界市旅游城镇化水平呈先上升后下降态势,而社会治理综合发展水平则呈现较小波动变化特征,增速相对弱后于旅游城镇化水平。（2）旅游城镇化与社会治理的耦合协调度呈先上升后下降态势,经历了“一般失调—勉强协调—初级协调—良好协调—初级协调”的耦合类型转变过程,旅游城镇化超前型特征明显;从空间分异看,旅游城镇化与社会治理耦合协调度在东西和南北方向上是先扩大再收缩的态势,表现向武陵源区集聚的发展特征。（3）旅游城镇化系统的障碍度小于社会治理系统,从指标障碍度平均值看,第三产业产值比重＞第三产业就业人口比重＞旅游收入占GDP比重＞旅游人次＞每万人口交通事故死亡率。（4）未来十年张家界市旅游城镇化与社会治理耦合协调度将持续上升,但在2026年会有所下降,最终在2028年会处于优质耦合协调阶段。