Direct and Indirect Causal Effects via Potential Outcomes*

Abstract. The use of the concept of ‘direct’ versus ‘indirect’ causal effects is common, not only in statistics but also in many areas of social and economic sciences. The related terms of ‘biomarkers’ and ‘surrogates’ are common in pharmacological and biomedical sciences. Sometimes this concept is represented by graphical displays of various kinds. The view here is that there is a great deal of imprecise discussion surrounding this topic and, moreover, that the most straightforward way to clarify the situation is by using potential outcomes to define causal effects. In particular, I suggest that the use of principal stratification is key to understanding the meaning of direct and indirect causal effects. A current study of anthrax vaccine will be used to illustrate ideas.     

Causal Reasoning from Longitudinal Data*

Abstract. This paper reviews some of the key statistical ideas that are encountered when trying to find empirical support to causal interpretations and conclusions, by applying statistical methods on experimental or observational longitudinal data. In such data, typically a collection of individuals are followed over time, then each one has registered a sequence of covariate measurements along with values of control variables that in the analysis are to be interpreted as causes, and finally the individual outcomes or responses are reported. Particular attention is given to the potentially important problem of confounding. We provide conditions under which, at least in principle, unconfounded estimation of the causal effects can be accomplished. Our approach for dealing with causal problems is entirely probabilistic, and we apply Bayesian ideas and techniques to deal with the corresponding statistical inference. In particular, we use the general framework of marked point processes for setting up the probability models, and consider posterior predictive distributions as providing the natural summary measures for assessing the causal effects. We also draw connections to relevant recent work in this area, notably to Judea Pearl's formulations based on graphical models and his calculus of so‐called do‐probabilities. Two examples illustrating different aspects of causal reasoning are discussed in detail.     

Conditional Likelihood Estimators for Hidden Markov Models and Stochastic Volatility Models

ABSTRACT.  This paper develops a new contrast process for parametric inference of general hidden Markov models, when the hidden chain has a non-compact state space. This contrast is based on the conditional likelihood approach, often used for ARCH-type models. We prove the strong consistency of the conditional likelihood estimators under appropriate conditions. The method is applied to the Kalman filter (for which this contrast and the exact likelihood lead to asymptotically equivalent estimators) and to the discretely observed stochastic volatility models.     

A circular-cone test for testing homogeneity against a simple tree order

Several methods exist for the problem of testing the equality of several treatments against the one-sided alternative that the treatments are better than the control. These methods include Dunnett's test, Bartholomew's likelihood-ratio test, the Abelson-Tukey-Schaafsma-Smid optimal-contrast test, and the multiple-contrast test of Mukerjee, Robertson, and Wright. A new test is proposed based on an approximation of the likelihood-ratio test of Bartholomew. This test involves using a circular cone in place of the alternative-hypothesis cone. The circular-cone test has excellent power characteristics similar to those of Bartholomew's test. Moreover, it has the advantages of being simpler to compute and may be used with unequal sample sizes.     

Bayesian analysis of outlier problems using divergence measures

A Bayesian approach is presented for detecting influential observations using general divergence measures on the posterior distributions. A sampling-based approach using a Gibbs or Metropolis-within-Gibbs method is used to compute the posterior divergence measures. Four specific measures are proposed, which convey the effects of a single observation or covariate on the posterior. The technique is applied to a generalized linear model with binary response data, an overdispersed model and a nonlinear model. An asymptotic approximation using Laplace method to obtain the posterior divergence is also briefly discussed.     

An integrated production and inventory model for a whole manufacturing supply chain involving reverse logistics with finite horizon period

This paper proposes a model and solution method for coordinating integrated production and inventory cycles in a whole manufacturing supply chain involving reverse logistics for multiple items with finite horizon period. A whole manufacturing supply chain involving reverse logistic consists of tier-2 suppliers supplying raw materials to tier-1 suppliers, tier-1 suppliers producing parts, a manufacturer which manufactures and assembles parts from tier-1 suppliers into finished products, distributors distributing finished products to retailers, retailers selling products to end customers and a third party which collects the used finished products from end customers, dissembles collected products into parts, and feed the parts back to the supply chain. In this system, we consider a finite horizon period. A mathematical model for representing the behaviors of the system is developed. Solution methods based on decentralized and a combination of decentralized and centralized decision making process, referred to as the semi-centralized decision making process, are proposed to solve the model while the centralized decision making process is solved by a mixed integer nonlinear programming method. A numerical example is used to demonstrate the model and the solutions based on the three types of the coordination.     

The Quality of Urban Environments in the Brazilian Amazon

In the Brazilian Amazon during the 1980s,urban population growth outstripped rural growth, andby 1991, most of the region's population resided inurban areas. Much of this urban growth involvedestablishment of unplanned housing with inadequateinfrastructure, which resulted in rising pollution. This paper compares indicators of environmentalquality in urban populations of the Amazon in 1980 and1991, and among different kinds of urban populationsin 1991. The results show that environmental qualityin the region deteriorated during the 1980s as theproduction of and exposure to environmental hazardsrose while resources to ward off hazards eroded. Thefindings also show that environmental quality wasparticularly poor in more rapidly growing urbancenters. The urban Amazon may not afford an adequatestandard of living and this may generate out-migrationfrom the region.     

从政府单一管理到综合治理——我国人口发展治理体系建设的政策分析

政府单一管理的传统计划生育管理体制已经不适应当今现实。根据社会治理理论,人口发展治理体系建设需要转换政府职能;缩小政府管制范围,扩大市场机制的应用范围和强度;激励公众参与,建立社会制衡机制。在具体的建设当中要注意处理好四对关系。     

Double Sampling Ratio-product Estimator of a Finite Population Mean in Sample Surveys

It is well known that two-phase (or double) sampling is of significant use in practice when the population parameter(s) (say, population mean X¯) of the auxiliary variate x is not known. Keeping this in view, we have suggested a class of ratio-product estimators in two-phase sampling with its properties. The asymptotically optimum estimators (AOEs) in the class are identified in two different cases with their variances. Conditions for the proposed estimator to be more efficient than the two-phase sampling ratio, product and mean per unit estimator are investigated. Comparison with single phase sampling is also discussed. An empirical study is carried out to demonstrate the efficiency of the suggested estimator over conventional estimators.