Efficient Monte Carlo simulation via the generalized splitting method

We describe a new Monte Carlo algorithm for the consistent and unbiased estimation of multidimensional integrals and the efficient sampling from multidimensional densities. The algorithm is inspired by the classical splitting method and can be applied to general static simulation models. We provide examples from rare-event probability estimation, counting, and sampling, demonstrating that the proposed method can outperform existing Markov chain sampling methods in terms of convergence speed and accuracy.     

White and nonwhite trends in first birth timing: Comparisons using vital registration and current population surveys

The magnitude of racial differences in first birth timing vary greatly depending upon the data sources from which they are estimated. Vital registration data (Heuser 1976; with updates from the National Center for Health Statistics 1974–1990) show that in recent years nonwhites have higher risks of a first birth at virtually all ages compared to whites. As a result very large and historically novel differentials in childlessness are forecast using these data (see Rindfuss et al. 1988; Chen & Morgan 1991; Morgan & Chen 1992). However, retrospective fertility history data collected from the 1980, 1985 and 1990 Current Population Surveys (CPS) suggest much smaller racial differences in completed childlessness and isolate racial differences in probabilities of first births at young ages. Differences also exist between theses two series for whites prior to the mid-1960s but not afterwards. Reasons for these differing estimates are suggested and examined. We conclude that a substantial portion of the differences result from an accumulation of biases in the vital registration estimates that affect primarily estimates of first birth timing. Thus, the CPS data provide a more firm basis for racial comparisons of first birth timing.     

The Ethnic Composition of Families in Russia in 1989: Insights into the Soviet “Nationalities Policy”

A sample from the 1989 Soviet census is used to study the ethnic composition of families in the Russian Federation on the eve of the breakup of the Soviet Union. The aim is to gain insight into the consequences of the Soviet “nationalities policy” through examining the marriage patterns of different ethnic groups and the nature of the relations between these groups. The analysis is based on general log-linear models. The main findings are: there was a relatively well-pronounced tendency toward endogamy; Russians were the least endoga-mous, while Chechens were the most endoga-mous among the 11 ethnic groups included in the analysis; “zones of attraction” related to exogamy were well discernible, the two most pronounced being within the Eastern Slav and Turkic groups; testing for cohort effects revealed a decrease in endogamy when older and middle cohorts were compared, while the differences between middle and younger cohorts were in many cases not statistically significant.     

Could Pronatalist Policies Discourage Childbearing?

This article builds on research in psychology, economics, and other fields, suggesting that, under certain conditions, extrinsic incentives could undermine intrinsic motivation, producing results opposite to those originally intended. It explores the relevance of these findings for population policies and particularly for pronatalist measures, and argues that reproductive behavior is intrinsically motivated, thus potentially subject to having the intrinsic motivation for childbearing adversely affected by policy interventions. Specifically, it examines whether, when, and how the contingency, universe, adequacy, and other aspects of pronatalist incentives could affect childbearing motivation. For example, parity‐targeted incentives seeking to compel higher fertility could be perceived as controlling and undermine that motivation. Conversely, policies seeking to facilitate combining work and family responsibilities could strengthen the intrinsic motivation for childbearing.     

Sequential Monte Carlo for counting vertex covers in general graphs

In this paper we describe a sequential importance sampling (SIS) procedure for counting the number of vertex covers in general graphs. The optimal SIS proposal distribution is the uniform over a suitably restricted set, but is not implementable. We will consider two proposal distributions as approximations to the optimal. Both proposals are based on randomization techniques. The first randomization is the classic probability model of random graphs, and in fact, the resulting SIS algorithm shows polynomial complexity for random graphs. The second randomization introduces a probabilistic relaxation technique that uses Dynamic Programming. The numerical experiments show that the resulting SIS algorithm enjoys excellent practical performance in comparison with existing methods. In particular the method is compared with cachet—an exact model counter, and the state of the art SampleSearch, which is based on Belief Networks and importance sampling.     

Nuptiality in the Course of the Demographic Transition: The Experience of the Balkan Countries

The paper examines marriage patterns in four Balkan countries during the course of the demographic transition. It is shown by analysis of the available data that cultural and institutional factors, such as family type, kinship structure or religious doctrines, alone, cannot explain adequately all the features of nuptiality in the region. Without denying the importance of the ‘cultural-institutional’ approach, it was found necessary to expand it by taking into account the distinctive historical and developmental context in a given country or region. It is argued that the relative importance of marriage postponement (and celibacy), birth control, and out-migration, as parts of a complex system of ‘adjustments’ to sustained population growth, was determined by the rate of this growth, as well as by the pace of socio-economic development and a number of other factors (including institutional and cultural ones). The experience of the Balkan countries is explored with this assumption as a background.     

Markov chain importance sampling with applications to rare event probability estimation

We present a versatile Monte Carlo method for estimating multidimensional integrals, with applications to rare-event probability estimation. The method fuses two distinct and popular Monte Carlo simulation methods—Markov chain Monte Carlo and importance sampling—into a single algorithm. We show that for some applied numerical examples the proposed Markov Chain importance sampling algorithm performs better than methods based solely on importance sampling or MCMC.