Convergence of Heavy-tailed Monte Carlo Markov Chain Algorithms

Abstract.  In this paper, we use recent results of Jarner & Roberts ( Ann. Appl. Probab., 12, 2002, 224) to show polynomial convergence rates of Monte Carlo Markov Chain algorithms with polynomial target distributions, in particular random-walk Metropolis algorithms, Langevin algorithms and independence samplers. We also use similar methodology to consider polynomial convergence of the Gibbs sampler on a constrained state space. The main result for the random-walk Metropolis algorithm is that heavy-tailed proposal distributions lead to higher rates of convergence and thus to qualitatively better algorithms as measured, for instance, by the existence of central limit theorems for higher moments. Thus, the paper gives for the first time a theoretical justification for the common belief that heavy-tailed proposal distributions improve convergence in the context of random-walk Metropolis algorithms. Similar results are shown to hold for Langevin algorithms and the independence sampler, while results for the mixing of Gibbs samplers on uniform distributions on constrained spaces are rather different in character.     

Return Migrations of African‐Americans to the South: Reclaiming a Land of Promise,Going Home,or Both?*

Abstract Using samples of census data from the University of Minnesota Population Center's “Integrated Public Use Microdata Series” (IPUMS), we describe trends in African‐American migration to the South across recent decades, and explore the applicability of the concept of “return migration” to various demographic patterns. Our findings suggest that the return movement contains multiple migration streams involving African‐Americans of higher socio‐economic status (compared with both origin and destination populations) moving to both urban and rural destinations. These patterns represent clear differences from the earlier 20^th century's “Great Migration” of African‐Americans from South to North. The recent return migration streams suggest that the South may be replacing the North as a “land of promise” for some upwardly mobile African‐Americans, and may also reflect what Carol Stack (1996) has termed a “call to home” as a motivating factor shaping recent African‐American migration to the rural South.     

From leprosy to The Willow Tree: decoding disability and Islamic spirituality in Iranian film

The lack of attention in academic discourse to representations of disability in films from the Middle East has led to an incomplete picture of representations of disability in global cinema. For instance, the diverse meanings of disability in Iranian cinema and the influence of disability on the emergence of Iranian New Wave cinema have been almost completely ignored by scholars. A number of award-winning films from Iran have featured disability as central to their narratives – such as The House is Black (1963), Taste of Cherry (1997), The Color of Paradise (1999), The Willow Tree (2005), and The Painting Pool (2013). Disability in these films serves alternatively as a symbol of spiritual possibility, a mark of marginalization, and a covert social critique. These films examine the emotional, physical, and social implications of disability, while celebrating the cultural power of film to challenge social, religious, and artistic barriers.     

In the path of heroes: second-generation Tamil-Canadians after the LTTE

This paper explores how second-generation Tamil-Canadian university students have modified their ‘cultural heritage’ in the period after the defeat of the Liberation Tigers of Tamil Eelam (LTTE) in May 2009. Using a generational framework suggested by the work of Karl Mannheim, I show that the events of May 2009 situated second-generation Tamil-Canadian political activism as a response to the ambivalence of their parents to the conflict in Sri Lanka. Second-generation Tamil-Canadians are also shown to have altered the key LTTE symbol of the Maaveerar (great hero) to better fit a transnational social field that is framed by the new realities of post-LTTE Sri Lanka and by intolerance to imported conflict in Canada. I argue that the Tamil second generation is highly engaged with the politics of their cultural identity, and that this engagement may have a lasting influence on transnational Tamil identity and on the political status of the Tamil community within Canada.     

New flexible models generated by gamma random variables for lifetime modeling

In this paper we introduce a new three-parameter exponential-type distribution. The new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have constant, decreasing, increasing, upside-down bathtub and bathtub-shaped hazard rate functions. It also generalizes some well-known distributions. We discuss maximum likelihood estimation of the model parameters for complete sample and for censored sample. Additionally, we formulate a new cure rate survival model by assuming that the number of competing causes of the event of interest has the Poisson distribution and the time to this event follows the proposed distribution. Maximum likelihood estimation of the model parameters of the new cure rate survival model is discussed for complete sample and censored sample. Two applications to real data are provided to illustrate the flexibility of the new model in practice.     

Generalized Estimation of the BLUP in Mixed-Effects Models: A Comparison with ML and REML

The Best Linear Unbiased Predictor (BLUP) in mixed models is a function of the variance components and they are estimated using maximum likelihood (ML) or restricted ML methods. Nonconvergence of BLUP would occur due to a drawback of the standard likelihood-based approaches. In such situations, ML and REML either do not provide any BLUPs or all become equal. To overcome this drawback, we provide a generalized estimate (GE) of BLUP that does not suffer from the problem of negative or zero variance components, and compare its performance against the ML and REML estimates of BLUP. Simulated and published data are used to compare BLUP.     

Preliminary Development and Validation of the Social and Emotional Health Survey for Secondary School Students

This study reports on the preliminary development and validation of the Social and Emotional Health Survey (SEHS) with a sample of 4,189 (51 % female) California students in Grades 8, 10, and 12. The SEHS was designed to measure the psychological building blocks of adolescents’ positive mental health and is operationalized in the present study by a theoretical model comprised of 12 measured indicators that form four first-order domains (belief-in-self, belief-in-others, emotional competence, and engaged living) that, in turn, contribute to one underlying, second-order meta-construct called covitality. This study was the first to investigate the validity and utility of the adolescent covitality construct, which is conceptualized as the synergistic effect of positive mental health resulting from the interplay among multiple positive-psychological building blocks. Findings from confirmatory factor analyses, invariance analysis, and latent means testing all supported the theoretical model underlying the SEHS, indicating that the second-order covitality model was the best fit for both males and females. Results from a path-modeling analysis indicated that covitality was a strong predictor of students’ subjective well-being (operationalized as a composite of life satisfaction, positive affect, and negative affect), and findings from additional concurrent validity analyses indicated that adolescents’ covitality level was significantly associated with self-reported academic achievement, perceptions of school safety, substance use, and experiences of depressive symptoms. Implications for theory, practice, and future research are discussed.     

从葛逻禄到喀喇汗王朝

葛逻禄是由三个部落组成的联盟,唐代时分属唐朝4个都督府管辖。从766年起葛逻禄成为伊斯兰世界的紧邻,并在中亚形成一种势力。840年蒙古高原的回纥汗国灭亡,回纥散往四方,其一支逃往葛逻禄避难。喀喇汗王朝是葛逻禄统治者接受了回纥汗国阿史那汗族（或“阿夫拉西亚勃家族”的一支）归这一家族所有的可汗职位。在伊斯兰历史著作中有三条关于萨曼王朝的伊斯玛因于893年对西部喀喇汗国战争的报道,它们可以相互补充。此外,这三个报道中还有关于喀喇汗王朝与葛逻禄为同一部族的重要情报。     

Children's influence on household economic activity in Nigeria

This study estimates the effects of children's economic contributions on parents' allocation of time for income-earning activities, care of preschool children, non-income home production, and leisure activities in Ile-Ife, Nigeria. Fathers spent 65% of work time, mothers 20%, and children 15% during the assessment of family time allocation and income contribution. Demographic factors affecting the parents' time for the children include age of parents, age and sex of children and the number of other people living in the household. Economic factors affecting parents' time allocation include education, house value, wealth, and combined income of parents. Major observations noted were the following: 1) children contribute non-negligible amounts of income and time to their families' income-earning activities; 2) they play important roles in non-income home production and child care activities; 3) their presence has a considerable influence on their parent's allocation of time; 4) children appear to stimulate fathers to work longer hours at the expense of leisure; 5) young children reduce mothers' time in income-earning activities and leisure time; 6) older male children substitute for mothers' shorter work time; 7) older female children substitute for mothers' lesser home production time; and 8) older children of both sexes appear to increase mothers' leisure time.