On the Critical Value Behaviour of Multiple Decision Procedures

In this paper we investigate the asymptotic critical value behaviour of certain multiple decision procedures as e.g. simultaneous confidence intervals and simultaneous as well as stepwise multiple test procedures. Supposing that n hypotheses or parameters of interest are under consideration we investigate the critical value behaviour when n increases. More specifically, we answer e.g. the question by which amount the lengths of confidence intervals increase when an additional parameter is added to the statistical analysis. Furthermore, critical values of different multiple decision procedures as for instance step-down and step-up procedures will be compared. Some general theoretic results are derived and applied for various distributions.     

Asymptotic Bias in Parameter Estimation of AR-Processes Using Recursive Least Squares with Exponential Forgetting

The recursive least squares technique is often extended with exponential forgetting as a tool for parameter estimation in time-varying systems. The distribution of the resulting parameter estimates is, however, unknown when the forgetting factor is less than one. In this paper an approximative expression for bias of the recursively obtained parameter estimates in a time-invariant AR( n_a ) process with arbitrary noise is given, showing that the bias is non-zero and giving bounds on the approximation errors. Simulations confirm the approximation expressions.     

On predictive distributions and Bayesian networks

In this paper we are interested in discrete prediction problems for a decision-theoretic setting, where the task is to compute the predictive distribution for a finite set of possible alternatives. This question is first addressed in a general Bayesian framework, where we consider a set of probability distributions defined by some parametric model class. Given a prior distribution on the model parameters and a set of sample data, one possible approach for determining a predictive distribution is to fix the parameters to the instantiation with the maximum a posteriori probability. A more accurate predictive distribution can be obtained by computing the evidence (marginal likelihood), i.e., the integral over all the individual parameter instantiations. As an alternative to these two approaches, we demonstrate how to use Rissanen's new definition of stochastic complexity for determining predictive distributions, and show how the evidence predictive distribution with Jeffrey's prior approaches the new stochastic complexity predictive distribution in the limit with increasing amount of sample data. To compare the alternative approaches in practice, each of the predictive distributions discussed is instantiated in the Bayesian network model family case. In particular, to determine Jeffrey's prior for this model family, we show how to compute the (expected) Fisher information matrix for a fixed but arbitrary Bayesian network structure. In the empirical part of the paper the predictive distributions are compared by using the simple tree-structured Naive Bayes model, which is used in the experiments for computational reasons. The experimentation with several public domain classification datasets suggest that the evidence approach produces the most accurate predictions in the log-score sense. The evidence-based methods are also quite robust in the sense that they predict surprisingly well even when only a small fraction of the full training set is used.     

On Bartlett correction of empirical likelihood for regularly spaced spatial data

Bartlett correction constitutes one of the attractive features of empirical likelihood because it enables the construction of confidence regions for parameters with improved coverage probabilities. We study the Bartlett correction of spatial frequency domain empirical likelihood (SFDEL) based on general spectral estimating functions for regularly spaced spatial data. This general formulation can be applied to testing and estimation problems in spatial analysis, for example testing covariance isotropy, testing covariance separability as well as estimating the parameters of spatial covariance models. We show that the SFDEL is Bartlett correctable. In particular, the improvement in coverage accuracies of the Bartlett‐corrected confidence regions depends on the underlying spatial structures. The Canadian Journal of Statistics 47: 455–472; 2019 © 2019 Statistical Society of Canada     

Issues in the integration of religious education and worldviews education in an intercultural context

ABSTRACT

The Council of Europe’s 2008 ‘Recommendation’ advocates the study of ‘non-religious convictions’ in schools in addition to religions. In 2018, there is evidence of growing academic interest in the inclusion of non-religious worldviews in the school curriculum, but few European countries include such a study within religious education. The guidance document, Signposts, recognises that the integration of religions and non-religious worldviews is problematic for policy makers, teacher trainers and schools and that there is a need for further research. Norway and England are at significant but different stages in the process of integration. This article presents a comparative study which draws on the findings of research in both countries which has investigated the process at classroom and policy levels, and issues raised by this. Four issues are explored: practical challenges; differing understandings of the concept of worldviews; the inclusion of non-religious worldviews as a political issue and influences on the selection of worldviews. The article concludes with a discussion of issues and findings within a supranational context and makes recommendations which highlight the value of integration and the need for both contextual studies and further comparative research.     

Elementary School-age Children's Attitudes Toward Children in Same-Sex Parent Families

As numbers of families with same-sex parents increase in the United States, children are more likely to encounter diverse family structures. Given that young children can demonstrate in-group bias, prejudicial attitudes, and social exclusion, it is important to understand how children perceive their peers in diverse families. To our knowledge, no studies have assessed elementary-school-age children's attitudes about same-sex parent families. Here, 131 elementary school students (M_age = 7.79 years; 61 girls) viewed images of same-sex (female and male) and other-sex couples with a child and then were asked about their perceptions of these families, particularly the children. Results indicated participants' preferences toward children with other-sex versus same-sex parents. Developmental and practical implications about children's attitudes toward sexual minority parent families are discussed.     

Socializing Children About Family Structure: Perspectives of Lesbian and Gay Adoptive Parents

Despite increasing numbers of lesbian- and gay- (LG-) parent families, little research on LG-adoptive-parent families has examined parental beliefs and perceptions related to discussing their sexual minority status with their children. This study assessed 266 LG adoptive parents (160 lesbian mothers, 106 gay fathers) from the Modern Adoptive Families (MAF) study, a nationwide survey (2012–2013) of adoptive parents' pre- and post-placement experiences. A cultural socialization lens provided the framework for examining LG parenting beliefs and practices. Two measurement scales were developed to examine parents' perceptions and self-efficacy related to socializing their child about being in a sexual-minority-parent family. Results indicate that LG parents endorse the importance of unique socialization practices and generally feel confident engaging in these practices. Parent education, transracial adoption, endorsement of racial socialization, and socialization self-efficacy were positively associated with endorsement of socialization practices. Excellent reliability suggests the 2 scales have the potential of being psychometrically sound instruments with which to measure parental endorsement and related self-efficacy of socialization practices for families headed by sexual minority parents. Findings contribute to a deeper understanding of socialization and communication patterns in LG-headed families, especially those formed through adoption. Research, policy, and practice implications are discussed.     

Relationship of bird richness,abundance and assemblage to the built environment in a small island tropical urban setting: a Suva,Fiji case study

There have been few studies investigating the relationship between the built environment and the status of bird distributions in small island tropical urban areas. We present a study investigating the relationship between bird species richness, abundance and assemblage to the built environment in Suva, Fiji. Field surveys were taken at 54 randomly selected sites throughout the city, stratified by three building density classes and the central business district (CBD). At each site bird counts were recorded, along with environmental data such as average building height, within a 150 m radius. Land-use information was obtained from screen digitized high-resolution satellite imagery within the same radius. Distance to undeveloped patches of land within the urban area was calculated using a GIS. Analysis of the effects of the built environment was carried out for all species, and for exotic and native species separately. Abundance of exotics was significantly higher in the central business district (CBD) than all other urban density classes, and significantly higher than natives in all other density classes. We found a negative relationship between native species richness and distance to undeveloped patches, but no relationship for exotics. Species assemblage was not related to urban density class. We conclude that the status of native and exotic bird species in Suva is similar to what has been found in urban areas in temperate climates, and conservation efforts should focus on minimizing the amount of heavily urbanized “core areas” and protecting undeveloped areas of forested vegetation to improve bird biodiversity in small tropical islands cities.