South Africa's 'Rainbow People', National Pride and Happiness

Since the first free elections were held in April 1994, South Africans are popularly known as the 'rainbow people'. The paper inquires whether South Africans who experienced pride in their nation in the first years of democracy also perceived a greater sense of subjective well-being. It is proposed that national pride in post-apartheid South Africa might be fused with or work through self-esteem to lift levels of happiness. The paper traces the history of the new integrating civil religion of the rainbow people and the acceptance of the rainbow as a political symbol of unity among the diverse people of South Africa immediately after the 1994 elections and two years later. The proposed link between national pride and happiness was explored with data from two independent national surveys, the 1995 South African World Values Survey conducted by Markinor and a June 1996 MarkData syndicated omnibus survey. The study found that the appeal of the rainbow as political symbol was inclusive of all groups in society and that feelings of national pride and support for the rainbow ideal were positively associated with subjective well-being. As indicated by intensity and frequency measures, the majority of South Africans were proud of their country and could name a national achievement that inspired pride. Better-off South Africans tended to be happier and more satisfied with life but less proud, while the poor were less happy but fiercely proud of their country. Results suggest that belief in South Africa's 'rainbow nation' ideal may have assisted in boosting happiness during the transition to a stable democracy, thereby preventing alienation among the losers under the new political dispensation. Supporters of the ideal of the rainbow nation were more optimistic than others about the future of their country.     

Bayesian palaeoclimate reconstruction

Summary.  We consider the problem of reconstructing prehistoric climates by using fossil data that have been extracted from lake sediment cores. Such reconstructions promise to provide one of the few ways to validate modern models of climate change. A hierarchical Bayesian modelling approach is presented and its use, inversely, is demonstrated in a relatively small but statistically challenging exercise: the reconstruction of prehistoric climate at Glendalough in Ireland from fossil pollen. This computationally intensive method extends current approaches by explicitly modelling uncertainty and reconstructing entire climate histories. The statistical issues that are raised relate to the use of compositional data (pollen) with covariates (climate) which are available at many modern sites but are missing for the fossil data. The compositional data arise as mixtures and the missing covariates have a temporal structure. Novel aspects of the analysis include a spatial process model for compositional data, local modelling of lattice data, the use, as a prior, of a random walk with long-tailed increments, a two-stage implementation of the Markov chain Monte Carlo approach and a fast approximate procedure for cross-validation in inverse problems. We present some details, contrasting its reconstructions with those which have been generated by a method in use in the palaeoclimatology literature. We suggest that the method provides a basis for resolving important challenging issues in palaeoclimate research. We draw attention to several challenging statistical issues that need to be overcome.     

The fiducial argument and hacking's principle of irrelevance

In a searching analysis of the fiducial argument Hacking (1965) proposed the Principle of Irrelevance as a condition under which the argument is valid. His statement of the Principle was essentially non-mathematical and this paper presents a mathematical development of the Principle. The relationship with likelihood inference is explored and some of the proposed counter-examples to fiducial theory are considered. It is shown that even with the Principle of Irrelevance examples of non-uniqueness of fiducial distributions exist.     

A Survey of the Teaching of Statistics in M.B.A. Programs

A survey of business schools was conducted to obtain information about the current state of the teaching of business statistics to students enrolled in M.B.A. degree programs. The survey was undertaken for and presented at a June 1986 conference on “Making Statistics More Effective in Schools of Business,” held at the University of Chicago's Graduate School of Business. Information was elicited concerning both the required statistics sequence and elective statistics courses for M.B.A. students, as well as computer usage in these courses. This article summarizes the information obtained from the survey.     

Hellinger distance as a penalized log likelihood

The present paper studies the minimum Hellinger distance estimator by recasting it as the maximum likelihood estimator in a data driven modification of the model density. In the process, the Hellinger distance itself is expressed as a penalized log likelihood function. The penalty is the sum of the model probabilities over the non-observed values of the sample space. A comparison of the modified model density with the original data provides insights into the robustness of the minimum Hellinger distance estimator. Adjustments of the amount of penalty leads to a class of minimum penalized Hellinger distance estimators, some members of which perform substantially better than the minimum Hellinger distance estimator at the model for small samples, without compromising the robustness properties of the latter.     

Notes on likelihood intervals and profiling

In many applications, decisions are made on the basis of function of parameters g(θ). When the value of g(theta;) is calculated using estimated values for te parameters, its is important to have a measure of the uncertainty associated with that value of g(theta;). Likelihood ratio approaches to finding likelihood intervals for functions of parameters have been shown to be more reliable, in terms of coverage probability, than the linearization approach. Two approaches to the generalization of the profiling algorithm have been proposed in the literature to enable construction of likelihood intervals for a function of parameters (Chen and Jennrich, 1996; Bates and Watts, 1988). In this paper we show the equivalence of these two methods. We also provide and analysis of cases in which neither profiling algorithm is appropriate. For one of these cases an alternate approach is suggested Whereas generalized profiling is based on maximizing the likelihood function given a constraint on the value of g(θ), the alternative algorithm is based on optimizing g(θ) given a constraint on the value of the likelihood function.     

Locally quadratic log likelihood and data-based transformations

The investigation of multi-parameter likelihood functions is simplified if the log likelihood is quadratic near the maximum, as then normal approximations to the likelihood can be accurately used to obtain quantities such as likelihood regions. This paper proposes that data-based transformations of the parameters can be employed to make the log likelihood more quadratic, and illustrates the method with one of the simplest bivariate likelihoods, the normal two-parameter likelihood.