Rethinking Risk Attitude: Aspiration as Pure Risk

There exists no completely satisfactory theory of risk attitude in current normative decision theories. Existing notions confound attitudes to pure risk with unrelated psychological factors such as strength of preference for certain outcomes, and probability weighting. In addition traditional measures of risk attitude frequently cannot be applied to non-numerical consequences, and are not psychologically intuitive. I develop Pure Risk theory which resolves these problems – it is consistent with existing normative theories, and both internalises and generalises the intuitive notion of risk being related to the probability of not achieving one’s aspirations. Existing models which ignore pure risk attitudes may be misspecified, and effects hitherto modelled as loss aversion or utility curvature may be due instead to Pure Risk attitudes.     

Two-sample Pitman closeness comparison under progressive Type-II censoring

In this paper, we consider two problems concerning two independent progressively Type-II censored samples. We first consider the Pitman closeness (PC) of order statistics from two independent progressively censored samples to a specific population quantile. We then consider the point prediction of a future progressively censored order statistic and discuss the determination of the closest progressively censored order statistic from the current sample according to the simultaneous closeness probabilities. For both these problems, explicit expressions are derived for the pertinent PC probabilities, and then special cases are given as examples. For various censoring schemes, we also present numerical results for the standard uniform, standard exponential, and standard normal distributions. Finally, a distribution-free result for the median is obtained.     

Sample moments of the autocorrelations of moving average processes and a modification to bartlett'sasymptotic variance formula

In this paper we express the sample autocorrelations for a moving average process of order q as a function of its own theoretical autocorrelations and the sample autocorrelations for the generating white noise series. Approximate analytic expressions are then obtained forthe moments of the sample autocorrelations of the moving average process.

Using these expressions, together with numerical evidence, we show that Bartlett's asymptotic formula for the variance of the sample autocorrelations of moving average processes, which is used widely in identifying these processes, is a large overestimate when considering finitesample sizes.

Our approach is for motivational purposes and so is purely formal, the amount of mathematics presented being kept to a minimum.     

Nonparametric Regression as an Example of Model Choice

Nonparametric regression can be considered as a problem of model choice. In this article, we present the results of a simulation study in which several nonparametric regression techniques including wavelets and kernel methods are compared with respect to their behavior on different test beds. We also include the taut-string method whose aim is not to minimize the distance of an estimator to some “true” generating function f but to provide a simple adequate approximation to the data. Test beds are situations where a “true” generating f exists and in this situation it is possible to compare the estimates of f with f itself. The measures of performance we use are the L²- and the L^∞-norms and the ability to identify peaks.     

The significance of place in middle childhood: qualitative research from Wales

The paper presents some key findings of qualitative research with older primary school children in Wales on their attachments to places and cultures. There is discussion of children's perspectives on the global, national and local arenas. We argue both that there are continuities with adult perspectives and that the children's views on place and identity need to be understood in the context of the social location of middle childhood. The study shows children making relatively little use of culturally-filled categories of local, national and global place-identifications. The differences they articulate are largely framed in terms of divisions between groups of people rather than in the characteristics of place, and generally related back to the self.     

Toward a dimensional model of risk and protective factors influencing children's early cognitive,social, and emotional development during the COVID-19 pandemic

Variation in infants’ home environment is implicated in their cognitive and psycho-social development. The pandemic has intensified variations in home environments through exacerbating socioeconomic inequalities, and increasing psychological stressors for some families. This study investigates the effects of parental (predominantly maternal) mental health, enriching activities and screen use on 280 24- to 52-month-olds’ executive functions, internalising and externalising problems, and pro-social behaviour; with socioeconomic status and social support as contextual factors. Our results indicate that aspects of the home environment are differentially associated with children’s cognitive and psycho-social development. Parents who experienced sustained mental distress during the pandemic tended to report higher child externalising and internalising problems, and executive function difficulties at follow-up. Children who spent more time engaged in enriching activities with their parents showed stronger executive functions and social competence six months later. Screen use levels during the first year of the pandemic were not associated with outcomes. To mitigate the risk of persistent negative effects for this ‘pandemic generation’ of infants, our study highlights the importance of supporting parents’ mental health. As our results demonstrate the impact of social support on mental health, investing in support services and interventions promoting building support networks are likely to be beneficial.     

TALKING ABOUT PROBABILITIES: A LOGICAL PROBLEM FOR OR/MS

The correct interpretation of a natural language statement is determined as much by convention and shared meanings as by logical content. Therefore, when the word “probability” is used in the statement of a decision problem, the intended interpretation is not always clear. If such a statement also contains explicit probability formulae, confusion and even paradox may result. In this article, a problem involving cascaded inference is interpreted in four ways, three of which are regarded by the authors as legitimate or reasonable. The problem was originally suggested by Einhorn [3] and further discussed by Libby [10]. It is suggested here that a formal, mathematicist interpretation of the word “probability” might lead to inappropriate analyses of some decisions.     

Determining the minimum duration of treatment in tuberculosis: An order restricted non-inferiority trial design

Tuberculosis (TB) is one of the biggest killers among infectious diseases worldwide. Together with the identification of drugs that can provide benefits to patients, the challenge in TB is also the optimisation of the duration of these treatments. While conventional duration of treatment in TB is 6 months, there is evidence that shorter durations might be as effective but could be associated with fewer side effects and may be associated with better adherence. Based on a recent proposal of an adaptive order-restricted superiority design that employs the ordering assumptions within various duration of the same drug, we propose a non-inferiority (typically used in TB trials) adaptive design that effectively uses the order assumption. Together with the general construction of the hypothesis testing and expression for type I and type II errors, we focus on how the novel design was proposed for a TB trial concept. We consider a number of practical aspects such as choice of the design parameters, randomisation ratios, and timings of the interim analyses, and how these were discussed with the clinical team.