Practical stability of approximating discrete-time filters with respect to model mismatch using relative entropy concepts

This paper establishes practical stability results for an important range of approximate discrete-time filtering problems involving mismatch between the true system and the approximating filter model. Using local consistency assumption, the practical stability established is in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Significantly, these practical stability results do not require the approximating model to be of the same model type as the true system. Our analysis applies to a wide range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationally tractable filters.

Parent decisions regarding paid work and care of the child

Australia has witnessed a continual increase in maternal employment over the past two decades, which has placed focus on child care- its effects on the child and on early childhood education and care policy and provision. The engagement of women in the paid workforce contributes to national economic development, and is recognised in government policy incentives such as cash subsidies and tax relief for child care fees. These incentives are targeted towards mothers, to encourage them to engage in paid work. Making a contribution to the family’s economy and to a mother’s economic self sufficiency are two key drivers for women’s engagement in satisfying paid work. Many women also seek to maintain a personal investment in the development of their career, simultaneously ensuring that the child is experiencing suitable care. Policies that support women’s choices for satisfying workforce engagement and care arrangements are prudent for ensuring productivity of the economy as well as for enhancing the wellbeing of parents and children (OECD, 2007). Policies that provide family friendly employment arrangements, paid parental leave, and child care support, directly affect maternal employment decisions. Availability of family friendly employment policies is viewed as one way to not only promote gender equity in employment opportunities but also support the wellbeing of children and families (OECD, 2007). Yet there are not comprehensive and coherent policies on work and family in Australia. Australia is due to implement its first paid parental leave scheme in January, 2011. At the time of the data collection of this research, June 2007 to December 2008, Australia had no statutory provision for paid parental leave. To date, most research has focused on the consequences of paid work and care decisions made by women. Far less is known about the processes of decision-making and reasons underlying women’s choices. Investigation of what is most salient for women as they make decisions regarding engagement in paid work, and care for their child is important in order to inform policy and practices related to parental leave, family friendly employment and care for the child. This prospective longitudinal research was of 124 Australian expectant first-time mothers who completed questionnaires in their third trimester of pregnancy, and again at six and twelve months postpartum. First-time expectant mothers' decisions regarding engaging in paid work and selecting care for their child represent those of a group who are invested in motherhood and have usually had direct experience of engaging in paid work. They therefore provide an important insight into society’s idealised views about motherhood and the emotional and social uncertainty of making personal decisions where the consequences of such decisions are unknown. These decisions reflect public beliefs about the role of women in contributing to the country’s productivity and decisions about providing for the economic and emotional care needs of their family. As so little is known about the reasoning and processes of decision-making of women’s choices regarding paid work and care of the child this research was designed to capture expectant first-time mother’s preferred options for engaging in paid work and the care of their child, and investigate their actual decisions made at six and 12 months postpartum. To capture preferred options, decisions and outcomes of decisions regarding paid work and care of the child a prospective longitudinal research design was utilised. This design had three important components that addressed key limitations in the extant literature. First the research commenced in pregnancy in order to investigate preferences and beliefs about paid work and care and to examine baseline data that may influence decisions made as the women returned to paid work. Second the research involved longitudinal tracking from the antenatal time point to six and 12 months postpartum in order to identify the influences on decisions made. Third the research measured outcomes of the decisions made at each time point. This research examined the intentions, preferences, beliefs, influences, and outcomes of the decisions about engagement in paid work and choice of care. The analyses examined factors predicting return to paid work, the timing of return and extent of engagement in paid work; the care for the child; satisfaction with paid work; satisfaction with care for the child, motherhood and fulfilment; and maternal wellbeing at six and 12 months postpartum. The factors of interest were both rational/economic (availability and extent of paid and unpaid maternity leave; flexible work patterns) and emotional/affective (career satisfaction, investment in motherhood, and concern with quality of care for the child). Results indicated a group preference, and realisation for, return to paid work within the first year after the birth of a child but with reduction in hours to part-time. Most women saw paid work not only as a source of income but also as source of personal satisfaction. There were four key themes arising from this research. First, the women strived to feel emotionally secure when deciding about engaging in paid work and care of the child. To achieve emotional security women made their decisions for paid work and care of the child differently. A woman’s decision for maternal employment is a function of her personal beliefs, preferences and context regarding paid work and care of the child. She adjusts her established work identity with her new identity as a mother. The second key theme from this research is that the women made their decisions for maternal employment in response to their personal context and there were different levels of opportunities between the women’s choices. There is inequity of entitlement regarding work conditions associated with a woman’s education level. This has implications for the woman’s engagement in paid work, and her child’s health and wellbeing. The third key theme is that the quality of the child’s care mattered to the women in the research. They preferred care provided by parents and/or relatives more than any other types of care. The fourth key theme identified that satisfaction and wellbeing outcomes experienced as a result of maternal employment decisions were a complex interaction between multiple factors that change across time with the ongoing development of the mother’s identity, and the development of the child. The implications for policy within Australia are that the employment of mothers in the workforce necessitates that non-parental care becomes a public concern, where there is universal access to good quality affordable care for every child, not just for those who can afford it. This is equitable and represents real choice while supporting the rights of the child (Thorpe, Cloney & Tayler, 2010), protecting and promoting the public interest (Cleveland & Krashinsky, 2010). Children’s health and wellbeing will be supported (Moore & Oberklaid, 2010) while children are in non-parental care, and they will be exposed to environments and experiences that support their learning and development. The significant design of the research enabled the trajectories of first-time expectant women to be tracked from the antenatal point to 12 months postpartum. But there were limitations: the small sample size, the over-representation of the sample being highly educated and the nature of a longitudinal research that is set within the economic, social and political context at that time. These limitations are discussed in relation to suggestions for future research.

Practical stability with respect to model mismatch of approximate discrete-time output feedback control

This paper establishes a practical stability result for discrete-time output feedback control involving mismatch between the exact system to be stabilised and the approximating system used to design the controller. The practical stability is in the sense of an asymptotic bound on the amount of error bias introduced by the model approximation, and is established using local consistency properties of the systems. Importantly, the practical stability established here does not require the approximating system to be of the same model type as the exact system. Examples are presented to illustrate the nature of our practical stability result.

The impact of nonlinear exposure risk relationships on seasonal time series data: modelling danish neonatal birth anthropometric data

Background Birth weight and length have seasonal fluctuations. Previous analyses of birth weight by latitude effects identified seemingly contradictory results, showing both 6 and 12 monthly periodicities in weight. The aims of this paper are twofold: (a) to explore seasonal patterns in a large, Danish Medical Birth Register, and (b) to explore models based on seasonal exposures and a non-linear exposure-risk relationship. Methods Birth weight and birth lengths on over 1.5 million Danish singleton, live births were examined for seasonality. We modelled seasonal patterns based on linear, U- and J-shaped exposure-risk relationships. We then added an extra layer of complexity by modelling weighted population-based exposure patterns. Results The Danish data showed clear seasonal fluctuations for both birth weight and birth length. A bimodal model best fits the data, however the amplitude of the 6 and 12 month peaks changed over time. In the modelling exercises, U- and J-shaped exposure-risk relationships generate time series with both 6 and 12 month periodicities. Changing the weightings of the population exposure risks result in unexpected properties. A J-shaped exposure-risk relationship with a diminishing population exposure over time fitted the observed seasonal pattern in the Danish birth weight data. Conclusion In keeping with many other studies, Danish birth anthropometric data show complex and shifting seasonal patterns. We speculate that annual periodicities with non-linear exposure-risk models may underlie these findings. Understanding the nature of seasonal fluctuations can help generate candidate exposures.