'Bayesian Optimisation for Nurse Scheduling'

A Bayesian optimisation algorithm for a nurse scheduling problem is presented, which involves choosing a suitable scheduling rule from a set for each nurse's assignment. When a human scheduler works, he normally builds a schedule systematically following a set of rules. After much practice, the scheduler gradually masters the knowledge of which solution parts go well with others. He can identify good parts and is aware of the solution quality even if the scheduling process is not yet completed, thus having the ability to finish a schedule by using flexible, rather than fixed, rules. In this paper, we design a more human-like scheduling algorithm, by using a Bayesian optimisation algorithm to implement explicit learning from past solutions. A nurse scheduling problem from a UK hospital is used for testing. Unlike our previous work that used Genetic Algorithms to implement implicit learning [1], the learning in the proposed algorithm is explicit, i.e. we identify and mix building blocks directly. The Bayesian optimisation algorithm is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, new rule strings have been obtained. Sets of rule strings are generated in this way, some of which will replace previous strings based on fitness. If stopping conditions are not met, the conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. For clarity, consider the following toy example of scheduling five nurses with two rules (1: random allocation, 2: allocate nurse to low-cost shifts). In the beginning of the search, the probabilities of choosing rule 1 or 2 for each nurse is equal, i.e. 50%. After a few iterations, due to the selection pressure and reinforcement learning, we experience two solution pathways: Because pure low-cost or random allocation produces low quality solutions, either rule 1 is used for the first 2-3 nurses and rule 2 on remainder or vice versa. In essence, Bayesian network learns 'use rule 2 after 2-3x using rule 1' or vice versa. It should be noted that for our and most other scheduling problems, the structure of the network model is known and all variables are fully observed. In this case, the goal of learning is to find the rule values that maximize the likelihood of the training data. Thus, learning can amount to 'counting' in the case of multinomial distributions. For our problem, we use our rules: Random, Cheapest Cost, Best Cover and Balance of Cost and Cover. In more detail, the steps of our Bayesian optimisation algorithm for nurse scheduling are: 1. Set t = 0, and generate an initial population P(0) at random; 2. Use roulette-wheel selection to choose a set of promising rule strings S(t) from P(t); 3. Compute conditional probabilities of each node according to this set of promising solutions; 4. Assign each nurse using roulette-wheel selection based on the rules' conditional probabilities. A set of new rule strings O(t) will be generated in this way; 5. Create a new population P(t+1) by replacing some rule strings from P(t) with O(t), and set t = t+1; 6. If the termination conditions are not met (we use 2000 generations), go to step 2. Computational results from 52 real data instances demonstrate the success of this approach. They also suggest that the learning mechanism in the proposed approach might be suitable for other scheduling problems. Another direction for further research is to see if there is a good constructing sequence for individual data instances, given a fixed nurse scheduling order. If so, the good patterns could be recognized and then extracted as new domain knowledge. Thus, by using this extracted knowledge, we can assign specific rules to the corresponding nurses beforehand, and only schedule the remaining nurses with all available rules, making it possible to reduce the solution space. Acknowledgements The work was funded by the UK Government's major funding agency, Engineering and Physical Sciences Research Council (EPSRC), under grand GR/R92899/01. References [1] Aickelin U, "An Indirect Genetic Algorithm for Set Covering Problems", Journal of the Operational Research Society, 53(10): 1118-1126,

How useful is expert opinion for predicting the distribution of a species within and beyond the region of expertise? A case study using brush-tailed rock-wallabiesPetrogale penicillata

1. Species' distribution modelling relies on adequate data sets to build reliable statistical models with high predictive ability. However, the money spent collecting empirical data might be better spent on management. A less expensive source of species' distribution information is expert opinion. This study evaluates expert knowledge and its source. In particular, we determine whether models built on expert knowledge apply over multiple regions or only within the region where the knowledge was derived. 2. The case study focuses on the distribution of the brush-tailed rock-wallaby Petrogale penicillata in eastern Australia. We brought together from two biogeographically different regions substantial and well-designed field data and knowledge from nine experts. We used a novel elicitation tool within a geographical information system to systematically collect expert opinions. The tool utilized an indirect approach to elicitation, asking experts simpler questions about observable rather than abstract quantities, with measures in place to identify uncertainty and offer feedback. Bayesian analysis was used to combine field data and expert knowledge in each region to determine: (i) how expert opinion affected models based on field data and (ii) how similar expert-informed models were within regions and across regions. 3. The elicitation tool effectively captured the experts' opinions and their uncertainties. Experts were comfortable with the map-based elicitation approach used, especially with graphical feedback. Experts tended to predict lower values of species occurrence compared with field data. 4. Across experts, consensus on effect sizes occurred for several habitat variables. Expert opinion generally influenced predictions from field data. However, south-east Queensland and north-east New South Wales experts had different opinions on the influence of elevation and geology, with these differences attributable to geological differences between these regions. 5. Synthesis and applications. When formulated as priors in Bayesian analysis, expert opinion is useful for modifying or strengthening patterns exhibited by empirical data sets that are limited in size or scope. Nevertheless, the ability of an expert to extrapolate beyond their region of knowledge may be poor. Hence there is significant merit in obtaining information from local experts when compiling species' distribution models across several regions.

Bayesian latent trait modeling of migraine symptom data

Definition of disease phenotype is a necessary preliminary to research into genetic causes of a complex disease. Clinical diagnosis of migraine is currently based on diagnostic criteria developed by the International Headache Society. Previously, we examined the natural clustering of these diagnostic symptoms using latent class analysis (LCA) and found that a four-class model was preferred. However, the classes can be ordered such that all symptoms progressively intensify, suggesting that a single continuous variable representing disease severity may provide a better model. Here, we compare two models: item response theory and LCA, each constructed within a Bayesian context. A deviance information criterion is used to assess model fit. We phenotyped our population sample using these models, estimated heritability and conducted genome-wide linkage analysis using Merlin-qtl. LCA with four classes was again preferred. After transformation, phenotypic trait values derived from both models are highly correlated (correlation = 0.99) and consequently results from subsequent genetic analyses were similar. Heritability was estimated at 0.37, while multipoint linkage analysis produced genome-wide significant linkage to chromosome 7q31-q33 and suggestive linkage to chromosomes 1 and 2. We argue that such continuous measures are a powerful tool for identifying genes contributing to migraine susceptibility.

Cosmoscapes and the promotion of uncosmopolitan values

Globality generates increasingly diffuse networks of human and non-human innovators, carriers and icons of exotic, polyethnic cosmopolitan difference; and this diffusion is increasingly hard to ignore or police (Latour 1993). In fact, such global networks of material-symbolic exchange can frequently have the unintended consequence of promoting status systems and cultural relationships founded on uncosmopolitan values such as cultural appropriation and status-based social exclusion. Moreover, this materialsymbolic engagement with cosmopolitan difference could also be rather mundane, engaged in routinely without any great reflexive consciousness or capacity to destabilise current relations of cultural power, or interpreted unproblematically as just one component of a person’s social environment. Indeed, Beck’s (2006) argument is that cosmopolitanism, in an age of global risk, is being forced upon us unwillingly, so there should be no surprise if it is a bitter pill for some to swallow. Within these emergent cosmopolitan networks, which we call ‘cosmoscapes’, there is no certainty about the development of ethical or behavioural stances consistent with claims foundational to the current literature on cosmopolitanism. Reviewing historical and contemporary studies of globality and its dynamic generative capacity, this paper considers such literatures in the context of studies of cultural consumption and social status. When one positions these diverse bodies of literature against one another, it becomes clear that the possibility of widespread cosmopolitan cultural formations is largely unpromising.

Embedding values through global education in social sciences pre-service teacher education : linking the head and heart

This chapter aims to situate values education as a core component of social science pre-service teacher education. In particular, it reflects on an experiment in embedding a values laden Global Education perspective in a fourth year social science curriculum method unit. This unit was designed and taught by the researcher on the assumption that beginning social science teachers need to be empowered with pedagogical skills and new dispositions to deal with value laden emerging global and regional concerns in their secondary school classrooms. Moreover, it was assumed that when pre-service teachers engage in dynamic and interactive learning experiences in their curriculum unit, they commence the process of ‘capacity building’ those skills which prepare them for their own lifelong professional learning. This approach to values education also aimed at providing pre-service teachers with opportunities to ‘create deep understandings of teaching and learning’ (Barnes, 1989, p. 17) by reflecting on the ways in which ‘pedagogy can be transformative’ (Lovat and Toomey, 2011 add page no from Chapter One). It was assumed that this tertiary experience would foster the sine qua non of teaching – a commitment to students and their learning. Central to fostering new ‘dispositions’ through this approach, was the belief in the power of pedagogy to make the difference in enhancing student participation and learning. In this sense, this experiment in values education in secondary social science pre-service teacher education aligns with the Troika metaphor for a paradigm change, articulated by Lovat and Toomey (2009) in Chapter One.

Bayesian spatiotemporal analysis of socio-ecologic drivers of Ross River Virus transmission in Queensland, Australia

This study aims to examine the impact of socio-ecologic factors on the transmission of Ross River virus (RRV) infection and to identify areas prone to social and ecologic-driven epidemics in Queensland, Australia. We used a Bayesian spatiotemporal conditional autoregressive model to quantify the relationship between monthly variation of RRV incidence and socio-ecologic factors and to determine spatiotemporal patterns. Our results show that the average increase in monthly RRV incidence was 2.4% (95% credible interval (CrI): 0.1–4.5%) and 2.0% (95% CrI: 1.6–2.3%) for a 1°C increase in monthly average maximum temperature and a 10 mm increase in monthly average rainfall, respectively. A significant spatiotemporal variation and interactive effect between temperature and rainfall on RRV incidence were found. No association between Socio-economic Index for Areas (SEIFA) and RRV was observed. The transmission of RRV in Queensland, Australia appeared to be primarily driven by ecologic variables rather than social factors.

Response to "a step in the right direction : commentary on expected values for pedometer-determined physical activity in youth"

The figure Beets took exception to displays sex‐ and age‐specific median values of aggregated published expected values for pedometer determined physical activity.

Assigning metabolic equivalent (MET) values to the 2002 Census Occupational Classification System

Background: The Current Population Survey (CPS) and the American Time Use Survey (ATUS) use the 2002 census occupation system to classify workers into 509 separate occupations arranged into 22 major occupational categories. Methods: We describe the methods and rationale for assigning detailed MET estimates to occupations and present population estimates (comparing outputs generated by analysis of previously published summary MET estimates to the detailed MET estimates) of intensities of occupational activity using the 2003 ATUS data comprised of 20,720 respondents, 5,323 (2,917 males and 2,406 females) of whom reported working 6+ hours at their primary occupation on their assigned reporting day. Results: Analysis using the summary MET estimates resulted in 4% more workers in sedentary occupations, 6% more in light, 7% less in moderate, and 3% less in vigorous compared to using the detailed MET estimates. The detailed estimates are more sensitive to identifying individuals who do any occupational activity that is moderate or vigorous in intensity resulting in fewer workers in sedentary and light intensity occupations. Conclusions: Since CPS/ATUS regularly captures occupation data it will be possible to track prevalence of the different intensity levels of occupations. Updates will be required with inevitable adjustments to future occupational classification systems.

Expected values for steps/day in special populations

Objective To assemble expected values for free-living steps/day in special populations living with chronic illnesses and disabilities. Method Studies identified since 2000 were categorized into similar illnesses and disabilities, capturing the original reference, sample descriptions, descriptions of instruments used (i.e., pedometers, piezoelectric pedometers, accelerometers), number of days worn, and mean and standard deviation of steps/day. Results Sixty unique studies represented: 1) heart and vascular diseases, 2) chronic obstructive lung disease, 3) diabetes and dialysis, 4) breast cancer, 5) neuromuscular diseases, 6) arthritis, joint replacement, and fibromyalgia, 7) disability (including mental retardation/intellectual difficulties), and 8) other special populations. A median steps/day was calculated for each category. Waist-mounted and ankle-mounted instruments were considered separately due to fundamental differences in assessment properties. For waist-mounted instruments, the lowest median values for steps/day are found in disabled older adults (1214 steps/day) followed by people living with COPD (2237 steps/day). The highest values were seen in individuals with Type 1 diabetes (8008 steps/day), mental retardation/intellectual disability (7787 steps/day), and HIV (7545 steps/day). Conclusion This review will be useful to researchers/practitioners who work with individuals living with chronic illness and disability and require such information for surveillance, screening, intervention, and program evaluation purposes. Keywords: Exercise; Walking; Ambulatory monitoring

Waist circumference cut-off values for the prediction of cardiovascular risk factors clustering in Chinese school-aged children : a cross-sectional study

Background: Waist circumference has been identified as a valuable predictor of cardiovascular risk in children. The development of waist circumference percentiles and cut-offs for various ethnic groups are necessary because of differences in body composition. The purpose of this study was to develop waist circumference percentiles for Chinese children and to explore optimal waist circumference cut-off values for predicting cardiovascular risk factors clustering in this population.----- ----- Methods: Height, weight, and waist circumference were measured in 5529 children (2830 boys and 2699 girls) aged 6-12 years randomly selected from southern and northern China. Blood pressure, fasting triglycerides, low-density lipoprotein cholesterol, high-density lipoprotein cholesterol, and glucose were obtained in a subsample (n = 1845). Smoothed percentile curves were produced using the LMS method. Receiver-operating characteristic analysis was used to derive the optimal age- and gender-specific waist circumference thresholds for predicting the clustering of cardiovascular risk factors.----- ----- Results: Gender-specific waist circumference percentiles were constructed. The waist circumference thresholds were at the 90th and 84th percentiles for Chinese boys and girls respectively, with sensitivity and specificity ranging from 67% to 83%. The odds ratio of a clustering of cardiovascular risk factors among boys and girls with a higher value than cut-off points was 10.349 (95% confidence interval 4.466 to 23.979) and 8.084 (95% confidence interval 3.147 to 20.767) compared with their counterparts.----- ----- Conclusions: Percentile curves for waist circumference of Chinese children are provided. The cut-off point for waist circumference to predict cardiovascular risk factors clustering is at the 90th and 84th percentiles for Chinese boys and girls, respectively.