Fast rates for estimation error and oracle inequalities for model section

We consider complexity penalization methods for model selection. These methods aim to choose a model to optimally trade off estimation and approximation errors by minimizing the sum of an empirical risk term and a complexity penalty. It is well known that if we use a bound on the maximal deviation between empirical and true risks as a complexity penalty, then the risk of our choice is no more than the approximation error plus twice the complexity penalty. There are many cases, however, where complexity penalties like this give loose upper bounds on the estimation error. In particular, if we choose a function from a suitably simple convex function class with a strictly convex loss function, then the estimation error (the difference between the risk of the empirical risk minimizer and the minimal risk in the class) approaches zero at a faster rate than the maximal deviation between empirical and true risks. In this paper, we address the question of whether it is possible to design a complexity penalized model selection method for these situations. We show that, provided the sequence of models is ordered by inclusion, in these cases we can use tight upper bounds on estimation error as a complexity penalty. Surprisingly, this is the case even in situations when the difference between the empirical risk and true risk (and indeed the error of any estimate of the approximation error) decreases much more slowly than the complexity penalty. We give an oracle inequality showing that the resulting model selection method chooses a function with risk no more than the approximation error plus a constant times the complexity penalty.

Effect of geometry on the melting rates of iron rods burning in high pressure oxygen

The effect of sample geometry on the melting rates of burning iron rods was assessed. Promoted-ignition tests were conducted with rods having cylindrical, rectangular, and triangular cross-sectional shapes over a range of cross-sectional areas. The regression rate of the melting interface (RRMI) was assessed using a statistical approach which enabled the quantification of confidence levels for the observed differences in RRMI. Statistically significant differences in RRMI were observed for rods with the same cross-sectional area but different cross-sectional shape. The magnitude of the proportional difference in RRMI increased with the cross-sectional area. Triangular rods had the highest RRMI, followed by rectangular rods, and then cylindrical rods. The dependence of RRMI on rod shape is shown to relate to the action of molten metal at corners. The corners of the rectangular and triangular rods melted faster than the faces due to their locally higher surface area to volume ratios. This phenomenon altered the attachment geometry between liquid and solid phases, increasing the surface area available for heat transfer, causing faster melting. Findings relating to the application of standard flammability test results in industrial situations are also presented.

Wear it or wear the cost : current seatbelt wearing rates in Queensland

Observational seatbelt wearing studies are a valuable tool for obtaining up-to-date information about rates of use. Given that one quarter of vehicle occupants killed on Queensland roads in recent years were not wearing seatbelts, it is important that authorities are able to identify non-wearers and take steps to increase compliance with seatbelt laws to reduce the severity of crashes and, therefore, the road toll. An observational study of seatbelt use was conducted in metropolitan, regional and rural locations throughout Queensland in May and June, 2010. Trained observers took note of seatbelt use of all occupants of passenger vehicles, noting their gender, approximate age group, seating position, vehicle type, licence type (i.e. visible L or P plates), mobile phone use, and the date, time and location of the observation. Of 19,579 observations, 99.04% (19,391) of occupants were observed wearing seatbelts, as only 0.96% of occupants (188) were not wearing a seatbelt. There were differences in seatbelt wearing rates for a number of study variables, although most were very small. However, seatbelt wearing rates were 3.84% lower for drivers observed using a mobile phone than for those who were not. While compliance with seatbelt laws seems to be very high, it is still concerning that so few non-wearers represent a disproportionately large proportion of road fatalities and serious injuries in Queensland. Road safety authorities must therefore continue to find ways to improve seatbelt use, as small gains in wearing rates will translate into significant fatality reductions.

Using approximate Bayesian computation to estimate transmission rates of nosocomial pathogens

In this paper, we apply a simulation based approach for estimating transmission rates of nosocomial pathogens. In particular, the objective is to infer the transmission rate between colonised health-care practitioners and uncolonised patients (and vice versa) solely from routinely collected incidence data. The method, using approximate Bayesian computation, is substantially less computer intensive and easier to implement than likelihood-based approaches we refer to here. We find through replacing the likelihood with a comparison of an efficient summary statistic between observed and simulated data that little is lost in the precision of estimated transmission rates. Furthermore, we investigate the impact of incorporating uncertainty in previously fixed parameters on the precision of the estimated transmission rates.

Time-dependent rates of molecular evolution

For over half a century, it has been known that the rate of morphological evolution appears to vary with the time frame of measurement. Rates of microevolutionary change, measured between successive generations, were found to be far higher than rates of macroevolutionary change inferred from the fossil record. More recently, it has been suggested that rates of molecular evolution are also time dependent, with the estimated rate depending on the timescale of measurement. This followed surprising observations that estimates of mutation rates, obtained in studies of pedigrees and laboratory mutation-accumulation lines, exceeded long-term substitution rates by an order of magnitude or more. Although a range of studies have provided evidence for such a pattern, the hypothesis remains relatively contentious. Furthermore, there is ongoing discussion about the factors that can cause molecular rate estimates to be dependent on time. Here we present an overview of our current understanding of time-dependent rates. We provide a summary of the evidence for time-dependent rates in animals, bacteria and viruses. We review the various biological and methodological factors that can cause rates to be time dependent, including the effects of natural selection, calibration errors, model misspecification and other artefacts. We also describe the challenges in calibrating estimates of molecular rates, particularly on the intermediate timescales that are critical for an accurate characterization of time-dependent rates. This has important consequences for the use of molecular-clock methods to estimate timescales of recent evolutionary events.

Can rodents enhance germination rates in rainforest seeds?

The decline of large coevolved frugivorous species within fragmented habitats can have an effect on ecological processes, for example, seed dispersal and germination. It is therefore necessary for more resilient species to ensure essential processes are maintained within the system. This study investigates the influence of two rodent species, Melomys cervinipes (Fawn-footed Melomys) and Rattus fuscipes (Bush Rat), on the germination process of rainforest fruits. Both species are endemic to north Queensland rainforest and commonly found in fragmented habitats in high densities. We found in 85% of fruit species tested, rodent feeding increased seed germination rate by a factor of 3.5. Our results suggest that rodents can play a significant role in enhancing germination rates of fruits in the tropical rainforest of far north Queensland.

Environmental and economic evaluation of N fertilizer rates in a maize crop in Italy : a spatial and temporal analysis using crop models

Crop simulation models have the potential to assess the risk associated with the selection of a specific N fertilizer rate, by integrating the effects of soil-crop interactions on crop growth under different pedo-climatic and management conditions. The objective of this study was to simulate the environmental and economic impact (nitrate leaching and N2O emissions) of a spatially variable N fertilizer application in an irrigated maize field in Italy. The validated SALUS model was run with 5 nitrogen rates scenarios, 50, 100, 150, 200, and 250 kg N ha−1, with the latter being the N fertilization adopted by the farmer. The long-term (25 years) simulations were performed on two previously identified spatially and temporally stable zones, a high yielding and low yielding zone. The simulation results showed that N fertilizer rate can be reduced without affecting yield and net return. The marginal net return was on average higher for the high yield zone, with values ranging from 1550 to 2650 € ha−1 for the 200 N and 1485 to 2875 € ha−1 for the 250 N. N leaching varied between 16.4 and 19.3 kg N ha−1 for the 200 N and the 250 N in the high yield zone. In the low yield zone, the 250 N had a significantly higher N leaching. N2O emissions varied between 0.28 kg N2O ha−1 for the 50 kg N ha−1 rate to a maximum of 1.41 kg N2O ha−1 for the 250 kg N ha−1 rate.

Unintended pregnancies : reducing rates by improving access to contraception

Unintended pregnancies have significant social, health and financial costs. Importantly, there is surprisingly little information available about the prevalence of unintended pregnancy in Australia. We are currently investigating unintended pregnancy and access to contraception among women aged 18–23 years in rural and urban areas of New South Wales. This is the first step toward understanding how access to effective contraception can be improved and could act as a pilot study for a regular survey of fertility.

Miscarriage, preterm delivery, and stillbirth: Large variations in rates within a cohort of Australian women

Objectives We aimed to use simple clinical questions to group women and provide their specific rates of miscarriage, preterm delivery, and stillbirth for reference. Further, our purpose was to describe who has experienced particularly low or high rates of each event. Methods Data were collected as part of the Australian Longitudinal Study on Women's Health, a national prospective cohort. Reproductive histories were obtained from 5806 women aged 31–36 years in 2009, who had self-reported an outcome for one or more pregnancy. Age at first birth, number of live births, smoking status, fertility problems, use of in vitro fertilisation (IVF), education and physical activity were the variables that best separated women into groups for calculating the rates of miscarriage, preterm delivery, and stillbirth. Results Women reported 10,247 live births, 2544 miscarriages, 1113 preterm deliveries, and 113 stillbirths. Miscarriage was correlated with stillbirth (r = 0.09, P<0.001). The calculable rate of miscarriage ranged from 11.3 to 86.5 miscarriages per 100 live births. Women who had high rates of miscarriage typically had fewer live births, were more likely to smoke and were more likely to have tried unsuccessfully to conceive for ≥12 months. The highest proportion of live preterm delivery (32.2%) occurred in women who had one live birth, had tried unsuccessfully to conceive for ≥12 months, had used IVF, and had 12 years education or equivalent. Women aged 14–19.99 years at their first birth and reported low physical activity had 38.9 stillbirths per 1000 live births, compared to the lowest rate at 5.5 per 1000 live births. Conclusion Different groups of women experience vastly different rates of each adverse pregnancy event. We have used simple questions and established reference data that will stratify women into low- and high-rate groups, which may be useful in counselling those who have experienced miscarriage, preterm delivery, or stillbirth, plus women with fertility intent.