Approximate Bayesian computation (ABC) gives exact results under the assumption of model error

Approximate Bayesian computation (ABC) or likelihood-free inference algorithms are used to find approximations to posterior distributions without making explicit use of the likelihood function, depending instead on simulation of sample data sets from the model. In this paper we show that under the assumption of the existence of a uniform additive model error term, ABC algorithms give exact results when sufficient summaries are used. This interpretation allows the approximation made in many previous application papers to be understood, and should guide the choice of metric and tolerance in future work. ABC algorithms can be generalized by replacing the 0-1 cut-off with an acceptance probability that varies with the distance of the simulated data from the observed data. The acceptance density gives the distribution of the error term, enabling the uniform error usually used to be replaced by a general distribution. This generalization can also be applied to approximate Markov chain Monte Carlo algorithms. In light of this work, ABC algorithms can be seen as calibration techniques for implicit stochastic models, inferring parameter values in light of the computer model, data, prior beliefs about the parameter values, and any measurement or model errors.Comment: 33 pages, 1 figure, to appear in Statistical Applications in Genetics and Molecular Biology 201

Micro-experimental analysis of the small-group reading lesson : social and cognitive consequences of silent reading

Includes bibliographical references (p. 18-20

Re-examining the Impact of the National Minimum Wage on Earnings, Employment and Hours: The Importance of Recession and Firm Size

Research to date suggests that the UK National Minimum Wage (NMW) has raised the earnings of low paid workers, without significantly affecting their employment opportunities. We re-examine existing evidence and suggest the picture is less clear cut. We explore whether the impacts of the NMW differ for workers in different size firms. Examining more recent data we investigate whether the NMW has affected the employment opportunities of low paid workers during the recession. In contrast to previous research we find some evidence to suggest that the introduction of the NMW may have had a small adverse impact on the employment opportunities of particular low paid workers, although, in line with previous research, for many low paid workers we find no impact. In general, it is not obvious that the impacts of the NMW on employment have differed over the business cycle. In comparison to other workers, low paid workers are more likely to work in smaller firms. We find that on average any potentially harmful effects of the NMW on the employment chances of low paid workers tend to be more significant amongst employees in large firms. Identification of the average hours effects of the NMW is hampered by the difficulty in finding a suitable control group

The impact on employment of the age related increases in the National Minimum Wage

In this paper we use a regression discontinuity approach to analyse the effect of the legislated increase in the UK National Minimum Wage (NMW) at age 22 on various labour market outcomes. Using data from the Labour Force Survey we find a statistically significant 5% point increase in the employment rate of the low skilled at age 22 years. This is almost wholly explained by a decline in unemployment among men and inactivity among women. We find no effect before the NMW was introduced and no effect at age 21 or 23 years. Our results are robust to a range of specification and tests

The employment and hours of work effects of the changing National Minimum Wage

This report is about the employment impacts of National Minimum Wage (NMW) rises in the period 2001-2006. This was a period where the NMW rose substantially in excess of average earnings. The report presents results based on analysis of individual Labour Force Survey (LFS) data and Annual Survey of Hours and Earnings (ASHE) data together with local area analysis. The focus of the analysis is threefold. First, it investigates changes in wages as a response to increases in the NMW. Second, it analyses employment to see if changes in the NMW influenced individual job retention and job exit, job entry, local area employment and unemployment rates. Third, it focusses on analysis of hours worked to see if employers changed hours worked as a response to changes in the NMW

The UK Minimum Wage at Age 22: A Regression Discontinuity Approach

A regression discontinuity approach is used to analyse the effect of the legislated increase in the UK National Minimum Wage (NMW) that occurs at age 22 on various labour market outcomes. Using data from the Labour Force Survey we find a 2- 4% point increase in the employment rate of low skilled individuals. Unemployment declines among men and inactivity among women. We find no such effect before the NMW was introduced and no robust impacts at age 21 or 23 years. Our results are robust to a range of specification tests.Minimum Wage Legislation, Low Wage

The influence of great toe valgus on pronation and frontal plane knee motion during running

Injury rates in running range from 19.4‐79.3%, with injuries at the knee comprising 42.1%. Pronation and altered frontal plane knee joint range of motion have been linked to such injuries. The influence of foot structure on pronation and knee kinematics has not been examined in running. This study examined associations between great toe valgus angle, peak pronation angle and frontal plane range of movement at the knee joint during overground running while barefoot. Great toe valgus angle while standing, and peak pronation angle and frontal plane range of motion of the dominant leg during stance while running barefoot on an indoor track were recorded in fifteen recreational runners. There was a large, negative association between great toe valgus angle and peak pronation angle (r = -0.52, p = 0.04), and a strong positive association between great toe valgus angle and frontal plane range of motion at the knee joint (r = 0.67, p = 0.006). The results suggest that great toe position plays an important role in foot stability and upstream knee-joint motion. The role of forefoot structure as a factor for knee-joint injury has received little attention and could be a fruitful line of enquiry in the exploration of factors underpinning running-related knee injuries

ABC for Climate: Dealing with Expensive Simulators

A single molecule or molecule complex detection method is disclosed in certain aspects, comprising nano- or micro-fluidic channels.U