Recent new methods in Bayesian simulation have provided ways of evaluating posterior distributions in the presence of analytically or computationally intractable likelihood functions. Despite representing a substantial methodological advance, existing methods based on rejection sampling or Markov chain Monte Carlo can be highly inefficient and accordingly require far more iterations than may be practical to implement. Here we propose a sequential Monte Carlo sampler that convincingly overcomes these inefficiencies. We demonstrate its implementation through an epidemiological study of the transmission rate of tuberculosis.

Flint revisitedAs explained in your April 2017 cover story, "The murky tale of Flint's deceptive water data", the Lead and Copper Rule (bit.ly/2tE5dlF) states that action needs to be taken if the 90th percentile is above 15 ppb or, equivalently, if this value is exceeded in more than 10% of the homes tested. Looking into the details of §141.80(3) of the rule, one finds that the algorithm for computing the percentile is ambiguous for sample sizes where 0.9n is not an integer. This is not a problem for the sample sizes stipulated by §141.86(c), but it is for the Flint monitoring sample with n = 71. As shown in Hyndman and Fan, 1 there are many ways to compute the sample percentile. However, one can show that only the inverse of the empirical cumulative distribution function, i.e. type = 1, fulfils the required duality between the proportion and the percentile. The percentile is thus obtained by first ordering the sample in ascending order and then selecting the observation where the index is equal to the first integer number greater or equal to 0.9n.For the Flint data this would mean index 64, resulting in the 90th percentile being 18 ppb. The reported percentile value in your article instead appears to be the type=5 result of 18.8 ppb (rounded to 19 ppb). Clearly, this does not make a big difference in this particular case, but might be of importance in other situations.Altogether, the proportion of non-conforming samples appears to be a more intuitive quantity to use instead of the percentile. As a statistician, one also wonders why the rule does not try to account for uncertainty arising from only having a sample from the pool of high-risk sites and potential measurement error, for example by using survey sampling methods. The decision to act could in this context be formulated based on a statistical hypothesis test -as routinely done in statistical quality control. Further details and R code can be found at bit.ly/2uMzlvh.

Gendered and racial inequalities persist in even the most progressive of workplaces. There is increasing evidence to suggest that all aspects of employment, from hiring to performance evaluation to promotion, are affected by gender and cultural background. In higher education, bias in performance evaluation has been posited as one of the reasons why few women make it to the upper echelons of the academic hierarchy. With unprecedented access to institution-wide student survey data from a large public university in Australia, we investigated the role of conscious or unconscious bias in terms of gender and cultural background. We found potential bias against women and teachers with non-English speaking backgrounds. Our findings suggest that bias may decrease with better representation of minority groups in the university workforce. Our findings have implications for society beyond the academy, as over 40% of the Australian population now go to university, and graduates may carry these biases with them into the workforce.

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In Bayesian inference, complete knowledge about a vector of model parameters, θ ∈ Θ, obtained by fitting a model M, is contained in the posterior distribution. Here, prior beliefs about the model parameters as expressed through the prior distribution, π(θ), are updated by observing data y obs ∈ Y through the likelihood function π(y obs |θ) of the model. Using Bayes' Theorem, the resulting posterior distribution π(θ|y obs ) = p(y obs |θ)π(θ) Θ p(y obs |θ)π(θ)dθ , contains all necessary information required for analysis of the model, including model checking and validation, predictive inference and decision making. Typically, the complexity of the model and/or prior means that the posterior distribution, π(θ|y obs ), is not available in closed form, and so numerical methods are needed to proceed with the inference. A common approach makes use of Monte Carlo integration to enumerate the necessary integrals.This relies on the ability to draw samples θ (1) , θ (2) , . . . , θ (N ) ∼ π(θ|y obs ) from the posterior distribution so that a finite sample approximation to the posterior is given by the empirical *