Taking error into account when fitting models using Approximate Bayesian Computation.

Stochastic computer simulations are often the only practical way of answering questions relating to ecological management. However, due to their complexity, such models are difficult to calibrate and evaluate. Approximate Bayesian Computation (ABC) offers an increasingly popular approach to this problem, widely applied across a variety of fields. However, ensuring the accuracy of ABC's estimates has been difficult. Here, we obtain more accurate estimates by incorporating estimation of error into the ABC protocol. We show how this can be done where the data consist of repeated measures of the same quantity and errors may be assumed to be normally distributed and independent. We then derive the correct acceptance probabilities for a probabilistic ABC algorithm, and update the coverage test with which accuracy is assessed. We apply this method, which we call error-calibrated ABC, to a toy example and a realistic 14-parameter simulation model of earthworms that is used in environmental risk assessment. A comparison with exact methods and the diagnostic coverage test show that our approach improves estimation of parameter values and their credible intervals for both models.

Semi-automatic selection of summary statistics for ABC model choice.

A central statistical goal is to choose between alternative explanatory models of data. In many modern applications, such as population genetics, it is not possible to apply standard methods based on evaluating the likelihood functions of the models, as these are numerically intractable. Approximate Bayesian computation (ABC) is a commonly used alternative for such situations. ABC simulates data x for many parameter values under each model, which is compared to the observed data x obs. More weight is placed on models under which S(x) is close to S(x obs), where S maps data to a vector of summary statistics. Previous work has shown the choice of S is crucial to the efficiency and accuracy of ABC. This paper provides a method to select good summary statistics for model choice. It uses a preliminary step, simulating many x values from all models and fitting regressions to this with the model as response. The resulting model weight estimators are used as S in an ABC analysis. Theoretical results are given to justify this as approximating low dimensional sufficient statistics. A substantive application is presented: choosing between competing coalescent models of demographic growth for Campylobacter jejuni in New Zealand using multi-locus sequence typing data.

Estimating age of mature adults from the degeneration of the sternal end of the clavicle.

The sternal end of the clavicle has been illustrated to be useful in aging young adults, however, no studies have investigated what age-related changes occur to the sternal end post epiphyseal fusion. In this study, three morphological features (i.e., surface topography, porosity, and osteophyte formation) were examined and scored using 564 clavicles of individuals of European ancestry (n = 318 males; n = 246 females), with known ages of 40+ years, from four documented skeletal collections: Hamann-Todd, Pretoria, St. Bride's, and Coimbra. An ordinal scoring method was developed for each of the three traits. Surface topography showed the strongest correlation with age, and composite scores (formed by summing the three separate trait scores) indicated progressive degeneration of the surface with increasing chronological age. Linear regression analyses were performed on the trait scores to produce pooled-sample age estimation equations. Blind tests of the composite score method and regression formulae on 56 individuals, aged 40+ years, from Christ Church Spitalfields, suggest accuracies of 96.4% for both methods. These preliminary results display the first evidence of the utility of the sternal end of the clavicle in aging older adult individuals. However, in the current format, these criteria should only be applied to individuals already identified as over 40 years in order to refine the age ranges used for advanced age. These findings do suggest the sternal end of the clavicle has potential to aid age estimates beyond the traditional "mature adult" age category (i.e., 46+ years), and provides several suggestions for future research.

A tutorial introduction to Bayesian inference for stochastic epidemic models using Approximate Bayesian Computation.

Likelihood-based inference for disease outbreak data can be very challenging due to the inherent dependence of the data and the fact that they are usually incomplete. In this paper we review recent Approximate Bayesian Computation (ABC) methods for the analysis of such data by fitting to them stochastic epidemic models without having to calculate the likelihood of the observed data. We consider both non-temporal and temporal-data and illustrate the methods with a number of examples featuring different models and datasets. In addition, we present extensions to existing algorithms which are easy to implement and provide an improvement to the existing methodology. Finally, R code to implement the algorithms presented in the paper is available on https://github.com/kypraios/epiABC.