Non-linear regression models for Approximate Bayesian Computation

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics is increased. Here we propose a machine-learning approach to the estimation of the posterior density by introducing two innovations. The new method fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics, and then adaptively improves estimation using importance sampling. The new algorithm is compared to the state-of-the-art approximate Bayesian methods, and achieves considerable reduction of the computational burden in two examples of inference in statistical genetics and in a queueing model.Comment: 4 figures; version 3 minor changes; to appear in Statistics and Computin

Arsenic toxicity to cladocerans isolated and associated with iron: implications for aquatic environments

ABSTRACT Arsenic is an ametal ubiquitous in nature and known by its high toxicity. Many studies have tried to elucidate the arsenic metabolism in the cell and its impact to plants, animals and human health. In aqueous phase, inorganic arsenic is more common and its oxidation state (As III and As V) depends on physical and chemical environmental conditions. The aim of this study was to evaluate toxicity of arsenic to Daphnia similis and Ceriodaphnia silvestrii, isolated and associated with iron. The results showed differences in toxicity of As III and As V to both species. Effective concentration (EC50) mean values were 0.45 mg L-1 (As III) and 0.54 mg L-1 (As V) for D. similis, and 0.44 mg L-1 (As III) and 0.69 mg L-1 (As V) for C. silvestrii. However, As V IC25 mean value was 0.59 mg L-1, indicating that C. silvestrii has mechanisms to reduce arsenic toxicity. On the other hand, when associated with iron at 0.02 and 2.00 mg L-1, EC50 values decreased for D. similis (0.34 and 0.38 mg L-1) as well as C. silvestrii (0.37 and 0.37 mg L-1), showing synergistic effect of these substances