Approximate Bayesian Computation (ABC) methods are increasingly used for inference in situations in which the likelihood function is either computationally costly or intractable to evaluate. Extensions of the basic ABC rejection algorithm have improved the computational efficiency of the procedure and broadened its applicability. The ABC - Population Monte Carlo (ABC-PMC) approach has become a popular choice for approximate sampling from the posterior. ABC-PMC is a sequential sampler with an iteratively decreasing value of the tolerance, which specifies how close the simulated data need to be to the real data for acceptance. We propose a method for adaptively selecting a sequence of tolerances that improves the computational efficiency of the algorithm over other common techniques. In addition we define a stopping rule as a by-product of the adaptation procedure, which assists in automating termination of sampling. The proposed automatic ABC-PMC algorithm can be easily implemented and we present several examples demonstrating its benefits in terms of computational efficiency.

We examined parameter optimisation in the JSBACH (Kaminski et al., 2013; Knorr and Kattge, 2005; Reick et al., 2013) ecosystem model, applied to two boreal forest sites (Hyytiala and Sodankyla) in Finland. We identified and tested key parameters in soil hydrology and forest water and carbon-exchange-related formulations, and optimised them using the adaptive Metropolis (AM) algorithm for Hyytil with a 5-year calibration period (2000-2004) followed by a 4-year validation period (2005-2008). Sodankyla acted as an independent validation site, where optimisations were not made. The tuning provided estimates for full distribution of possible parameters, along with information about correlation, sensitivity and identifiability. Some parameters were correlated with each other due to a phenomenological connection between carbon uptake and water stress or other connections due to the set-up of the model formulations. The latter holds especially for vegetation phenology parameters. The least identifiable parameters include phenology parameters, parameters connecting relative humidity and soil dryness, and the field capacity of the skin reservoir. These soil parameters were masked by the large contribution from vegetation transpiration. In addition to leaf area index and the maximum carboxylation rate, the most effective parameters adjusting the gross primary production (GPP) and evapotranspiration (ET) fluxes in seasonal tuning were related to soil wilting point, drainage and moisture stress imposed on vegetation. For daily and half-hourly tunings the most important parameters were the ratio of leaf internal CO2 concentration to external CO2 and the parameter connecting relative humidity and soil dryness. Effectively the seasonal tuning transferred water from soil moisture into ET, and daily and half-hourly tunings reversed this process. The seasonal tuning improved the month-to-month development of GPP and ET, and produced the most stable estimates of water use efficiency. When compared to the seasonal tuning, the daily tuning is worse on the seasonal scale. However, daily parametrisation reproduced the observations for average diurnal cycle best, except for the GPP for Sodankyla validation period, where half-hourly tuned parameters were better. In general, the daily tuning provided the largest reduction in model-data mismatch. The models response to drought was unaffected by our parametrisations and further studies are needed into enhancing the dry response in JSBACH.

Bayesian inference plays an important role in phylogenetics, evolutionary biology, and in many other branches of science. It provides a principled framework for dealing with uncertainty and quantifying how it changes in the light of new evidence. For many complex models and inference problems, however, only approximate quantitative answers are obtainable. Approximate Bayesian computation (ABC) refers to a family of algorithms for approximate inference that makes a minimal set of assumptions by only requiring that sampling from a model is possible. We explain here the fundamentals of ABC, review the classical algorithms, and highlight recent developments.

The application of mean-field rate theory equations have proven to be a versatile method in simulating defect dynamics and temporal changes in the microstructure of materials. The reliability and usefulness of the method, however, depends critically on the defect interaction parameters used. In this study, we show that the main interaction parameter, the sink strength, intrinsically depends on the detrapping, or the dissociation process itself. We present a theory on how to determine the appropriate sink strengths. The correct sink strength required for a detrapping defect, is considerably larger than the values commonly used, and thus should not be neglected.

A measurement of beauty hadron production at mid-rapidity in proton-lead collisions at a nucleon-nucleon centre-of-mass energy root s(NN) = 5.02 TeV is presented. The semi-inclusive decay channel of beauty hadrons into J/psi is considered, where the J/psi mesons are reconstructed in the dielectron decay channel at mid-rapidity down to transverse momenta of 1.3 GeV/c. The bb production cross section at mid-rapidity, d sigma(bb)/dy, and the total cross section extrapolated over full phase space, sigma(bb), are obtained. This measurement is combined with results on inclusive J/psi production to determine the prompt J/psi cross sections. The results in p-Pb collisions are then scaled to expectations from pp collisions at the same centre-of-mass energy to derive the nuclear modification factor R-pPb, and compared to models to study possible nuclear modifications of the production induced by cold nuclear matter effects. RpPb is found to be smaller than unity at low pT for both J/psi coming from beauty hadron decays and prompt J/psi.

Ion beam processing of surfaces is well known to lead to sputtering, which conventionally is associated only with erosion of atoms from the material. We show here, by combination of experiments and a newly developed Monte Carlo algorithm, that in the case of nanoparticles in a regular two-dimensional array on surfaces, the redeposition of sputtered atoms may play a significant role on the system development. The simulations are directly compared to in situ experiments obtained using a dual focused Ga+ ion beam system and high resolution scanning electron microscopy, and explain the size evolution by a combination of sputtering and redeposition of sputtered material on neighboring particles. The effect is found to be dependent on the size of the nanoparticles: if the nanoparticle size is comparable to the ion range, the reposition is negligible. For larger nanoparticles the redeposition becomes significant and is able to compensate up to 20% of the sputtered material, effectively reducing the process of sputtering. The redeposition may even lead to significant growth: this was seen for the nanoparticles with the sizes much smaller than the ion range. Furthermore, the algorithm shows that significant redeposition is possible when the large size neighboring nanoparticles are present.