We compute the Bayesian evidence for models considered in the main analysis of Planck cosmic microwave background data. By utilizing carefully defined nearest-neighbor distances in parameter space, we reuse the Monte Carlo Markov chains already produced for parameter inference to compute Bayes factors B for many different model-data set combinations. The standard 6-parameter flat cold dark matter model with a cosmological constant (ΛCDM) is favored over all other models considered, with curvature being mildly favored only when cosmic microwave background lensing is not included. Many alternative models are strongly disfavored by the data, including primordial correlated isocurvature models (lnB=-7.8), nonzero scalar-to-tensor ratio (lnB=-4.3), running of the spectral index (lnB=-4.7), curvature (lnB=-3.6), nonstandard numbers of neutrinos (lnB=-3.1), nonstandard neutrino masses (lnB=-3.2), nonstandard lensing potential (lnB=-4.6), evolving dark energy (lnB=-3.2), sterile neutrinos (lnB=-6.9), and extra sterile neutrinos with a nonzero scalar-to-tensor ratio (lnB=-10.8). Other models are less strongly disfavored with respect to flat ΛCDM. As with all analyses based on Bayesian evidence, the final numbers depend on the widths of the parameter priors. We adopt the priors used in the Planck analysis, while performing a prior sensitivity analysis. Our quantitative conclusion is that extensions beyond the standard cosmological model are disfavored by Planck data. Only when newer Hubble constant measurements are included does ΛCDM become disfavored, and only mildly, compared with a dynamical dark energy model (lnB∼+2).

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The accurate automated classification of variable stars into their respective subtypes is difficult. Machine learning–based solutions often fall foul of the imbalanced learning problem, which causes poor generalization performance in practice, especially on rare variable star subtypes. In previous work, we attempted to overcome such deficiencies via the development of a hierarchical machine learning classifier. This ‘algorithm-level’ approach to tackling imbalance yielded promising results on Catalina Real-Time Survey (CRTS) data, outperforming the binary and multiclass classification schemes previously applied in this area. In this work, we attempt to further improve hierarchical classification performance by applying ‘data-level’ approaches to directly augment the training data so that they better describe underrepresented classes. We apply and report results for three data augmentation methods in particular: Randomly Augmented Sampled Light curves from magnitude Error (RASLE), augmenting light curves with Gaussian Process modelling (GpFit) and the Synthetic Minority Oversampling Technique (SMOTE). When combining the ‘algorithm-level’ (i.e. the hierarchical scheme) together with the ‘data-level’ approach, we further improve variable star classification accuracy by 1–4 per cent. We found that a higher classification rate is obtained when using GpFit in the hierarchical model. Further improvement of the metric scores requires a better standard set of correctly identified variable stars, and perhaps enhanced features are needed.