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The outer layers of the Earth's atmosphere are known as the ionosphere, a plasma of free electrons and positively charged atomic ions. The electron density of the ionosphere varies considerably with time of day, season, geographical location and the sun's activity. Maps of electron density are useful because local changes in this density can produce inaccuracies in the Navy Navigation Satellite System (NNSS) and Global Positioning System (GPS). Satellite to ground-based receiver measurements produce tomographic information about the density in the form of path integrated snap-shots of the total electron content which must be inverted to generate maps. We propose a Bayesian approach to the inversion problem using spatial priors which allow us parsimoniously to include knowledge of how density varies with height. Less helpfully, this parameterisation does not lend itself well to standard Metropolis-Hastings algorithms and so we develop a much more efficient form of Markov chain Monte Carlo sampler using a transformation of variables based on a principal components analysis of initial output.

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Purpose The purpose of this study is to present a hybrid approach to model and predict long-term energy peak load using Bayesian and Holt–Winters (HW) exponential smoothing techniques. Design/methodology/approach Bayesian inference is administered by Markov chain Monte Carlo (MCMC) sampling techniques. Machine learning tools are used to calibrate the values of the HW model parameters. Hybridization is conducted to reduce modeling uncertainty. The technique is applied to real load data. Monthly peak load forecasts are calculated as weighted averages of HW and MCMC estimates. Mean absolute percentage error and the coefficient of determination (R2) indices are used to evaluate forecasts. Findings The developed hybrid methodology offers advantages over both individual combined techniques and reveals more accurate and impressive results with R2 above 0.97. The new technique can be used to assist energy networks in planning and implementing production projects that can ensure access to reliable and modern energy services to meet the sustainable development goal in this sector. Originality/value This is original research.

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