The development of a consistent framework for Calphad model sensitivity is necessary for the rational reduction of uncertainty via new models and experiments. In the present work, a sensitivity theory for Calphad was developed, and a closed-form expression for the log-likelihood gradient and Hessian of a multi-phase equilibrium measurement was presented. The inherent locality of the defined sensitivity metric was mitigated through the use of Monte Carlo averaging. A case study of the Cr–Ni system was used to demonstrate visualizations and analyses enabled by the developed theory. Criteria based on the classical Cramér–Rao bound were shown to be a useful diagnostic in assessing the accuracy of parameter covariance estimates from Markov Chain Monte Carlo. The developed sensitivity framework was applied to estimate the statistical value of phase equilibria measurements in comparison with thermochemical measurements, with implications for Calphad model uncertainty reduction.

In the rural areas of the eastern Amhara region where livelihoods are predominantly based on agriculture with almost all the rural people earning their income from agriculture, awareness toward clean energy, and efficient appliances is at a very infant stage. As an indication, the research comes up with energy utilization is mainly of biomass-based with traditional stoves of very low efficiency. However, the future demand of the community toward the clean and improved efficient appliances has got a better preference over other energy technologies. Regarding the factor in determining the energy and energy appliance type choice, accessibility is found as the major reason.

The type of energy sources and energy technologies utilized for cooking and lighting have their own effect on health, environmental degradation, and overall economic development. Therefore, the primary objective of this study was to analyze the general trend of household energy source and energy technology utilization in rural areas of the Eastern Amhara region. The study utilized primary and secondary data collected over stratified systematically sampled households and from energy experts in the area. The study examined the utilization of various forms of energy and energy technology for the most common household energy-intensive processes (injera baking and stew cooking) as well as lighting. The development of different estimates across the whole population of the study region to indicate the relations among different factors was done through different statistical approaches; and the finding of the analysis revealed that 57.7% of the energy share is biomass-based firewood from which 99.5% of this source was used only for food preparation. The two main determinant factors of the community in selecting the energy types are found to be accessibility and health impact.