Small-Sample Bayesian Analysis of Environment, Income, Internet and Happiness Nexus Amid COVID-19 Pandemic

Research on the dramatic consequences of COVID-19 is important but is challenged by data scarcity problems. In such cases, as frequentist inference requires a sufficiently large dataset to provide significant results, Bayesian inference becomes an alternative approach. To show the Bayesian framework’s advantage in addressing this problem, the research implements a case study on the effects of ecological footprint (EF), environmental performance index (EPI), economic growth, and the Internet on happiness in RCEP (Regional Comprehensive Economic Partnership) for a period of time when the pandemic is in full swing. By utilizing a thoughtful Bayesian approach via the Metropolis-Hasting sampler, the findings are summarized: (i) with insufficient sample size, in contrast to frequentist estimation, thoughtful Bayesian inference can obtain meaningful outcomes, that is, EPI and economic growth positively affect happiness, while EF and internet are negatively related to happiness; (ii) Specifically, from the methodological view, in case of a well-specified prior used, Bayesian inference is robust to different prior specifications; (iii) A generalized conclusion is that, in the face of a small sample, by adding an informative prior to a model parameter of interest, Bayesian simulations so far outperform naïve Bayesian estimation. The authors strongly recommend implementing thoughtful Bayesian estimation in small sample investigations.