In this article we show how the pooled-variance two-sample t-statistic arises from a Bayesian formulation of the two-sided point null testing problem, with emphasis on teaching. We identify a reasonable and useful prior giving a closed-form Bayes factor that can be written in terms of the distribution of the two-sample t-statistic under the null and alternative hypotheses respectively. This provides a Bayesian motivation for the two-sample t-statistic, which has heretofore been buried as a special case of more complex linear models, or given only roughly via analytic or Monte Carlo approximations. The resulting formulation of the Bayesian test is easy to apply in practice, and also easy to teach in an introductory course that emphasizes Bayesian methods. The priors are easy to use and simple to elicit, and the posterior probabilities are easily computed using available software, in some cases using spreadsheets. The Bayesian Two-Sample t-TestMithat Gönen, Wesley O. Johnson, Yonggang Lu, and Peter H. WestfallSummary. In this article we show how the pooled-variance two-sample t-statistic arises from a Bayesian formulation of the two-sided point null testing problem, with emphasis on teaching. We identify a reasonable and useful prior giving a closed-form Bayes factor that can be written in terms of the distribution of the two-sample t-statistic under the null and alternative hypotheses respectively. This provides a Bayesian motivation for the twosample t-statistic, which has heretofore been buried as a special case of more complex linear models, or given only roughly via analytic or Monte Carlo approximations. The resulting formulation of the Bayesian test is easy to apply in practice, and also easy to teach in an introductory course that emphasizes Bayesian methods. The priors are easy to use and simple to elicit, and the posterior probabilities are easily computed using available software, in some cases using spreadsheets.

Sustainable food consumption and production play an increasingly important role in improving food security and quality in the food system worldwide. Consumers' food consumption patterns in China, a rapidly emerging economy with the largest population and one of the largest consumer markets in the world, significantly influence the structure of global trade flows and the sustainable ecosystem and environment. In this paper, we assess the emerging demand for imported wild and sustainable Alaskan salmon fillet and varietal parts in China's market through consumers' stated purchase intentions for the products. We use an ordered logit model to link consumers' purchase intentions with potential influencing factors and identify important factors, including consumers' consumption habits, perceptions, and social demographic characteristics. Due to differences between western and Chinese consumers on how different parts of fish are consumed, seemingly low-value salmon heads and bones may carry significant value if being imported and sold to Chinese consumers. We believe that our study is an important step in helping to build a sustainable business model, thereby creating a win-win situation for both the importing and exporting countries in order to allocate resources efficiently, feed people with healthy food, avoid food waste, and fulfill the economic value of products.

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Many Bayes factors have been proposed for comparing population means in two-sample (independent samples) studies. Recently, Wang and Liu (2015) presented an “objective” Bayes factor (BF) as an alternative to a “subjective” one presented by Gönen et al. (2005). Their report was evidently intended to show the superiority of their BF based on “undesirable behavior” of the latter. A wonderful aspect of Bayesian models is that they provide an opportunity to “lay all cards on the table.” What distinguishes the various BFs in the two-sample problem is the choice of priors (cards) for the model parameters. This article discusses desiderata of BFs that have been proposed, and proposes a new criterion to compare BFs, no matter whether subjectively or objectively determined: A BF may be preferred if it correctly classifies the data as coming from the correct model most often. The criterion is based on a famous result in classification theory to minimize the total probability of misclassification. This criterion is objective, easily verified by simulation, shows clearly the effects (positive or negative) of assuming particular priors, provides new insights into the appropriateness of BFs in general, and provides a new answer to the question, “Which BF is best?”