Bayesian quasi-likelihoods constructed from estimating functions enable the use of semi-parametric inference in Bayesian inference. This makes Bayesian inference applicable to problems with looser parametric assumptions. Loosening parametric assumptions can simplify model specifications and inference designs. This is especially beneficial for environmental studies, which is an interdisciplinary subject covering a wide range of topics. This study focuses on the adoption of quasi-likelihoods in two environmental applications that are common in environmental studies.

The first application discussed in this study is the construction of quasi-likelihoods from composite score functions for Bayesian inference on spatio-temporal models. Nonetheless, composite score functions are a class of estimating functions with a complex structure. Quasi-likelihoods constructed from estimating functions with complex structures usually deform. To solve the deformation problem, we demonstrate and explain theoretically why the deformation happens. Then, we introduce a method of quasi-likelihood regularization which effectively handles the deformation and restores the nice statistical properties of the quasi-likelihoods. For an empirical demonstration, we apply the quasi-likelihood regularization for Bayesian inference on a spatio-temporal model studying the concentration of ground-level ozone in Hong Kong.

The second application discussed in this study is a Bayesian Randomized Response Technique (RRT) method, which mitigates the response distortion resulting from dishonest answers in survey studies. In studies of attributes related to deviant behavior, respondents may provide untruthful answers to hide their sensitive attributes. RRT is a classic technique for mitigating response distortion, but few studies have used RRT to analyze multiple quantitative attributes. Therefore, we formulate a Bayesian RRT method, whose (quasi-)likelihood is constructed from certain moment equations, so as to develop a reliable and stable RRT method for the analysis of multiple quantitative attributes. Simulation studies are conducted to justify the effectiveness of the Bayesian RRT method, and an empirical study is conducted to demonstrate the method.

Recently, the Hong Kong government has proposed a quantity-based municipal solid waste charging scheme aiming at reducing the generation of waste in Hong Kong. It is expected that the implementation of the scheme will induce illegal waste dumping. In this study, we construct a behavioral model based on psychological theories to identify the key determinants of illegal waste dumping. As illegal waste dumping is a sensitive behavior, we demonstrate how the Bayesian RRT method can be applied to mitigate the distortion from dishonest answers when fitting the behavioral model. The coefficient analysis of the fitted behavioral model reveals the effectiveness of various policy mixes for deterring illegal waste dumping.