Tags:Conjugate Prior, Credible Interval, Normal Distribution and Posterior Distribution
Abstract:
Aquatic life and water quality can be negatively impacted by suspended particles. They may lessen water clarity and obstruct sunlight, which may prevent aquatic plants from photosynthesis. A risk to human health if consumed, they can also transport nutrients and toxins like germs and heavy metals that can affect aquatic life. Thus minimizing suspended particles is a crucial part of managing water quality. This study is aimed at modeling suspended solids in the two major reservoirs in Oyo state (Asejire and Eleyele reservoirs). Bayesian inference, because of its incorporation of prior information, flexibility, probability estimations and prediction was used for this study. Suspended solids in both reservoirs observed over a period of 200 months from 2003 to 2019 assumes Normal Distribution. A conjugate prior for normal density was used to give an update of knowledge about suspended solids inform of the posterior distribution with unknown mean and known precision. The posterior mean and precision for Asejire Reservoir and that of Eleyele Reservoir was obtained. In addition, the 95% credible interval was obtained for the two reservoirs. It is likely that the true (unknown) Bayesian estimate of suspended solids in Asejire Reservoir and Eleyele Reservoir would lie within a particular interval. Using the knowledge of the posterior distribution, the posterior predictive distribution of future observation was determined. There is an update of belief about the posterior mean of suspended solids in both reservoirs in Oyo state. Also the posterior median and standard deviation were evaluated if rounding was ignored. Concerned authorities should be informed that Eleyele reservoir is more polluted with suspended solids than Asejire reservoir.
On the Bayesian Modeling of Suspended Solids in Oyo State Reservoirs