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The main aim of this paper is to present a Bayesian analysis of Multivariate GARCH(l, m) (M-GARCH) models including estimation of the coefficient parameters as well as the model order, by combining a set of existing MCMC algorithms in the literature. The proposed algorithm focuses on the BEKK formulation of the multivariate GARCH model. The estimation procedure will be designed as a custom MCMC with embedded Reversible Jump MCMC (RJMCMC) and Delayed Rejection Metropolis-Hastings (DRMH) steps implemented using the statistical software R. The RJMCMC steps allow three variants of BEKK models (constant, diagonal and full) to be indexed and this index included as a parameter to be estimated. The proposed MCMC algorithms are validated using extensive simulation experiments followed by a case study using bivariate data derived from the daily share prices for BHP Group Limited, Rio Tinto Group, and Fortescue Metals Group Limited on the ASX over from September 2013 to December 2021. [ABSTRACT FROM AUTHOR]

With continued pressure upon fisheries, alongside improved fisheries management in some places, there has been a decline in fish catches with changes in the structure of the ecosystem affecting its' functionality. The use of scientific based indicator frameworks in an attempt to pursue sustainable fisheries is a common trend, however the management decisions are often socially driven and can deviate, or even, conflict with the science. This study aimed to investigate British Gen Z perceptions upon what creates a sustainable fishing industry through a series of three studies. A compilation of 82 statements, derived from practitioner indicator systems, was used by 23 participants in a concept mapping process consisting of five steps; create statements, sort & rate statements, multi-dimensional scaling of sorted units, cluster analysis, and label the clusters. The next stage of the study looked to refine the large number of statements by statistically verifying them with exploratory factor analysis and confirmatory composite analysis using split halves of a sample containing 657 participants and generating a three-factor solution of Community, Ecological Management and, Economic. The domain was then switched to the descriptive typology and a further 179 British Gen Z evaluated the fisheries at Hastings and Brixham based upon case studies which further validated the three-factor solution. The significance of this study demonstrates that consumers, who influence policy and management of fisheries through their purchasing behaviour, interpret sustainable fisheries differently to science which is evidenced by the merging of the elements of ecologically and management. [ABSTRACT FROM AUTHOR]