International Journal of Scientific and Research Publications, Volume 3, Issue 2, February 2013 1 ISSN 2250-3153 www.ijsrp.org Bayesian Ecometrics – A genial device to ponder Ecological Data Analysis Subbiah, M * , Kamal Nasir, V ** , Srinivasan, M.R *** , Naveed, MS **** * Department of Mathematics, L.N Government College, Ponneri, India ** Department of Mathematics, The New College, Royapettah, Chennai, Tamil Nadu, India *** Department of Statistics, University of Madras, Chennai, Tamilnadu, India **** Department of Zoology, The New College, Royapettah, Chennai Tamil Nadu, India Abstract- Bayesian statistics is becoming an important statistical tool for practitioners to deal with analysis of complex data and complicated statistical models. The impact of Bayesian analysis in combination with Markov Chain Monte Carlo (MCMC) technology is realized optimally in the domain of applications. The ecological data could be a storehouse of natural history and experimental data is used to address hidden uncertainty. Bayesian inference could be the most straightforward and natural way of analyzing and interpreting the related ecological hypotheses. This study basically aims to exploit the inbuilt advantages of Bayesian approach in studying the prevalence of Meiofaunal population from the data collected at five different (Pulicat, Royapuram, Napier, Marina, Adyar) coastal areas of Chennai, India. Index Terms- Bayesian methods, MCMC, Meiofauna, Sparseness, WinBUGS I. INTRODUCTION tatistics has a significant and unique characteristic that has been influenced largely by many other sciences with which it could interact. The list of other faculties include an extensively large number of areas such as atmospheric, bio medical, economic sciences, ecological, educational, psychological, public health, market research and many more. Most or all these studies could provide an ample scope for statistical intervention or contribution with their objective and vast array of data in high dimensional or hierarchical methods. The challenges in data analysis has also been faced and during these kind of interventions, yet the powerful advanced computational developments lead or assist statistics into a greater and broader purview of data modeling and effective and meaningful interpretations. It is also to point out that with a visible better growth in the communication between statistics and other disciplines of science, a scope in incorporate subject matter, experts‟ opinion has been increased in many data analyses and model building. Piegorsch et al (1998) have observed this twin advantage as an upward spiral so that science and society could benefit with the interactions of disciplines. Statistic in a wider perspective could be classified as long run frequentist and Bayesian paradigms. A lot of conceptual and computational difference exists between these two methodologies; however this work does not intend to compare or contrast the two procedures. The principle aim of the paper is to have a broader outline of three fold aspects; building the theory, computations and an application specifically to an ecological study. As recent decades could witness a surge in the application of Bayesian statistics and many researchers have pointed out the advantages from model formulation to interpretation of the results, this present work could be considered as another application of Bayesiansim to a more complicated study in that usual “log run” or “identical sample” assumptions might not hold apparently. The paper has been organized as follows; section 2 lists recent and appropriate Bayesian literature pertains in particular to many ecological data. Section 3 covers a quick overview of conceptual and computational aspects of Bayesian statistics. The ecological data that has been considered for the present study is elaborated in section 4. An illustrative data analysis has been presented in section 5 and concluding remarks in section 6. II. BAYESIANS AT WORK From the mid 20 th century, with the availability of fast, accurate and affordable computing algorithms and machines, Bayesian approach could find a large scale applications in many fields from agriculture to business; medicine to social psychological studies; education to economics. However, this work aims in presenting a few yet more reasonable list of literature in environmental, ecological or generally bio scientific studies. Stephans et al (2006) have pointed out the way ecologists and evolutionary biologists who deal with high natural variability system and dependence of statistical procedure for their inference. A chronological sequence of articles could provide many interesting applications of Bayesian methods ranging from parameter estimations to linear model to meta-analysis. As noted earlier. Piegorsch et al (1998) have discussed some selected applications of statistical theory to environmental sciences that include atmospheric pollution, mortality analysis, space-time modeling of acid rain, ecological monitoring and assessment and animal populations. Gurevitch and Hedges (1999) have elaborated the methods for the meta-analysis of ecological data that include fixed vs mixed models and regression-type analyses. In Qian et al (2000) have presented a non parametric Bayesian binary response model that could be applied to many applications such as a study on fish response to acid deposition in Adirondack lakes (USA). S