Informatics Publishing Limited

Nora Muda ¹, Norashikin Ramli ¹

Affiliations
1 School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, MY

Abstract

Malaysia is a country which is rich in natural resources and one of it is gold. Gold has become an important national commodity. This study focused on gold production in Malaysia and also in 102 countries from 1995 to 2010. The Hierarchical Bayesian Model is selected to determine and explained the scenario of gold production in Malaysia. Through the analysis of hierarchical Bayesian model of the cumulative gold production in Malaysia and other countries for 15 years, the posterior mean of gold production in 102 countries are determined. Variance Partition Coefficient (VPC) is also calculated to quantify percentage of total variation in world gold production attributable to between countries variation. This study has found that the posterior mean for Malaysia and world gold production in hierarchical Bayesian are 3646 kg and 24 180 kg respectively. VPC reading obtained is 0.9226 which indicates that 93% of the total variations were contributed by variation between countries. This shows that the variation of gold production between countries is large and also the correlation of gold production within countries is high.

Keywords

Gold, Posterior Mean, Total Variation, Variance Partition Coefficient, World Gold Production

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Nurul Nadia Zulkefri ¹, Nora Muda ¹, Mohd Nazalan Mohd Najimudin ², Nor Muhammad Mahadi ³, Abdul Munir Abdul Murad ⁴, Nursyafiqi Zainuddin ²

Affiliations
1 School of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, Bangi, 43600, Selangor, MY
2 School of Biological Sciences, Universiti Sains Malaysia, 11800 Georgetown, Penang, MY
3 Malaysia Genome Institute, Ministry of Science, Technology and Innovation, 43000 Kajang, Selango, MY
4 School of Bioscience and Biotechnology, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, Bangi, 43600, Selangor, MY

Abstract

The synthesis of small RNA (sRNA) were extracted from Glaciozyma Antarctica PII2 (G. Antarctica) yeast using the Next-Generation Sequencing (NGS) technology. Statistical approach is used in this study to analyze sRNA from G. Antarctica in order to increase the production of this yeast given in biological conditions such as temperature, time and medium of growth. Hence, this study uses the analysis of variance (ANOVA) with F-test statistic (FANOVA) and shrinkage F-test (FS) to analyze the NGS data in identifying factors affecting the differential expression level of genes from G. Antarctica. FANOVA statistics are computed on a gene-by-gene basis from the residual sum of squares (SSE). Whereas FS-test refers to the shrinking of variance estimators from the variance estimators of the gene-by-gene ( σ  g 2 ) F-value obtained from ANOVA. Then, the analysis results between FANOVA-test and FS-test are compared in order to identify which statistical test is best in analyzing significantly differentially expressed gene based on accuracy value and area under the Receiver Operator Characteristics (ROC) curve. The statistical test with higher accuracy value and has a larger area under the ROC curve is the best statistical test. We found that both FANOVA and FS tests show that the majority of genes that are significantly differentially expressed are most affected by the main effects temperature (A) and time (B) and the interaction effect between temperature and time (AB). As for the best test, we found that FS-test is the best statistical test compared to FANOVA-test in this study of identifying significantly differentially expressed genes in G. Antarctica.

Keywords

ANOVA Model, F Statistics, Shrinkage Estimator, Yeast

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