Bootstrap Approach to Correlation Analysis of Two Mineral Components in a Geological Field

Abstract

In this article we considered pairs bootstrap through a truncated geometric bootstrap method for stationary time series data. Construction of valid inferential procedures through the estimates of standard error, coefficient of variation and other measures of statistical precision such as bootstrap confidence interval were considered. The method was used to confirm the correlation between Silicon Oxide (S_iO₂) and Aluminium Oxide (Al₂O₃) from a geological data. A typical problem is that can these components exist together or they are mutually exclusive. We attempt to solve these problem through bootstrap approach to correlation analysis and show that pair bootstrap method through truncated geometric bootstrap method for stationary process revealed the correlation coefficient between Silicon oxide (SiO₂) and Aluminium oxide (Al₂O₃) from the same geological field.  The computed measure of statistical precisions such as standard error, coefficient of variation and bootstrap-t confidence interval revealed the correlation analysis of the bivariate stochastic processes of SiO₂ and Al₂O₃ components from the same geological field.

The correlation analysis of the bivariate stochastic process of SiO₂ and Al₂O₃ components through bootstrap method discussed in this paper revealed that the correlation coefficient are negative and bootstrap confidence intervals are negatively skewed for all bootstrap replicates. This implies that as one component increases, the other component decreases, which mean that the two components are mutually exclusive and the abundance of one mineral prevents the other in the same oil reservoir of the same geological field.

Key words: Pair bootstrap, standard error, coefficient of variation, bootstrap-t confidence interval and correlation analysis.