First, we look at an example data set which assists with the introduction of the core concepts of probability in Part I of this book. The set was recorded at the Arkansas Children’s Hospital Research Institute as part of the IMAGE study. The data set includes records of 76 typically developing children (subjects) between the ages of 3 and 10. The 24 recorded variables listed in Table 1.1 are metabolites, metabolite ratios, percentages for two pathways, or reaction networks in humans. Both of these pathways have recently been linked to autism spectrum disorder.
Table 1.1: Metabolites, ratios and percentages of two reaction networks in humans.
Units : [latex]\mu[/latex]M and nM are micromolar and nanomolar respectively, nmol[latex]/[/latex]mg is nanomole per milligram, [latex]/[/latex] denotes unitless, and ox. abbreviates oxidized.
 VariableUnit VariableUnit VariableUnit
1Methionine[latex]\mu[/latex]M2SAMnM3SAHnM
4SAM/SAH[latex]/[/latex]5% DNA methylation[latex]/[/latex]68-OHGnmol[latex]/[/latex]mg
7Adenosine[latex]\mu[/latex]M8Homocysteine[latex]\mu[/latex]M9Cysteine[latex]\mu[/latex]M
10Glu.-Cys.[latex]\mu[/latex]M11Cys.-Gly.[latex]\mu[/latex]M12tGSH[latex]\mu[/latex]M
13fGSH[latex]\mu[/latex]M14GSSG[latex]\mu[/latex]M15fGSH/GSSG[latex]/[/latex]
16tGSH/GSSG[latex]/[/latex]17ChlorotyrosinenM18NitrotyrosinenM
19Tyrosine[latex]\mu[/latex]M20Tryptophane[latex]\mu[/latex]M21fCystinenM
22fCysteinenM23fCystine/fCysteine[latex]/[/latex]24% ox. glutathione[latex]/[/latex]

The 76 children, therefore, originate the 76 measurements. Every measurement contains a value for each of the 24 variables. Figure 1.1 shows the recorded values for the metabolites Adenosine and Homocysteine. At first glance, the values for the recorded concentrations range between 0 and 0.4 [latex]\mu[/latex]M for Adenosine and between 2 to 8 [latex]\mu[/latex]M for Homocysteine. We can assume that the measured concentrations of Adenosine and Homocysteine of subject 19, for example, are not dependent on the measurements for the two metabolites of subject 52. Put differently, if the 76 subjects were randomly selected the measured concentrations of both metabolites are then independent for any two subjects.