Optimum model selection and statistical analysis for DNA sequences

In this article, we study the statistical characteristics and examine the performance of original representation and mathematical modelling of deoxyribonucleic acid (DNA) sequences. The proposed mathematical modelling approach is presented to create closed formulas for the original DNA data sequences with different methods. Accuracy of representation is studied based on evaluation metric values. The root Mean Squared Error (RMSE) and correlation coefficient (R) are used for examining the accuracy of all mathematical models to select the optimum one for DNA representation. In addition, statistical parameters such as energy, entropy, standard deviation, variance, mean, range, Mean Absolute Deviation (MAD), skewness and kurtosis are also used for the selection of the optimum model for DNA representation. Finally, spectral estimation methods are used for exon prediction, which means determination of the coding region (exon) for actual sequences and selected mathematical model: Sum of Sinusoids (SoS) with 8 terms and Gaussian with 8 terms. The exon prediction results from original DNA sequences and mathematically modelled DNA sequences coincide and ensure the success of the proposed sum-of--sinusoids for modelling of DNA sequences, while the Gaussian model is not appropriate for this task.