Journal of Advanced Statistics

8

Authors: Md. Moyazzem Hossain, Faruq Abdulla

Bangladesh is recognized as a rice-eating nation; nevertheless, large quantities of potatoes are produced and consumed each year. In Bangladesh, potato has gradually gained popularity. Potato is used as food crop as well as vegetable by both the poor and rich people. Recently, the government has been trying to diversify food habits and encourage potato consumption to reduce pressure on rice. In this regard, potato can play an important role as an alternative and a multipurpose food crop of Bangladesh. This study considered the published secondary data of yearly potato production in Bangladesh over the period 1971 to 2013. The best selected Box-Jenkins ARIMA model for forecasting the potato production for whole Bangladesh is ARIMA(0,2,1). The comparison between the original series and forecasted series shows that the fitted model behaved statistically well and is suitable to forecast the potato productions in Bangladesh.

13

Authors: Mehdi Razzaghi, Dong Zhang

To determine the genes that are differentially expressed between samples in microarray experiments, traditionally the expression levels were assessed by taking the intensity levels at a spot on the array and flagging the gene if the magnitude of the fold change exceeded a threshold. Recently, however, there has been much effort to improve the methodology by incorporating the variability of the intensity ratios. While the Student’s t-test and several of its variants have been proposed by several authors, a methodology that has found widespread popularity is the application of the mixture model in a hierarchical approach whereby the mean of the distribution of the normalized log ratios is assumed to be a random variable having a mixture of two components. One component is a point mass distribution concentrated at zero to represent the non-differentially expressed genes and another component is a suitable distribution with zero mean to represent the differentially expressed genes. The normal and the Laplace distributions have been previously suggested for the differentially expressed genes component of the mixture. But, once again, the symmetry assumption can make these distributions unsuitable. Here, we take a more general approach and apply the beta-normal model to describe the distribution of the mean of the differentially expressed genes. The advantage of this approach is that we no longer assume symmetry for the distribution and let the data determine its shape. We show that our approach includes the earlier results based on normality assumption as a special case. Simulation results demonstrate that there are advantages in using the more general beta-normal distribution. An example with a microarray experimental data is utilized to provide further illustration.