Detection of a brain tumour in medical images is always a challenging task. Factors like size, shape, and position of tumour vary from different patient’s brain. So, it's important to know the exact shape, size and position of a tumour in the brain making it a challenging task for detection. Some patients exhibit high glioma (HG) type tumor while others show low glioma (LG) type. So, knowing the detailed properties of a tumour to detect them in medical images is mandatory. So far many algorithms have been implemented on how to detect and extract the tumours in medical images, they used techniques such as hybrid approach with support vector machine (SVM), back propagation and dice coefficient. Among these algorithm which used back propagation as base classifier had a highest accuracy of 90%. In this work feature extraction of the medical images of patients’ tumors in database is extracted using Histogram of Oriented Gradient, later these images are classified into tumor and non tumor images using SVM. The detection of brain tumours in patient’s image is achieved by testing the performance of SVM based on Receiver Operating Characteristics (ROC). ROC include true positive rate, true negative rate, false positive rate and false negative rate. Using ROC we calculated accuracy, sensitivity and specificity values for all the medical images of the database. For image data folder of HG in vector form, SVM gave an accuracy of 97% for 95th slice of T1 modality with high true positive rate of 0.97 remaining highest among other modalities. Whereas SVM gave an accuracy of 87% for 135th slice of T1 modality with high true positive rate of 0.8 and low false positive rate of 0.06 among other image data folder of HG. For image data folder of LG, SVM gave an accuracy of 62% for the 90th slice of FLAIR modality with the high true positive rate of 0.5 and low false positive rate of 0.25 among all others. For synthetic data folder of HG, SVM gave an accuracy of 62% for a 100th slice of FLAIR modality with the high true positive rate of 0.5 and low false positive rate of 0.06 among all others. For synthetic data folder of LG, SVM gave an accuracy of 62% for a 100th slice of FLAIR modality with the high true positive rate of 0.5 and low false positive rate of 0.06 among all others.

This thesis focuses on (1) the statistical methodologies for the estimation of spatial data with outliers and (2) classification accuracy of disease diagnosis. Chapter I, Robust Estimation for Spatial Markov Random Field Models: Markov Random Field (MRF) models are useful in analyzing spatial lattice data collected from semiconductor device fabrication and printed circuit board manufacturing processes or agricultural field trials. When outliers are present in the data, classical parameter estimation techniques (e.g., least squares) can be inefficient and potentially mislead the analyst. This chapter extends the MRF model to accommodate outliers and proposes robust parameter estimation methods such as the robust M- and RA-estimates. Asymptotic distributions of the estimates with differentiable and non-differentiable robustifying function are derived. Extensive simulation studies explore robustness properties of the proposed methods in situations with various amounts of outliers in different patterns. Also provided are studies of analysis of grid data with and without the edge information. Three data sets taken from the literature illustrate advantages of the methods. Chapter II, Extending the Skill Test for Disease Diagnosis: For diagnostic tests, we present an extension to the skill plot introduced by Mozer and Briggs (2003). The method is motivated by diagnostic measures for osteoporosis in a study. By restricting the area under the ROC curve (AUC) according to the skill statistic, we have an improved diagnostic test for practical applications by considering the misclassification costs. We also construct relationships, using the Koziol-Green model and mean-shift model, between the diseased group and the healthy group for improving the skill statistic. Asymptotic properties of the skill statistic are provided. Simulation studies compare the theoretical results and the estimates under various disease rates and misclassification costs. We apply the proposed method in classification of osteoporosis data.