Objective: To develop a Bayesian inversion framework on longitudinal chest CT scans which can perform efficient multi-class classification of lung cancer. Methods: While the unavailability of large number of training medical images impedes the performance of lung cancer classifiers, the purpose built deep networks have not performed well in multi-class classification. The presented framework employs particle filtering approach to address the non-linear behaviour of radiomic features towards benign and cancerous (stages I, II, III, IV) nodules and performs efficient multi-class classification (benign, early stage cancer, advanced stage cancer) in terms of posterior probability function. A joint likelihood function incorporating diagnostic radiomic features is formulated which can compute likelihood of cancer and its pathological stage. The proposed research study also investigates and validates diagnostic features to discriminate accurately between early stage (I, II) and advanced stage (III, IV) cancer. Results: The proposed stochastic framework achieved 86% accuracy on the benchmark database which is better than the other prominent cancer detection methods. Conclusion: The proposed classification framework can aid radiologists in accurate interpretation of lung CT images at an early stage and can lead to timely medical treatment of cancer patients.