Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/2399 2022 2022 Department Basic Sciences, College of Nursing, Mosul University, Nineveh, Iraq Shaymaa Riyadh Thanoon This research provides a conceptual framework and examples for applying Bayesian techniques to binary and vector data.  For the binary data, for observations take on one of two possible values, Bayesian logistic regression and Bayesian networks are techniques,  applicable Bayesian logistic regression places priors on the coefficients and derives the posterior using the likelihoods under a logistic model. Bayesian networks represent dependencies between binary variables graphically and perform inference using conditional probability tables. For vector data, where observations are multi-dimensional, Bayesian linear regression places priors on the regression coefficients and finds posterior using the likelihoods under linear model. Gaussian process regression models the relationship between inputs and outputs as a draw from a   Gaussian process prior and computes the posterior process given observed data. The research provides the conceptual framework underlying Bayesian analysis, including key concepts such as prior and posterior distributions. It highlights the advantages of Bayesian methods like the ability to incorporate domain knowledge and model uncertainty. Numerical examples demonstrate how Bayesian techniques can be applied to binary and vector data classification tasks. The abstract summarizes the core ideas and contributions of the research on this topic. 2023 2023 31 38 10.54216/GJMSA.0100104 https://www.americaspg.com/articleinfo/33/show/2399