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Computational Statistics: From Descriptive Analysis to Bayesian Methods and Stochastic Algorithms
This work traces a progression from the foundations of statistical computing to advanced probabilistic modeling. It begins with descriptive statistics and core inferential tools, including hypothesis testing, confidence intervals, and Bayesian analysis. Both continuous (normal, t, chi-squared, gamma, beta, uniform) and discrete (Bernoulli, binomial, Poisson, etc.) distributions are covered, leading into computational methods like random number generation, simulation, Monte Carlo, and MCMC. The text advances to reverse-engineering unknown distributions and maximum likelihood, before concluding with modern frameworks including the EM algorithm, Gaussian Mixture Models, and the multivariate normal distribution.