Accessible to any scientist or student with a reasonable background in statistics, this updated book presents a unique blend of stochastic process theory, statistical inference, and scientific applications of stochastic modeling of scientific data. With an emphasis on real data applications, this second edition covers the numerous developments in methodology and computation since the original publication. It provides a more balanced treatment of Bayesian approaches to statistical inference and includes more recent scientific example problems that involve the statistical analysis of stochastic models.