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APMTH 231 teaches statistical inference and estimation from a signal processing perspective. The courses aims to teach students a) to think about probabilistic models of data, b) how to develop estimation and inference algorithms, and c) how to apply it to real data. The course emphasizes the entire pipeline from writing a model, estimating its parameters and performing inference utilizing sports data, neuroscience data, geyser eruption data and other sources. The course also teaches students how to assess the goodness of fit of models to data, diagnostic tools to detect lack of fit, and ways to improve models. A basic course in probability and random variables, e.g. at the level of STAT 110, a background in linear algebra, and a level of mathematical maturity.