Published online by Cambridge University Press: 22 May 2026
This final chapter sketches ways to expand the inference toolkit introduced in the book. We explore more flexible prediction functions, including splines, generalised additive models and local regression. These methods improve expressivity while controlling complexity, helping avoid overfitting. We also show how differential equations – commonly used in scientific modelling – fit naturally into the probabilistic framework by defining parameterised function families. Inherently, stochastic systems can be modelled using Markov processes, allowing inference via familiar likelihood-based methods. Finally, we discuss generative language models, focusing on the GPT architecture. GPT models define probability distributions over token sequences using autoregressive neural networks trained via cross-entropy loss. Though the underlying architecture is complex, the core modelling idea – predicting the next word given prior context – builds directly on probabilistic and machine learning principles developed throughout the book.
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