This paper introduces a general model, the Hierarchical Dynamic Model (HDM), that encompasses various parametric models for continuous data. The HDM consists of hidden layers of state-space or dynamic causal models, arranged in a hierarchical structure where the output of one layer serves as input to another. This hierarchy allows the model to handle a wide range of data types and complexities, from static linear models to nonlinear time-series analysis with system noise. A key feature is that all these models can be inverted using the same scheme, dynamic expectation maximisation (DEM), which optimizes the conditional density on model states, parameters, and hyperparameters. The paper demonstrates that the brain has the necessary anatomical and physiological machinery to implement this inversion, suggesting that the brain can analyze sensory input using sophisticated algorithms. The inversion scheme is formulated as a simple neural network, providing a useful framework for understanding inference and learning in the brain. The paper also discusses the implications for understanding normal brain function and pathological processes associated with psychiatric disorders.This paper introduces a general model, the Hierarchical Dynamic Model (HDM), that encompasses various parametric models for continuous data. The HDM consists of hidden layers of state-space or dynamic causal models, arranged in a hierarchical structure where the output of one layer serves as input to another. This hierarchy allows the model to handle a wide range of data types and complexities, from static linear models to nonlinear time-series analysis with system noise. A key feature is that all these models can be inverted using the same scheme, dynamic expectation maximisation (DEM), which optimizes the conditional density on model states, parameters, and hyperparameters. The paper demonstrates that the brain has the necessary anatomical and physiological machinery to implement this inversion, suggesting that the brain can analyze sensory input using sophisticated algorithms. The inversion scheme is formulated as a simple neural network, providing a useful framework for understanding inference and learning in the brain. The paper also discusses the implications for understanding normal brain function and pathological processes associated with psychiatric disorders.