MIDAS - multi-instrument Bayesian data analysis in Python

Introduction

MIDAS is a framework for Bayesian and integrated data analysis in Python.

Use diagnostic models from any source

MIDAS is designed to work with any diagnostic model which can by called from within Python, and does not require models to be implemented within a specific framework. Instead, MIDAS provides tools to create a lightweight wrapper around external forward-models which allows them to interface with MIDAS.

Efficient inference through analytic propagation of derivatives

Efficient MAP estimation and MCMC sampling in inference problems with ~20 or more free parameters relies heavily on the ability to calculate the derivative of the posterior log-probability with respect to those parameters.

Given the Jacobian of a diagnostic model (i.e. the derivatives of the model predictions with respect to the model inputs) MIDAS will automatically propagate those derivatives through the subsequent steps in calculating the posterior log-probability, so the gradient of the posterior log-probability can be calculated analytically.

This allows MIDAS tackle large-scale problems with hundreds or thousands of free parameters, or to solve smaller problems quickly and routinely.

Easy interfacing to the Python scientific software ecosystem

MIDAS is designed to be used easily with external libraries, for example using optimisers from scipy.optimize to maximise the posterior log-probability, or MCMC samplers from inference-tools to sample from the posterior.

Modularity to allow easy exchange of models

Analysis in MIDAS is built from three types of models:

• Diagnostic forward-models which make predictions of diagnostic signals.

• Likelihood functions which model the uncertainties on measured data.

• Plasma field models which give a parametrised description of the plasma state.

Each of these model types have interfaces defined by an associated abstract base-class, which allows them to communicate with the framework. This abstraction means that models can be easily swapped in and out of the analysis without requiring code changes.

For example, a forward-model for a Thomson-scattering diagnostic is able to request the values of the electron temperature and density from their associated field models, but is completely independent of the specific choice of parametrisation for those fields.

Contents:

• Getting started
  • Installation
  • Structure of a MIDAS analysis
  • Jupyter notebook examples
• Adding diagnostics to a MIDAS analysis
  • Specifying diagnostic models
  • Specifying likelihood functions
  • Creating a DiagnosticLikelihood
• Defining the prior distribution
• Specifying models for the plasma fields
• Constructing the posterior
• Parameters and field requests
  • ParameterVector
  • Parameters
  • FieldRequest
  • Fields
• Diagnostic model classes
  • DiagnosticModel
  • LinearDiagnosticModel
• Built-in field models
  • PiecewiseLinearField
  • FieldModel
• Built-in prior distributions
  • BasePrior
  • GaussianPrior
  • GaussianProcessPrior
  • ExponentialPrior
  • BetaPrior
• The Likelihoods module
  • DiagnosticLikelihood
  • Built-in likelihood functions
  • Uncertainty models
  • Abstract base classes
• The PlasmaState class
  • PlasmaState
• Evaluating the posterior
  • log_probability()
  • gradient()
  • cost()
  • cost_gradient()
  • component_log_probabilities()
  • get_model_predictions()
  • sample_model_predictions()