Mici

AbstractIntegrationTransition <: AbstractTransition

Abstract supertype for integration transitions in MCMC samplers. Integration transitions update the state according to the Hamiltonian dynamics of the system, typically using a numerical integrator.

AbstractIntegrator

Abstract supertype for numerical integrators used to simulate Hamiltonian dynamics in MCMC samplers.

AbstractMetropolisIntegrationTransition{T} <: AbstractIntegrationTransition

Abstract supertype for Metropolis-adjusted integration transitions in MCMC samplers, parameterized by: T – type of the integration time (e.g., Float64)

AbstractMiciSampler{S, I} <: AbstractMCMC.AbstractSampler

Abstract supertype for Mici samplers, parameterized by the system type S and integrator type I.

AbstractMomentumTransition <: AbstractTransition

Abstract supertype for momentum transitions in MCMC samplers. Momentum transitions update the momentum component of the state, typically by resampling from a distribution or applying a transformation.

AbstractState{P,S,I}

Abstract supertype for states of MCMC samplers, parameterized by: P – type of the phase point (e.g., PhasePoint{T}) S – type of the system (e.g., EuclideanSystem) I – type of the integrator (e.g., LeapfrogIntegrator)

Concrete subtypes of AbstractState should contain at least the following fields: - phase_point::P – the current phase point of the sampler - system::S – the Hamiltonian system being sampled - integrator::I – the integrator used for simulating Hamiltonian dynamics

AbstractSystem

Abstract supertype for Hamiltonian systems with energy h(q, p) = h₁(q) + h₂(q, p) for position q and momentum p and where the energy is decomposed into two components, h₁ and h₂.

In a standard Euclidean System, h₁ and h₂ correspond to potential energy and kinetic energy respectively. However, solving the Hamiltonian dynamics in more complex systems may benefit from a more flexible distinction between (position) and (momentum, position) energy components.

AbstractTractableFlowSystem <: AbstractSystem

Abstract supertype for systems where the Hamiltonian dynamics can be solved in closed form, allowing for exact flow transitions in MCMC samplers.

AbstractTransition

Abstract supertype for transitions in MCMC samplers. A transition represents a change in state of the Markov chain in either position or momentum.

EuclideanSystem{M, L} <: AbstractTractableFlowSystem

Struct for a Euclidean Hamiltonian system, where the kinetic energy is defined by a metric M

HMC{S,I,TI,TM} <: AbstractMiciSampler{S,I}

Struct representing a Hamiltonian Monte Carlo sampler, parameterized by:

• S - type of the system (e.g., EuclideanSystem),
• I - type of the integrator (e.g., LeapfrogIntegrator),
• TI - type of the integration transition (e.g., StaticMetropolisIntegrationTransition),
• TM - type of the momentum transition (e.g., IndependentMomentumTransition).

IndependentMomentumTransition <: AbstractMomentumTransition

Struct representing an independent momentum transition, where the momentum is resampled independently from a distribution defined by the system (e.g., a Gaussian distribution with covariance given by the metric of the system).

MetropolisHMCState{P, S, I} <: AbstractState{P,S,I}

Concrete state type for a Metropolis-adjusted Hamiltonian Monte Carlo sampler.

PhasePoint

Struct representing a point in the phase space of a Hamiltonian system, consisting of: q – current position p – current momentum logdens – log density at the current position grad – gradient of the log density at the current position valid – indicator for whether the log density and gradient are up-to-date

StaticMetropolisIntegrationTransition{T} <: AbstractMetropolisIntegrationTransition{T}

Struct for a static Metropolis-adjusted integration transition, where the integration time is fixed.

metropolis_integration_transition!(state::MetropolisHMCState, rng::AbstractRNG, integration_time::Real)

Perform a Metropolis-adjusted integration transition

Indicate the log density and gradient needs to be updated at the current position.

Flow transition for h₁

Flow transition for h₂

All systems must implement a field ℓ, a function for evaluating the log density and gradient of the target distribution.