Library

RJChain

A structure that represents a Reversible Jump Markov Chain Monte Carlo (RJMCMC) chain.

Fields

• n::Int: The number of jumps in the chain. Each jump represents a transition from one state to another.
• states::Vector{Any}: A vector of states in the chain. Each state represents a point in the parameter space.
• jumptypes::Vector{Int}: A vector of the attempted jump types from the current state. Each jump type corresponds to a different type of transition that can be proposed.
• α::Vector{Float64}: A vector of acceptance probabilities for each proposed state. The acceptance probability determines whether a proposed state is accepted or rejected.
• accept::Vector{Bool}: A vector of results from the acceptance calculation. Each element is a boolean indicating whether the corresponding proposed state was accepted (true) or rejected (false).
• proposedstates::Vector{Any}: A vector of proposed states. Each proposed state is a potential next state in the chain.

Constructor

The constructor for RJChain takes an integer n and initializes a chain with n jumps. All vectors are initialized with n elements. The states, α, and proposedstates vectors are initialized with undefined values, the jumptypes vector is initialized with zeros, and the accept vector is initialized with false.

RJChain(n::Int)

Constructs a new RJChain with n jumps.

Arguments

• n::Int: The number of jumps in the chain.

Returns

• A new RJChain with n jumps. The states, α, and proposedstates vectors are initialized with undefined values, the jumptypes vector is initialized with zeros, and the accept vector is initialized with false.

RJMCMCStruct

A structure that contains information required for creating and running a Reversible Jump Markov Chain Monte Carlo (RJMCMC) chain.

Fields

• burnin::Int: The number of steps for the burn-in phase of the chain. During this phase, the chain is allowed to converge towards a stationary distribution.
• iterations::Int: The number of steps for the actual chain that will be returned. This is the part of the chain that is used for inference.
• njumptypes::Int: The number of different types of jumps that can be proposed.
• jumpprobability::Distributions.Categorical: A categorical distribution that represents the probability mass function for selecting each jump type.
• proposalfuns::Vector{Function}: An array of proposal functions. Each function should take the current state and a Metropolis-Hastings sampler as input and return a proposed state and any additional arguments needed for the acceptance function.
• acceptfuns::Vector{Function}: An array of acceptance functions. Each function should take the current state, proposed state, Metropolis-Hastings sampler, and any additional arguments from the proposal function as input and return the acceptance probability.

Function Signatures

The proposal and acceptance functions must have the following signatures:

(proposedstate, vararg) = proposalfuns[jt](mhs, currentstate)
α = acceptfuns[jt](mhs, currentstate, proposedstate, vararg)

where jt is the index of the jump type, mhs is a structure passed to the functions, currentstate is the current state of the chain, proposedstate is the proposed state, vararg is any additional arguments needed to be passed between related propose and accept functions, and α is the acceptance probability.

buildchain(rjs::RJMCMCStruct, mhs, initialstate)

Build a new RJMCMC chain using an initial state and a Metropolis-Hastings sampler.

Arguments

• rjs::RJMCMCStruct: An RJMCMCStruct object that contains the number of iterations for the new chain.
• mhs: A user-defined Metropolis-Hastings parameter structure passed propose/accept functions.
• initialstate: The initial state to start the new chain.

Returns

• chain::RJChain: A new RJChain object that has been initialized with the initial state and run for the specified number of iterations.

initchain(rjs::RJMCMCStruct, initialstate)

Initialize a new RJMCMC chain using an initial state and configures a burn-in.

Arguments

• rjs::RJMCMCStruct: An RJMCMCStruct object that contains the number of iterations for the new chain.
• initialstate: The initial state to start the new chain.

Returns

• newchain::RJChain: A new RJChain object that has been initialized with the initial state and configured for burn-in.

initchain(rjs::RJMCMCStruct, burninchain::RJChain)

Initialize a new RJMCMC chain using the last state of a burn-in chain.

Arguments

• rjs::RJMCMCStruct: An RJMCMCStruct object that contains the number of iterations for the new chain.
• burninchain::RJChain: An RJChain object that represents the burn-in chain. The last state of this chain is used to initialize the new chain.

Returns

• newchain::RJChain: A new RJChain object that has been initialized with the last state of the burn-in chain.

runchain!(rjs::RJMCMCStruct, rjc::RJChain, iterations, mhs)

Run the RJMCMC chain for a specified number of iterations using a Metropolis-Hastings sampler.

Arguments

• rjs::RJMCMCStruct: An RJMCMCStruct object that contains the jump probabilities and proposal functions.
• rjc::RJChain: The RJChain object to run.
• iterations: The number of iterations to run the chain.
• mhs: A user-defined Metropolis-Hastings parameter structure passed propose/accept functions.

Modifies

• rjc::RJChain: The RJChain object is updated with the new states, jump types, proposed states, acceptance probabilities, and acceptance states.