Documentation strings

SMCModel(M!::F1, lG::F2, maxn::Int64, particle::Type, pScratch::Type) where
  {F1<:Function,F2<:Function}

• M! Mutation function
• lG Log potential function
• maxn Maximum n for which the model is well-defined
• particle Type of a particle
• pScratch Type of particle scratch space

SMCIO{Particle, ParticleScratch}

Structs of this type should be constructed using the provided constructor. Important fields:

• N::Int64 Number of particles $N$
• n::Int64 Number of steps $n$
• nthreads::Int64 Number of threads
• fullOutput::Bool Whether particle system history should be recorded
• essThreshold::Float64 Relative ESS Threshold $\tau$
• zetas::Vector{Particle} Time n particles $\zeta_n^1, \ldots, \zeta_n^N$
• eves::Vector{Int64} Time n Eve indices $E_n^1, \ldots, E_n^N$
• ws::Vector{Float64} Time n weights $W_n^1, \ldots, W_n^N$
• logZhats::Vector{Float64} $\log(\hat{Z}^N_1), \ldots, \log(\hat{Z}^N_n)$
• Vhat1s::Vector{Float64} $\hat{V}_1^N(1), \ldots, \hat{V}_n^N(1)$
• esses::Vector{Float64} Relative ESS values $\mathcal{E}_1^N, \ldots, \mathcal{E}_n^N$
• resample::Vector{Bool} Resampling indicators $R_1, \ldots, R_{n-1}$

Populated only if fullOutput == true

• allZetas::Vector{Vector{Particle}} All the particles
• allWs::Vector{Vector{Float64}} All the weights
• allAs::Vector{Vector{Int64}} All the ancestor indices
• allEves::Vector{Vector{Int64}} All the Eve indices

smc!(model::SMCModel, smcio::SMCIO)

Run the SMC algorithm for the given model and input/output arguments.

If smcio.nthreads == 1 the algorithm will run in serial.

csmc!(model::SMCModel, smcio::SMCIO, ref::Vector{Particle}, refout::Vector{Particle})

Run the conditional SMC algorithm for the given model, input/output arguments, reference path and output path.

It is permitted for ref and refout to be the same. If smcio.nthreads == 1 the algorithm will run in serial.

SMCIO{Particle, ParticleScratch}(N::Int64, n::Int64, nthreads::Int64,
  fullOutput::Bool, essThreshold::Float64 = 2.0) where
  {Particle, ParticleScratch}

Constructor for SMCIO structs.

eta(smcio::SMCIO{Particle}, f::F, hat::Bool, p::Int64) where {Particle, F<:Function}

Compute:

• !hat: $\eta^N_p(f)$
• hat: $\hat{\eta}_p^N(f)$

allEtas(smcio::SMCIO, f::F, hat::Bool) where F<:Function

Compute eta(smcio::SMCIO, f::F, hat::Bool, p) for p in {1, …, smcio.n}

slgamma(smcio::SMCIO, f::F, hat::Bool, p::Int64) where {Particle, F<:Function}

Compute:

• !hat: $(\eta^N_p(f) \geq 0, \log |\gamma^N_p(f)|)$
• hat: $(\hat{\eta}^N_p(f) \geq 0, \log |\hat{\gamma}_p^N(f)|)$

The result is returned as a Tuple{Bool, Float64}: the first component represents whether the returned value is non-negative, the second is the logarithm of the absolute value of the approximation.

allGammas(smcio::SMCIO, f::F, hat::Bool) where F<:Function

Compute slgamma(smcio::SMCIO, f::F, hat::Bool, p) for p in {1, …, smcio.n}

V(smcio::SMCIO{Particle}, f::F, hat::Bool, centred::Bool, p::Int64) where
  {Particle, F<:Function}

Compute:

• !hat & !centred: $V^N_p(f)$
• !hat & centred: $V^N_p(f-\eta_p^N(f))$
• hat & !centred: $\hat{V}_p^N(f)$
• hat & centred: $\hat{V}_p^N(f-\hat{\eta}_p^N(f))$

vpns(smcio::SMCIO, f::F, hat::Bool, centred::Bool, n::Int64) where F<:Function

Compute a vector of the values of, for p = 1, …, n,

• !hat & !centred: $v^N_{p,n}(f)$
• !hat & centred: $v^N_{p,n}(f-\eta_n^N(f))$
• hat & !centred: $\hat{v}_{p,n}^N(f)$
• hat & centred: $\hat{v}_{p,n}^N(f-\hat{\eta}_n^N(f))$

Note: if essThreshold <= 1.0, and resampling did not occur at every time, the length of the output will be less than n.

v(smcio::SMCIO, f::F, hat::Bool, centred::Bool, n::Int64) where F<:Function

Compute:

• !hat & !centred: $v^N_n(f)$
• !hat & centred: $v^N_n(f-\eta_n^N(f))$
• hat & !centred: $\hat{v}_n^N(f)$
• hat & centred: $\hat{v}_n^N(f-\hat{\eta}_n^N(f))$