Priors

The package currently support two priors, NIW for observations generated from gaussians, and Dirichlet Distribution for multinomial data.

Each prior is defined by the prior itself, and the distribution which is sampled from it.

Existing Priors

NIW (Gaussian)

For data generated from Gaussians we use a NIW prior, which a Multivariate Normal distribution is sampled from:

niw_hyperparams(κ::Float32, m::AbstractArray{Float32}, ν::Float32, ψ::AbstractArray{Float32})

mv_gaussian(μ::AbstractArray{Float32,1}
    Σ::AbstractArray{Float32,2}
    invΣ::AbstractArray{Float32,2}
    logdetΣ::Float32
    invChol::UpperTriangular)

Multinomial

For multinomial distribution we will a Dirichlet Distribution prior, and a Categorial Distribution is sampled from it.

multinomial_hyper(α::AbstractArray{Float32,1})

multinomial_hyper(α::AbstractArray{Float32,1})

Creating new Priors

If you require to create a new prior, you need to create both a distribution file, and a prior file (each in its designated folder). Note that the package only support conjugate priors.

The prior file must implement the following:

struct prior_hyper_params <: distribution_hyper_params
    ...
end

mutable struct prior_sufficient_statistics <: sufficient_statistics
    N::Float32 #Must have this, even if not needed!
    ...
end


function calc_posterior(prior:: prior_hyper_params, suff_statistics::prior_sufficient_statistics)
    if suff_statistics.N == 0
        return prior
    end
    return prior_hyper_params(...)
end

function sample_distribution(hyperparams::prior_hyper_params)
    return new_dist(...)
end

function create_sufficient_statistics(hyper::prior_hyper_params,posterior::prior_hyper_params,points::AbstractArray{Float32,2}, pts_to_group = 0)
    pts = copy(points)
    ...
    return prior_sufficient_statistics(size(points,2),...)
end

function log_marginal_likelihood(hyper::prior_hyper_params, posterior_hyper::prior_hyper_params, suff_stats::prior_sufficient_statistics)
    ...
    return value
end

function aggregate_suff_stats(suff_l::prior_sufficient_statistics, suff_r::prior_sufficient_statistics)
    return prior_sufficient_statistics(...)
end

For the distribution file you must implement the following:

struct new_dist <: distibution_sample
    ...
end


function log_likelihood!(r::AbstractArray,x::AbstractMatrix, distibution_sample::mv_gaussian , group::Int64 = -1)
     ...
    r .= (each sample log likelihood)
end