DFsCsn is a Julia package that provides tools for simulating statistical models considering spatio-temporal structures and skewness. It also facilitates sampling from the posterior distribution of these models. Please refer to Kuno and Murakami (2024) for details.

To install DFsCsn, use the following command in Julia's REPL:

using Pkg
Pkg.add("https://github.com/Kuno3/DFsCsn")

To start using DFsCsn, simply import the package:

using DFsCsn

DFsCsn allows you to specify parameters for your spatiotemporal model and run simulations. Here’s an example of how to set parameters and execute a simulation:

DFsCsnSimulator

Description: Initializes the simulation environment with specified parameters for D-FS-CSN.

Arguments:

• T::Int: Time length
• W::Array{Float64,2}: Adjacency matrix
• feature::Array{Float64,3}: Features
• beta::Array{Float64,1}(optional): Coefficinet
• sigma2::Float64(optional): Variance of observation noise
• tau2::Float64(optional): Variance of process noise
• rhoS::Float64(optional): Parameter for spatial dependence
• rhoT::Float64(optional): Parameter for temporal dependence
• l::Float64(optional): Parameter for skewness
• theta_init::Array{Float64,1}(optional): Initial value of theta
• seed::Int(optional): Seed for random sampling

Return:

• DFsCsnSimulator: An object that holds the simulation environment.

DCarSimulator

Description: Initializes the simulation environment with specified parameters for D-CAR.

Arguments:

• T::Int: Time length
• W::Array{Float64,2}: Adjacency matrix
• feature::Array{Float64,3}: Features
• beta::Array{Float64,1}(optional): Coefficinet
• sigma2::Float64(optional): Variance of observation noise
• tau2::Float64(optional): Variance of process noise
• rhoS::Float64(optional): Parameter for spatial dependence
• rhoT::Float64(optional): Parameter for temporal dependence
• theta_init::Array{Float64,1}(optional): Initial value of latent variable theta
• seed::Int(optional): Seed for random sampling

Return:

• DCarSimulator: An object that holds the simulation environment.

simulate

Description: Simulates data based on the initialized model.

Arguments:

• simulator::DFsCsnSimulator or simulator::DCarSimulator: The initialized simulator object.

Return:

• Nothing: The simulation result are stored in simulator.y

# Define parameters
T = 10 # Time length
W = [0 1 1 0; 1 0 0 1; 1 0 0 1; 0 1 1 0] # Adjacency matrix
feature = randn(T, size(W, 1), 2) # Features
simulator = DFsCsnSimulator(T, W, feature)
simulate(simulator)

The package also includes functions for sampling from posterior distributions, allowing for in-depth statistical analysis and inference.

DFsCsnPostSampler

Description: Initializes the sampling environment with specified parameters for D-FS-CSN.

Arguments:

• y::Array{Float64,2}: Observations
• W::Array{Float64,2}: Adjacency matrix
• nu2_beta::Float64(optional): Variance of the prior for beta (default is 100)
• a_sigma2::Float64(optional) and b_sigma2::Float64(optional): Parameter of the inverse gamma prior for sigma2 (default is 1 and 0.01)
• a_tau2::Float64(optional) and b_tau2::Float64(optional): Parameter of the inverse gamma prior for tau2(default is 1 and 0.01)
• nu2_l::Float64(optional): Variance of the prior for l(default is 100)
• seed::Int(optional): Seed for random sampling

Return:

• DFsCsnPostSampler: An object that holds the sampling environment.

DCarPostSampler

Description: Initializes the sampling environment with specified parameters for D-CAR.

Arguments:

• y::Array{Float64,2}: Observations
• W::Array{Float64,2}: Adjacency matrix
• nu2_beta::Float64(optional): Variance of the prior for beta (default is 100)
• a_sigma2::Float64(optional) and b_sigma2::Float64(optional): Parameter of the inverse gamma prior for sigma2 (default is 1 and 0.01)
• a_tau2::Float64(optional) and b_tau2::Float64(optional): Parameter of the inverse gamma prior for tau2(default is 1 and 0.01)
• seed::Int(optional): Seed for random sampling

Return:

• DCarPostSampler: An object that holds the sampling environment.

sampling

Description: Simulates data based on the initialized model.

Arguments:

• sampler::DFsCsnPostSampler or sampler::DCarPostSampler: The initialized simulator object.
• num_sample::Int: Number of samples
• burn_in::Int(optional): Number of saples for burn in
• thinning::Int(optional): Number of saples for thinning
• step_size::Float64(optional and only for DFsCsnPostSampler): Parameter for sampling
• num_step::Int(optional and only for DFsCsnPostSampler): Parameter for sampling
• rhoS_prop_scale::Float64(optional): Parameter for sampling
• theta_init::Matrix{Float64}(optional): Initial value for theta
• alpha_init::Matrix{Float64}(optional): Initial value for alpha
• beta_init::Vector{Float64}(optional): Initial value for beta
• sigma2_init::Vector{Float64}(optional): Initial value for sigma2
• tau2_init::Vector{Float64}(optional): Initial value for tau2
• rhoS_init::Vector{Float64}(optional): Initial value for rhoS
• rhoT_init::Vector{Float64}(optional): Initial value for rhoT
• l_init::Vector{Float64}(optional and only for DFsCsnPostSampler): Initial value for l

Return:

• Array: A dictionary of the samples from the posterior distribution.

# Define observations
y = simulator.y
W = simulator.W
feature = simulator.feature

# Sample from the posterior distribution
sampler = DFsCsnPostSampler(y, W, feature)
results = sampling(sampler, 1000)

DFsCsn is licensed under the MIT License.

Kuno, H., Murakami, D., 2024. Efficient bayesian dynamic closed skew-normal model for spatio-temporal data with preserving mean and covariance. Preprint