From b2537c95cd2ae40e9b3f08eb99e0777ab07ebaca Mon Sep 17 00:00:00 2001
From: Samuel Brand <sam055@mac.com>
Date: Mon, 12 Feb 2024 15:12:58 +0000
Subject: [PATCH 1/9] Create a standard prior for the RW as a `EpiAware` object

---
 EpiAware/src/latent-processes.jl | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/EpiAware/src/latent-processes.jl b/EpiAware/src/latent-processes.jl
index 361d48ee9..2d180c598 100644
--- a/EpiAware/src/latent-processes.jl
+++ b/EpiAware/src/latent-processes.jl
@@ -1,3 +1,5 @@
+const STANDARD_RW_PRIORS = (var_RW_dist = truncated(Normal(0.0, 0.05), 0.0, Inf),)
+
 """
     random_walk(n, ϵ_t = missing; latent_process_priors = (var_RW_dist = truncated(Normal(0., 0.05), 0., Inf),), ::Type{T} = Float64) where {T <: Real}
 
@@ -16,7 +18,7 @@ Constructs a random walk model.
     n,
     ϵ_t = missing,
     ::Type{T} = Float64;
-    latent_process_priors = (var_RW_dist = truncated(Normal(0.0, 0.05), 0.0, Inf),),
+    latent_process_priors = STANDARD_RW_PRIORS,
 ) where {T<:Real}
     rw = Vector{T}(undef, n)
     ϵ_t ~ MvNormal(ones(n))

From ee12bd5587e222e5f0bd1d56805a4d4cc800bc53 Mon Sep 17 00:00:00 2001
From: Samuel Brand <sam055@mac.com>
Date: Mon, 12 Feb 2024 15:13:44 +0000
Subject: [PATCH 2/9] add a time horizon variable to `EpiModel` struct, useful
 for when generating rather than making inference on data

---
 EpiAware/src/epimodel.jl | 1 +
 1 file changed, 1 insertion(+)

diff --git a/EpiAware/src/epimodel.jl b/EpiAware/src/epimodel.jl
index f2df9fbe8..2ddf8ddca 100644
--- a/EpiAware/src/epimodel.jl
+++ b/EpiAware/src/epimodel.jl
@@ -28,6 +28,7 @@ struct EpiModel{T<:Real} <: AbstractEpiModel
     cluster_coeff::T
     len_gen_int::Integer #length(gen_int) just to save recalc
     len_delay_int::Integer #length(delay_int) just to save recalc
+    time_horizon::Integer
 
     #Inner constructors for EpiModel object
     function EpiModel(gen_int, delay_int, cluster_coeff, time_horizon)

From 5c1aaf0a4524dfdd1ed5983688eb11d6d9d4401e Mon Sep 17 00:00:00 2001
From: Samuel Brand <sam055@mac.com>
Date: Mon, 12 Feb 2024 15:14:19 +0000
Subject: [PATCH 3/9] doc string for `log_infections` model

---
 EpiAware/src/models.jl | 32 +++++++++++++++++++++++++++++++-
 1 file changed, 31 insertions(+), 1 deletion(-)

diff --git a/EpiAware/src/models.jl b/EpiAware/src/models.jl
index 27c2a7f38..bd73c9b95 100644
--- a/EpiAware/src/models.jl
+++ b/EpiAware/src/models.jl
@@ -1,3 +1,33 @@
+"""
+    log_infections(y_t, epimodel::EpiModel, latent_process;
+                   latent_process_priors,
+                   transform_function = exp,
+                   n_generate_ahead = 0,
+                   pos_shift = 1e-6,
+                   neg_bin_cluster_factor = missing,
+                   neg_bin_cluster_factor_prior = Gamma(3, 0.05 / 3))
+
+A Turing model for Log-infections undelying observed epidemiological data.
+
+This function defines a log-infections model for epidemiological data.
+It takes the observed data `y_t`, an `EpiModel` object `epimodel`, and a `latent_process`
+model. It also accepts optional arguments for the `latent_process_priors`, `transform_function`,
+`n_generate_ahead`, `pos_shift`, `neg_bin_cluster_factor`, and `neg_bin_cluster_factor_prior`.
+
+## Arguments
+- `y_t`: Observed data.
+- `epimodel`: Epidemiological model.
+- `latent_process`: Latent process model.
+- `latent_process_priors`: Priors for the latent process model.
+- `transform_function`: Function to transform the latent process into infections. Default is `exp`.
+- `n_generate_ahead`: Number of time steps to generate ahead. Default is `0`.
+- `pos_shift`: Positive shift to avoid zero values. Default is `1e-6`.
+- `neg_bin_cluster_factor`: Missing value for the negative binomial cluster factor. Default is `missing`.
+- `neg_bin_cluster_factor_prior`: Prior distribution for the negative binomial cluster factor. Default is `Gamma(3, 0.05 / 3)`.
+
+## Returns
+A named tuple containing the generated quantities `I_t` and `latent_process_parameters`.
+"""
 @model function log_infections(
     y_t,
     epimodel::EpiModel,
@@ -15,7 +45,7 @@
     #Latent process
     time_steps = length(y_t) + n_generate_ahead
     @submodel _I_t, latent_process_parameters =
-        latent_process(data_length; latent_process_priors = latent_process_priors)
+        latent_process(time_steps; latent_process_priors = latent_process_priors)
 
     #Transform into infections
     I_t = transform_function.(_I_t)

From 63e8839bc0b189aad5da235a73a6fd2bc5bb13c6 Mon Sep 17 00:00:00 2001
From: Samuel Brand <sam055@mac.com>
Date: Mon, 12 Feb 2024 15:22:18 +0000
Subject: [PATCH 4/9] New doc strings reflecting changes in `EpiModel` eg extra
 constructor method

---
 EpiAware/src/epimodel.jl | 30 ++++++++++++++++--------------
 1 file changed, 16 insertions(+), 14 deletions(-)

diff --git a/EpiAware/src/epimodel.jl b/EpiAware/src/epimodel.jl
index 2ddf8ddca..a52451998 100644
--- a/EpiAware/src/epimodel.jl
+++ b/EpiAware/src/epimodel.jl
@@ -1,24 +1,24 @@
 abstract type AbstractEpiModel end
 
 
+
 """
-    struct EpiModel{T}
+    struct EpiModel{T<:Real} <: AbstractEpiModel
 
-The `EpiModel` struct represents a basic renewal model.
+EpiModel represents an epidemiological model with generation intervals, delay intervals, and observation delay kernel.
 
 # Fields
-- `gen_int::Vector{T}`: Discrete generation distribution.
-- `delay_int::Vector{T}`: Discrete delay distribution.
-- `delay_kernel::SparseMatrixCSC{T,Integer}`: Sparse matrix representing the action of convoluting
-    a series of infections with observation delay.
-- `cluster_coeff::T`: Cluster coefficient for negative binomial distribution of observations.
-- `len_gen_int::Integer`: Length of `gen_int` vector.
-- `len_delay_int::Integer`: Length of `delay_int` vector.
+- `gen_int::Vector{T}`: Discrete generation inteval, runs from 1, 2, ... to the end of the vector.
+- `delay_int::Vector{T}`: Discrete delay distribution runs from 0, 1, ... to the end of the vector less 1.
+- `delay_kernel::SparseMatrixCSC{T,Integer}`: Sparse matrix representing the observation delay kernel.
+- `cluster_coeff::T`: Cluster coefficient for negative binomial observations.
+- `len_gen_int::Integer`: Length of `gen_int`.
+- `len_delay_int::Integer`: Length of `delay_int`.
+- `time_horizon::Integer`: Length of the generated data.
 
 # Constructors
-- `EpiModel(gen_int, delay_int, truth_cluster_coeff, time_horizon)`: Constructs an `EpiModel` object.
-
-The `EpiModel` struct represents an epidemiological model with generation intervals, delay intervals, delay kernel, truth cluster coefficient, and length of generation and delay intervals.
+- `EpiModel(gen_int, delay_int, cluster_coeff, time_horizon::Integer)`: Constructs an EpiModel object with given generation intervals, delay intervals, cluster coefficient, and time horizon.
+- `EpiModel(gen_distribution::ContinuousDistribution, delay_distribution::ContinuousDistribution, cluster_coeff, time_horizon::Integer; Δd = 1.0, D_gen, D_delay)`: Constructs an EpiModel object with generation and delay distributions, cluster coefficient, time horizon, and optional parameters.
 
 """
 struct EpiModel{T<:Real} <: AbstractEpiModel
@@ -31,7 +31,7 @@ struct EpiModel{T<:Real} <: AbstractEpiModel
     time_horizon::Integer
 
     #Inner constructors for EpiModel object
-    function EpiModel(gen_int, delay_int, cluster_coeff, time_horizon)
+    function EpiModel(gen_int, delay_int, cluster_coeff, time_horizon::Integer)
         @assert all(gen_int .>= 0) "Generation interval must be non-negative"
         @assert all(delay_int .>= 0) "Delay interval must be non-negative"
         @assert sum(gen_int) ≈ 1 "Generation interval must sum to 1"
@@ -52,6 +52,7 @@ struct EpiModel{T<:Real} <: AbstractEpiModel
             cluster_coeff,
             length(gen_int),
             length(delay_int),
+            time_horizon,
         )
     end
 
@@ -59,7 +60,7 @@ struct EpiModel{T<:Real} <: AbstractEpiModel
         gen_distribution::ContinuousDistribution,
         delay_distribution::ContinuousDistribution,
         cluster_coeff,
-        time_horizon;
+        time_horizon::Integer;
         Δd = 1.0,
         D_gen,
         D_delay,
@@ -86,6 +87,7 @@ struct EpiModel{T<:Real} <: AbstractEpiModel
             cluster_coeff,
             length(gen_int),
             length(delay_int),
+            time_horizon,
         )
     end
 end

From f149a7ca3624dfaea6aae849c88b9a1ce85b9663 Mon Sep 17 00:00:00 2001
From: Samuel Brand <sam055@mac.com>
Date: Mon, 12 Feb 2024 23:20:27 +0000
Subject: [PATCH 5/9] refactor to claify exported functions

---
 EpiAware/src/EpiAware.jl | 10 ++++------
 1 file changed, 4 insertions(+), 6 deletions(-)

diff --git a/EpiAware/src/EpiAware.jl b/EpiAware/src/EpiAware.jl
index 2740ffdc3..ad85fdaa4 100644
--- a/EpiAware/src/EpiAware.jl
+++ b/EpiAware/src/EpiAware.jl
@@ -30,13 +30,11 @@ using Distributions,
     Parameters,
     QuadGK
 
+# Exported utilities
 export scan,
-    create_discrete_pmf,
-    growth_rate_to_reproductive_ratio,
-    generate_observation_kernel,
-    EpiModel,
-    log_daily_infections,
-    random_walk
+    create_discrete_pmf, growth_rate_to_reproductive_ratio, generate_observation_kernel
+
+export EpiModel, log_infections, random_walk
 
 include("utilities.jl")
 include("epimodel.jl")

From 381bf4080c4697563bbda9c8c10f487c343f9e65 Mon Sep 17 00:00:00 2001
From: Samuel Brand <sam055@mac.com>
Date: Mon, 12 Feb 2024 23:21:14 +0000
Subject: [PATCH 6/9] remove unnecessary comments

---
 EpiAware/src/epimodel.jl | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/EpiAware/src/epimodel.jl b/EpiAware/src/epimodel.jl
index eedbcf1d7..d8ad2334d 100644
--- a/EpiAware/src/epimodel.jl
+++ b/EpiAware/src/epimodel.jl
@@ -36,7 +36,7 @@ struct EpiModel{T<:Real} <: AbstractEpiModel
         @assert all(delay_int .>= 0) "Delay interval must be non-negative"
         @assert sum(gen_int) ≈ 1 "Generation interval must sum to 1"
         @assert sum(delay_int) ≈ 1 "Delay interval must sum to 1"
-        #construct observation delay kernel
+
         K = generate_observation_kernel(delay_int, time_horizon)
 
         new{eltype(gen_int)}(
@@ -64,8 +64,6 @@ struct EpiModel{T<:Real} <: AbstractEpiModel
             p -> p[2:end] ./ sum(p[2:end])
         delay_int = create_discrete_pmf(delay_distribution, Δd = Δd, D = D_delay)
 
-        #construct observation delay kernel
-        #Recall first element is zero delay
         K = generate_observation_kernel(delay_int, time_horizon)
 
         new{eltype(gen_int)}(

From f3fcc76fdcd091e0adacec0519d771316bb3fe27 Mon Sep 17 00:00:00 2001
From: Samuel Brand <sam055@mac.com>
Date: Mon, 12 Feb 2024 23:21:40 +0000
Subject: [PATCH 7/9] Include an initial value as an inferrable quantity for
 random_walk

---
 EpiAware/src/latent-processes.jl | 9 ++++++---
 1 file changed, 6 insertions(+), 3 deletions(-)

diff --git a/EpiAware/src/latent-processes.jl b/EpiAware/src/latent-processes.jl
index 2d180c598..16361a587 100644
--- a/EpiAware/src/latent-processes.jl
+++ b/EpiAware/src/latent-processes.jl
@@ -1,4 +1,6 @@
-const STANDARD_RW_PRIORS = (var_RW_dist = truncated(Normal(0.0, 0.05), 0.0, Inf),)
+const STANDARD_RW_PRIORS =
+    (var_RW_dist = truncated(Normal(0.0, 0.05), 0.0, Inf), init_rw_value_dist = Normal())
+
 
 """
     random_walk(n, ϵ_t = missing; latent_process_priors = (var_RW_dist = truncated(Normal(0., 0.05), 0., Inf),), ::Type{T} = Float64) where {T <: Real}
@@ -23,7 +25,8 @@ Constructs a random walk model.
     rw = Vector{T}(undef, n)
     ϵ_t ~ MvNormal(ones(n))
     σ²_RW ~ latent_process_priors.var_RW_dist
+    init_rw_value ~ latent_process_priors.init_rw_value_dist
     σ_RW = sqrt(σ²_RW)
-    rw .= cumsum(σ_RW * ϵ_t)
-    return rw, (; σ_RW)
+    rw .= init_rw_value .+ cumsum(σ_RW * ϵ_t)
+    return rw, (; σ_RW, init_rw_value)
 end

From 00646f9b67aa1913779a65be485323ad7d44c542 Mon Sep 17 00:00:00 2001
From: Samuel Brand <sam055@mac.com>
Date: Mon, 12 Feb 2024 23:22:11 +0000
Subject: [PATCH 8/9] Remove `n_generate_ahead` this can be covered by the time
 horizon of the epimodel struct

---
 EpiAware/src/models.jl | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/EpiAware/src/models.jl b/EpiAware/src/models.jl
index bd73c9b95..5f00d933d 100644
--- a/EpiAware/src/models.jl
+++ b/EpiAware/src/models.jl
@@ -34,7 +34,6 @@ A named tuple containing the generated quantities `I_t` and `latent_process_para
     latent_process;
     latent_process_priors,
     transform_function = exp,
-    n_generate_ahead = 0,
     pos_shift = 1e-6,
     neg_bin_cluster_factor = missing,
     neg_bin_cluster_factor_prior = Gamma(3, 0.05 / 3),
@@ -43,7 +42,7 @@ A named tuple containing the generated quantities `I_t` and `latent_process_para
     neg_bin_cluster_factor ~ neg_bin_cluster_factor_prior
 
     #Latent process
-    time_steps = length(y_t) + n_generate_ahead
+    time_steps = epimodel.time_horizon
     @submodel _I_t, latent_process_parameters =
         latent_process(time_steps; latent_process_priors = latent_process_priors)
 
@@ -52,7 +51,8 @@ A named tuple containing the generated quantities `I_t` and `latent_process_para
 
     #Predictive distribution
     case_pred_dists =
-        (epimodel.delay_kernel * I_t) .+ pos_shift .|> μ -> mean_cc_neg_bin(μ, α)
+        (epimodel.delay_kernel * I_t) .+ pos_shift .|>
+        μ -> mean_cc_neg_bin(μ, neg_bin_cluster_factor)
 
     #Likelihood
     y_t ~ arraydist(case_pred_dists)

From cf7b3219f2712e9b623aa5c1475e00e957b3b50d Mon Sep 17 00:00:00 2001
From: Samuel Brand <sam055@mac.com>
Date: Mon, 12 Feb 2024 23:23:09 +0000
Subject: [PATCH 9/9] Create vignette for running model along with unit tests
 for new or modified functions and StatsPlot test dep

---
 EpiAware/test/Manifest.toml                   | 809 +++++++++++++++++-
 EpiAware/test/Project.toml                    |   1 +
 .../toy_model_log_infs_RW.jl                  | 123 +++
 EpiAware/test/test_latent-processes.jl        |   2 +-
 EpiAware/test/test_models.jl                  |  40 +
 5 files changed, 958 insertions(+), 17 deletions(-)
 create mode 100644 EpiAware/test/predictive_checking/toy_model_log_infs_RW.jl
 create mode 100644 EpiAware/test/test_models.jl

diff --git a/EpiAware/test/Manifest.toml b/EpiAware/test/Manifest.toml
index acba947c6..5fc82e725 100644
--- a/EpiAware/test/Manifest.toml
+++ b/EpiAware/test/Manifest.toml
@@ -2,7 +2,7 @@
 
 julia_version = "1.10.0"
 manifest_format = "2.0"
-project_hash = "0dea5a2fa6648a3a05ed8cb24ee73213ffe76d33"
+project_hash = "24f5f05a5520371126c54806953bd0e40a21c57c"
 
 [[deps.ADTypes]]
 git-tree-sha1 = "41c37aa88889c171f1300ceac1313c06e891d245"
@@ -119,6 +119,18 @@ version = "2.3.0"
 uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
 version = "1.1.1"
 
+[[deps.Arpack]]
+deps = ["Arpack_jll", "Libdl", "LinearAlgebra", "Logging"]
+git-tree-sha1 = "9b9b347613394885fd1c8c7729bfc60528faa436"
+uuid = "7d9fca2a-8960-54d3-9f78-7d1dccf2cb97"
+version = "0.5.4"
+
+[[deps.Arpack_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "OpenBLAS_jll", "Pkg"]
+git-tree-sha1 = "5ba6c757e8feccf03a1554dfaf3e26b3cfc7fd5e"
+uuid = "68821587-b530-5797-8361-c406ea357684"
+version = "3.5.1+1"
+
 [[deps.ArrayInterface]]
 deps = ["Adapt", "LinearAlgebra", "Requires", "SparseArrays", "SuiteSparse"]
 git-tree-sha1 = "bbec08a37f8722786d87bedf84eae19c020c4efa"
@@ -152,9 +164,9 @@ version = "0.1.0"
 
 [[deps.AxisAlgorithms]]
 deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"]
-git-tree-sha1 = "01b8ccb13d68535d73d2b0c23e39bd23155fb712"
+git-tree-sha1 = "66771c8d21c8ff5e3a93379480a2307ac36863f7"
 uuid = "13072b0f-2c55-5437-9ae7-d433b7a33950"
-version = "1.1.0"
+version = "1.0.1"
 
 [[deps.AxisArrays]]
 deps = ["Dates", "IntervalSets", "IterTools", "RangeArrays"]
@@ -212,11 +224,28 @@ version = "0.13.8"
     Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
     Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
+[[deps.BitFlags]]
+git-tree-sha1 = "2dc09997850d68179b69dafb58ae806167a32b1b"
+uuid = "d1d4a3ce-64b1-5f1a-9ba4-7e7e69966f35"
+version = "0.1.8"
+
+[[deps.Bzip2_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "9e2a6b69137e6969bab0152632dcb3bc108c8bdd"
+uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
+version = "1.0.8+1"
+
 [[deps.CEnum]]
 git-tree-sha1 = "389ad5c84de1ae7cf0e28e381131c98ea87d54fc"
 uuid = "fa961155-64e5-5f13-b03f-caf6b980ea82"
 version = "0.5.0"
 
+[[deps.Cairo_jll]]
+deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
+git-tree-sha1 = "4b859a208b2397a7a623a03449e4636bdb17bcf2"
+uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
+version = "1.16.1+1"
+
 [[deps.Calculus]]
 deps = ["LinearAlgebra"]
 git-tree-sha1 = "f641eb0a4f00c343bbc32346e1217b86f3ce9dad"
@@ -249,6 +278,46 @@ weakdeps = ["InverseFunctions"]
     [deps.ChangesOfVariables.extensions]
     ChangesOfVariablesInverseFunctionsExt = "InverseFunctions"
 
+[[deps.Clustering]]
+deps = ["Distances", "LinearAlgebra", "NearestNeighbors", "Printf", "Random", "SparseArrays", "Statistics", "StatsBase"]
+git-tree-sha1 = "9ebb045901e9bbf58767a9f34ff89831ed711aae"
+uuid = "aaaa29a8-35af-508c-8bc3-b662a17a0fe5"
+version = "0.15.7"
+
+[[deps.CodecZlib]]
+deps = ["TranscodingStreams", "Zlib_jll"]
+git-tree-sha1 = "59939d8a997469ee05c4b4944560a820f9ba0d73"
+uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
+version = "0.7.4"
+
+[[deps.ColorSchemes]]
+deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "PrecompileTools", "Random"]
+git-tree-sha1 = "67c1f244b991cad9b0aa4b7540fb758c2488b129"
+uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
+version = "3.24.0"
+
+[[deps.ColorTypes]]
+deps = ["FixedPointNumbers", "Random"]
+git-tree-sha1 = "eb7f0f8307f71fac7c606984ea5fb2817275d6e4"
+uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
+version = "0.11.4"
+
+[[deps.ColorVectorSpace]]
+deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "Requires", "Statistics", "TensorCore"]
+git-tree-sha1 = "a1f44953f2382ebb937d60dafbe2deea4bd23249"
+uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4"
+version = "0.10.0"
+weakdeps = ["SpecialFunctions"]
+
+    [deps.ColorVectorSpace.extensions]
+    SpecialFunctionsExt = "SpecialFunctions"
+
+[[deps.Colors]]
+deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
+git-tree-sha1 = "fc08e5930ee9a4e03f84bfb5211cb54e7769758a"
+uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
+version = "0.12.10"
+
 [[deps.Combinatorics]]
 git-tree-sha1 = "08c8b6831dc00bfea825826be0bc8336fc369860"
 uuid = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
@@ -289,6 +358,12 @@ weakdeps = ["InverseFunctions"]
     [deps.CompositionsBase.extensions]
     CompositionsBaseInverseFunctionsExt = "InverseFunctions"
 
+[[deps.ConcurrentUtilities]]
+deps = ["Serialization", "Sockets"]
+git-tree-sha1 = "9c4708e3ed2b799e6124b5673a712dda0b596a9b"
+uuid = "f0e56b4a-5159-44fe-b623-3e5288b988bb"
+version = "2.3.1"
+
 [[deps.ConsoleProgressMonitor]]
 deps = ["Logging", "ProgressMeter"]
 git-tree-sha1 = "3ab7b2136722890b9af903859afcf457fa3059e8"
@@ -306,6 +381,11 @@ weakdeps = ["IntervalSets", "StaticArrays"]
     ConstructionBaseIntervalSetsExt = "IntervalSets"
     ConstructionBaseStaticArraysExt = "StaticArrays"
 
+[[deps.Contour]]
+git-tree-sha1 = "d05d9e7b7aedff4e5b51a029dced05cfb6125781"
+uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
+version = "0.6.2"
+
 [[deps.Crayons]]
 git-tree-sha1 = "249fe38abf76d48563e2f4556bebd215aa317e15"
 uuid = "a8cc5b0e-0ffa-5ad4-8c14-923d3ee1735f"
@@ -360,6 +440,17 @@ git-tree-sha1 = "23163d55f885173722d1e4cf0f6110cdbaf7e272"
 uuid = "b552c78f-8df3-52c6-915a-8e097449b14b"
 version = "1.15.1"
 
+[[deps.Distances]]
+deps = ["LinearAlgebra", "Statistics", "StatsAPI"]
+git-tree-sha1 = "66c4c81f259586e8f002eacebc177e1fb06363b0"
+uuid = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
+version = "0.10.11"
+weakdeps = ["ChainRulesCore", "SparseArrays"]
+
+    [deps.Distances.extensions]
+    DistancesChainRulesCoreExt = "ChainRulesCore"
+    DistancesSparseArraysExt = "SparseArrays"
+
 [[deps.Distributed]]
 deps = ["Random", "Serialization", "Sockets"]
 uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
@@ -440,11 +531,41 @@ git-tree-sha1 = "bdb1942cd4c45e3c678fd11569d5cccd80976237"
 uuid = "4e289a0a-7415-4d19-859d-a7e5c4648b56"
 version = "1.0.4"
 
+[[deps.EpollShim_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "8e9441ee83492030ace98f9789a654a6d0b1f643"
+uuid = "2702e6a9-849d-5ed8-8c21-79e8b8f9ee43"
+version = "0.0.20230411+0"
+
+[[deps.ExceptionUnwrapping]]
+deps = ["Test"]
+git-tree-sha1 = "dcb08a0d93ec0b1cdc4af184b26b591e9695423a"
+uuid = "460bff9d-24e4-43bc-9d9f-a8973cb893f4"
+version = "0.1.10"
+
+[[deps.Expat_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "4558ab818dcceaab612d1bb8c19cee87eda2b83c"
+uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
+version = "2.5.0+0"
+
 [[deps.ExprTools]]
 git-tree-sha1 = "27415f162e6028e81c72b82ef756bf321213b6ec"
 uuid = "e2ba6199-217a-4e67-a87a-7c52f15ade04"
 version = "0.1.10"
 
+[[deps.FFMPEG]]
+deps = ["FFMPEG_jll"]
+git-tree-sha1 = "b57e3acbe22f8484b4b5ff66a7499717fe1a9cc8"
+uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
+version = "0.4.1"
+
+[[deps.FFMPEG_jll]]
+deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "PCRE2_jll", "Zlib_jll", "libaom_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
+git-tree-sha1 = "466d45dc38e15794ec7d5d63ec03d776a9aff36e"
+uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
+version = "4.4.4+1"
+
 [[deps.FFTW]]
 deps = ["AbstractFFTs", "FFTW_jll", "LinearAlgebra", "MKL_jll", "Preferences", "Reexport"]
 git-tree-sha1 = "4820348781ae578893311153d69049a93d05f39d"
@@ -472,6 +593,18 @@ weakdeps = ["PDMats", "SparseArrays", "Statistics"]
     FillArraysSparseArraysExt = "SparseArrays"
     FillArraysStatisticsExt = "Statistics"
 
+[[deps.FixedPointNumbers]]
+deps = ["Statistics"]
+git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
+uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
+version = "0.8.4"
+
+[[deps.Fontconfig_jll]]
+deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "21efd19106a55620a188615da6d3d06cd7f6ee03"
+uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
+version = "2.13.93+0"
+
 [[deps.Formatting]]
 deps = ["Printf"]
 git-tree-sha1 = "8339d61043228fdd3eb658d86c926cb282ae72a8"
@@ -488,6 +621,18 @@ weakdeps = ["StaticArrays"]
     [deps.ForwardDiff.extensions]
     ForwardDiffStaticArraysExt = "StaticArrays"
 
+[[deps.FreeType2_jll]]
+deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
+git-tree-sha1 = "d8db6a5a2fe1381c1ea4ef2cab7c69c2de7f9ea0"
+uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
+version = "2.13.1+0"
+
+[[deps.FriBidi_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "aa31987c2ba8704e23c6c8ba8a4f769d5d7e4f91"
+uuid = "559328eb-81f9-559d-9380-de523a88c83c"
+version = "1.0.10+0"
+
 [[deps.FunctionWrappers]]
 git-tree-sha1 = "d62485945ce5ae9c0c48f124a84998d755bae00e"
 uuid = "069b7b12-0de2-55c6-9aab-29f3d0a68a2e"
@@ -509,12 +654,65 @@ version = "0.4.7"
 deps = ["Random"]
 uuid = "9fa8497b-333b-5362-9e8d-4d0656e87820"
 
+[[deps.GLFW_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"]
+git-tree-sha1 = "ff38ba61beff76b8f4acad8ab0c97ef73bb670cb"
+uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
+version = "3.3.9+0"
+
 [[deps.GPUArraysCore]]
 deps = ["Adapt"]
 git-tree-sha1 = "2d6ca471a6c7b536127afccfa7564b5b39227fe0"
 uuid = "46192b85-c4d5-4398-a991-12ede77f4527"
 version = "0.1.5"
 
+[[deps.GR]]
+deps = ["Artifacts", "Base64", "DelimitedFiles", "Downloads", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Preferences", "Printf", "Random", "Serialization", "Sockets", "TOML", "Tar", "Test", "UUIDs", "p7zip_jll"]
+git-tree-sha1 = "3458564589be207fa6a77dbbf8b97674c9836aab"
+uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
+version = "0.73.2"
+
+[[deps.GR_jll]]
+deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "FreeType2_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Qt6Base_jll", "Zlib_jll", "libpng_jll"]
+git-tree-sha1 = "77f81da2964cc9fa7c0127f941e8bce37f7f1d70"
+uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
+version = "0.73.2+0"
+
+[[deps.Gettext_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"]
+git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046"
+uuid = "78b55507-aeef-58d4-861c-77aaff3498b1"
+version = "0.21.0+0"
+
+[[deps.Glib_jll]]
+deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE2_jll", "Zlib_jll"]
+git-tree-sha1 = "e94c92c7bf4819685eb80186d51c43e71d4afa17"
+uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
+version = "2.76.5+0"
+
+[[deps.Graphite2_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011"
+uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472"
+version = "1.3.14+0"
+
+[[deps.Grisu]]
+git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2"
+uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe"
+version = "1.0.2"
+
+[[deps.HTTP]]
+deps = ["Base64", "CodecZlib", "ConcurrentUtilities", "Dates", "ExceptionUnwrapping", "Logging", "LoggingExtras", "MbedTLS", "NetworkOptions", "OpenSSL", "Random", "SimpleBufferStream", "Sockets", "URIs", "UUIDs"]
+git-tree-sha1 = "abbbb9ec3afd783a7cbd82ef01dcd088ea051398"
+uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
+version = "1.10.1"
+
+[[deps.HarfBuzz_jll]]
+deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"]
+git-tree-sha1 = "129acf094d168394e80ee1dc4bc06ec835e510a3"
+uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566"
+version = "2.8.1+1"
+
 [[deps.HypergeometricFunctions]]
 deps = ["DualNumbers", "LinearAlgebra", "OpenLibm_jll", "SpecialFunctions"]
 git-tree-sha1 = "f218fe3736ddf977e0e772bc9a586b2383da2685"
@@ -544,15 +742,9 @@ uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 
 [[deps.Interpolations]]
 deps = ["Adapt", "AxisAlgorithms", "ChainRulesCore", "LinearAlgebra", "OffsetArrays", "Random", "Ratios", "Requires", "SharedArrays", "SparseArrays", "StaticArrays", "WoodburyMatrices"]
-git-tree-sha1 = "88a101217d7cb38a7b481ccd50d21876e1d1b0e0"
+git-tree-sha1 = "721ec2cf720536ad005cb38f50dbba7b02419a15"
 uuid = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
-version = "0.15.1"
-
-    [deps.Interpolations.extensions]
-    InterpolationsUnitfulExt = "Unitful"
-
-    [deps.Interpolations.weakdeps]
-    Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
+version = "0.14.7"
 
 [[deps.IntervalSets]]
 git-tree-sha1 = "581191b15bcb56a2aa257e9c160085d0f128a380"
@@ -590,12 +782,30 @@ git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
 uuid = "82899510-4779-5014-852e-03e436cf321d"
 version = "1.0.0"
 
+[[deps.JLFzf]]
+deps = ["Pipe", "REPL", "Random", "fzf_jll"]
+git-tree-sha1 = "a53ebe394b71470c7f97c2e7e170d51df21b17af"
+uuid = "1019f520-868f-41f5-a6de-eb00f4b6a39c"
+version = "0.1.7"
+
 [[deps.JLLWrappers]]
 deps = ["Artifacts", "Preferences"]
 git-tree-sha1 = "7e5d6779a1e09a36db2a7b6cff50942a0a7d0fca"
 uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
 version = "1.5.0"
 
+[[deps.JSON]]
+deps = ["Dates", "Mmap", "Parsers", "Unicode"]
+git-tree-sha1 = "31e996f0a15c7b280ba9f76636b3ff9e2ae58c9a"
+uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
+version = "0.21.4"
+
+[[deps.JpegTurbo_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "60b1194df0a3298f460063de985eae7b01bc011a"
+uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
+version = "3.0.1+0"
+
 [[deps.KernelAbstractions]]
 deps = ["Adapt", "Atomix", "InteractiveUtils", "LinearAlgebra", "MacroTools", "PrecompileTools", "Requires", "SparseArrays", "StaticArrays", "UUIDs", "UnsafeAtomics", "UnsafeAtomicsLLVM"]
 git-tree-sha1 = "4e0cb2f5aad44dcfdc91088e85dee4ecb22c791c"
@@ -614,6 +824,18 @@ git-tree-sha1 = "fee018a29b60733876eb557804b5b109dd3dd8a7"
 uuid = "5ab0869b-81aa-558d-bb23-cbf5423bbe9b"
 version = "0.6.8"
 
+[[deps.LAME_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c"
+uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
+version = "3.100.1+0"
+
+[[deps.LERC_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "bf36f528eec6634efc60d7ec062008f171071434"
+uuid = "88015f11-f218-50d7-93a8-a6af411a945d"
+version = "3.0.0+1"
+
 [[deps.LLVM]]
 deps = ["CEnum", "LLVMExtra_jll", "Libdl", "Preferences", "Printf", "Requires", "Unicode"]
 git-tree-sha1 = "cb4619f7353fc62a1a22ffa3d7ed9791cfb47ad8"
@@ -632,6 +854,12 @@ git-tree-sha1 = "98eaee04d96d973e79c25d49167668c5c8fb50e2"
 uuid = "dad2f222-ce93-54a1-a47d-0025e8a3acab"
 version = "0.0.27+1"
 
+[[deps.LLVMOpenMP_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "d986ce2d884d49126836ea94ed5bfb0f12679713"
+uuid = "1d63c593-3942-5779-bab2-d838dc0a180e"
+version = "15.0.7+0"
+
 [[deps.LRUCache]]
 git-tree-sha1 = "b3cc6698599b10e652832c2f23db3cab99d51b59"
 uuid = "8ac3fa9e-de4c-5943-b1dc-09c6b5f20637"
@@ -641,11 +869,31 @@ weakdeps = ["Serialization"]
     [deps.LRUCache.extensions]
     SerializationExt = ["Serialization"]
 
+[[deps.LZO_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "e5b909bcf985c5e2605737d2ce278ed791b89be6"
+uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac"
+version = "2.10.1+0"
+
 [[deps.LaTeXStrings]]
 git-tree-sha1 = "50901ebc375ed41dbf8058da26f9de442febbbec"
 uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
 version = "1.3.1"
 
+[[deps.Latexify]]
+deps = ["Formatting", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "OrderedCollections", "Printf", "Requires"]
+git-tree-sha1 = "f428ae552340899a935973270b8d98e5a31c49fe"
+uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
+version = "0.16.1"
+
+    [deps.Latexify.extensions]
+    DataFramesExt = "DataFrames"
+    SymEngineExt = "SymEngine"
+
+    [deps.Latexify.weakdeps]
+    DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
+    SymEngine = "123dc426-2d89-5057-bbad-38513e3affd8"
+
 [[deps.Lazy]]
 deps = ["MacroTools"]
 git-tree-sha1 = "1370f8202dac30758f3c345f9909b97f53d87d3f"
@@ -689,12 +937,60 @@ version = "1.11.0+1"
 [[deps.Libdl]]
 uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
 
+[[deps.Libffi_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "0b4a5d71f3e5200a7dff793393e09dfc2d874290"
+uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
+version = "3.2.2+1"
+
+[[deps.Libgcrypt_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll", "Pkg"]
+git-tree-sha1 = "64613c82a59c120435c067c2b809fc61cf5166ae"
+uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4"
+version = "1.8.7+0"
+
+[[deps.Libglvnd_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"]
+git-tree-sha1 = "6f73d1dd803986947b2c750138528a999a6c7733"
+uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29"
+version = "1.6.0+0"
+
+[[deps.Libgpg_error_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "c333716e46366857753e273ce6a69ee0945a6db9"
+uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
+version = "1.42.0+0"
+
+[[deps.Libiconv_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "f9557a255370125b405568f9767d6d195822a175"
+uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
+version = "1.17.0+0"
+
+[[deps.Libmount_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "9c30530bf0effd46e15e0fdcf2b8636e78cbbd73"
+uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
+version = "2.35.0+0"
+
 [[deps.Libtask]]
 deps = ["FunctionWrappers", "LRUCache", "LinearAlgebra", "Statistics"]
 git-tree-sha1 = "345a40c746404dd9cb1bbc368715856838ab96f2"
 uuid = "6f1fad26-d15e-5dc8-ae53-837a1d7b8c9f"
 version = "0.8.6"
 
+[[deps.Libtiff_jll]]
+deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "LERC_jll", "Libdl", "XZ_jll", "Zlib_jll", "Zstd_jll"]
+git-tree-sha1 = "2da088d113af58221c52828a80378e16be7d037a"
+uuid = "89763e89-9b03-5906-acba-b20f662cd828"
+version = "4.5.1+1"
+
+[[deps.Libuuid_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "7f3efec06033682db852f8b3bc3c1d2b0a0ab066"
+uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700"
+version = "2.36.0+0"
+
 [[deps.LinearAlgebra]]
 deps = ["Libdl", "OpenBLAS_jll", "libblastrampoline_jll"]
 uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
@@ -791,11 +1087,22 @@ version = "0.4.2"
 deps = ["Base64"]
 uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
 
+[[deps.MbedTLS]]
+deps = ["Dates", "MbedTLS_jll", "MozillaCACerts_jll", "NetworkOptions", "Random", "Sockets"]
+git-tree-sha1 = "c067a280ddc25f196b5e7df3877c6b226d390aaf"
+uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
+version = "1.1.9"
+
 [[deps.MbedTLS_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
 version = "2.28.2+1"
 
+[[deps.Measures]]
+git-tree-sha1 = "c13304c81eec1ed3af7fc20e75fb6b26092a1102"
+uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
+version = "0.3.2"
+
 [[deps.MicroCollections]]
 deps = ["BangBang", "InitialValues", "Setfield"]
 git-tree-sha1 = "629afd7d10dbc6935ec59b32daeb33bc4460a42e"
@@ -815,6 +1122,12 @@ uuid = "a63ad114-7e13-5084-954f-fe012c677804"
 uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
 version = "2023.1.10"
 
+[[deps.MultivariateStats]]
+deps = ["Arpack", "LinearAlgebra", "SparseArrays", "Statistics", "StatsAPI", "StatsBase"]
+git-tree-sha1 = "68bf5103e002c44adfd71fea6bd770b3f0586843"
+uuid = "6f286f6a-111f-5878-ab1e-185364afe411"
+version = "0.10.2"
+
 [[deps.NNlib]]
 deps = ["Adapt", "Atomix", "ChainRulesCore", "GPUArraysCore", "KernelAbstractions", "LinearAlgebra", "Pkg", "Random", "Requires", "Statistics"]
 git-tree-sha1 = "d2811b435d2f571bdfdfa644bb806a66b458e186"
@@ -850,10 +1163,21 @@ git-tree-sha1 = "eda490d06b9f7c00752ee81cfa451efe55521e21"
 uuid = "c020b1a1-e9b0-503a-9c33-f039bfc54a85"
 version = "1.0.0"
 
+[[deps.NearestNeighbors]]
+deps = ["Distances", "StaticArrays"]
+git-tree-sha1 = "ded64ff6d4fdd1cb68dfcbb818c69e144a5b2e4c"
+uuid = "b8a86587-4115-5ab1-83bc-aa920d37bbce"
+version = "0.4.16"
+
 [[deps.NetworkOptions]]
 uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
 version = "1.2.0"
 
+[[deps.Observables]]
+git-tree-sha1 = "7438a59546cf62428fc9d1bc94729146d37a7225"
+uuid = "510215fc-4207-5dde-b226-833fc4488ee2"
+version = "0.5.5"
+
 [[deps.OffsetArrays]]
 git-tree-sha1 = "6a731f2b5c03157418a20c12195eb4b74c8f8621"
 uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
@@ -863,6 +1187,12 @@ weakdeps = ["Adapt"]
     [deps.OffsetArrays.extensions]
     OffsetArraysAdaptExt = "Adapt"
 
+[[deps.Ogg_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "887579a3eb005446d514ab7aeac5d1d027658b8f"
+uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
+version = "1.3.5+1"
+
 [[deps.OpenBLAS_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
 uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
@@ -873,6 +1203,18 @@ deps = ["Artifacts", "Libdl"]
 uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
 version = "0.8.1+2"
 
+[[deps.OpenSSL]]
+deps = ["BitFlags", "Dates", "MozillaCACerts_jll", "OpenSSL_jll", "Sockets"]
+git-tree-sha1 = "51901a49222b09e3743c65b8847687ae5fc78eb2"
+uuid = "4d8831e6-92b7-49fb-bdf8-b643e874388c"
+version = "1.4.1"
+
+[[deps.OpenSSL_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "60e3045590bd104a16fefb12836c00c0ef8c7f8c"
+uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
+version = "3.0.13+0"
+
 [[deps.OpenSpecFun_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
@@ -885,22 +1227,82 @@ git-tree-sha1 = "264b061c1903bc0fe9be77cb9050ebacff66bb63"
 uuid = "3bd65402-5787-11e9-1adc-39752487f4e2"
 version = "0.3.2"
 
+[[deps.Opus_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "51a08fb14ec28da2ec7a927c4337e4332c2a4720"
+uuid = "91d4177d-7536-5919-b921-800302f37372"
+version = "1.3.2+0"
+
 [[deps.OrderedCollections]]
 git-tree-sha1 = "dfdf5519f235516220579f949664f1bf44e741c5"
 uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
 version = "1.6.3"
 
+[[deps.PCRE2_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "efcefdf7-47ab-520b-bdef-62a2eaa19f15"
+version = "10.42.0+1"
+
 [[deps.PDMats]]
 deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse"]
 git-tree-sha1 = "949347156c25054de2db3b166c52ac4728cbad65"
 uuid = "90014a1f-27ba-587c-ab20-58faa44d9150"
 version = "0.11.31"
 
+[[deps.Parsers]]
+deps = ["Dates", "PrecompileTools", "UUIDs"]
+git-tree-sha1 = "8489905bcdbcfac64d1daa51ca07c0d8f0283821"
+uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
+version = "2.8.1"
+
+[[deps.Pipe]]
+git-tree-sha1 = "6842804e7867b115ca9de748a0cf6b364523c16d"
+uuid = "b98c9c47-44ae-5843-9183-064241ee97a0"
+version = "1.3.0"
+
+[[deps.Pixman_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "LLVMOpenMP_jll", "Libdl"]
+git-tree-sha1 = "64779bc4c9784fee475689a1752ef4d5747c5e87"
+uuid = "30392449-352a-5448-841d-b1acce4e97dc"
+version = "0.42.2+0"
+
 [[deps.Pkg]]
 deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
 uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 version = "1.10.0"
 
+[[deps.PlotThemes]]
+deps = ["PlotUtils", "Statistics"]
+git-tree-sha1 = "1f03a2d339f42dca4a4da149c7e15e9b896ad899"
+uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
+version = "3.1.0"
+
+[[deps.PlotUtils]]
+deps = ["ColorSchemes", "Colors", "Dates", "PrecompileTools", "Printf", "Random", "Reexport", "Statistics"]
+git-tree-sha1 = "862942baf5663da528f66d24996eb6da85218e76"
+uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
+version = "1.4.0"
+
+[[deps.Plots]]
+deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "JLFzf", "JSON", "LaTeXStrings", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "Pkg", "PlotThemes", "PlotUtils", "PrecompileTools", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "RelocatableFolders", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun", "UnitfulLatexify", "Unzip"]
+git-tree-sha1 = "c4fa93d7d66acad8f6f4ff439576da9d2e890ee0"
+uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+version = "1.40.1"
+
+    [deps.Plots.extensions]
+    FileIOExt = "FileIO"
+    GeometryBasicsExt = "GeometryBasics"
+    IJuliaExt = "IJulia"
+    ImageInTerminalExt = "ImageInTerminal"
+    UnitfulExt = "Unitful"
+
+    [deps.Plots.weakdeps]
+    FileIO = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
+    GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
+    IJulia = "7073ff75-c697-5162-941a-fcdaad2a7d2a"
+    ImageInTerminal = "d8c32880-2388-543b-8c61-d9f865259254"
+    Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
+
 [[deps.PrecompileTools]]
 deps = ["Preferences"]
 git-tree-sha1 = "03b4c25b43cb84cee5c90aa9b5ea0a78fd848d2f"
@@ -935,6 +1337,12 @@ git-tree-sha1 = "00099623ffee15972c16111bcf84c58a0051257c"
 uuid = "92933f4c-e287-5a05-a399-4b506db050ca"
 version = "1.9.0"
 
+[[deps.Qt6Base_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Vulkan_Loader_jll", "Xorg_libSM_jll", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_cursor_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "libinput_jll", "xkbcommon_jll"]
+git-tree-sha1 = "37b7bb7aabf9a085e0044307e1717436117f2b3b"
+uuid = "c0090381-4147-56d7-9ebc-da0b1113ec56"
+version = "6.5.3+1"
+
 [[deps.QuadGK]]
 deps = ["DataStructures", "LinearAlgebra"]
 git-tree-sha1 = "9b23c31e76e333e6fb4c1595ae6afa74966a729e"
@@ -971,13 +1379,11 @@ deps = ["Requires"]
 git-tree-sha1 = "1342a47bf3260ee108163042310d26f2be5ec90b"
 uuid = "c84ed2f1-dad5-54f0-aa8e-dbefe2724439"
 version = "0.4.5"
+weakdeps = ["FixedPointNumbers"]
 
     [deps.Ratios.extensions]
     RatiosFixedPointNumbersExt = "FixedPointNumbers"
 
-    [deps.Ratios.weakdeps]
-    FixedPointNumbers = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
-
 [[deps.RealDot]]
 deps = ["LinearAlgebra"]
 git-tree-sha1 = "9f0a1b71baaf7650f4fa8a1d168c7fb6ee41f0c9"
@@ -990,6 +1396,12 @@ git-tree-sha1 = "5c3d09cc4f31f5fc6af001c250bf1278733100ff"
 uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
 version = "1.3.4"
 
+[[deps.RecipesPipeline]]
+deps = ["Dates", "NaNMath", "PlotUtils", "PrecompileTools", "RecipesBase"]
+git-tree-sha1 = "45cf9fd0ca5839d06ef333c8201714e888486342"
+uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
+version = "0.6.12"
+
 [[deps.RecursiveArrayTools]]
 deps = ["Adapt", "ArrayInterface", "DocStringExtensions", "GPUArraysCore", "IteratorInterfaceExtensions", "LinearAlgebra", "RecipesBase", "SparseArrays", "StaticArraysCore", "Statistics", "SymbolicIndexingInterface", "Tables"]
 git-tree-sha1 = "2bd309f5171a628efdf5309361cd8a779b9e63a9"
@@ -1019,6 +1431,12 @@ git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
 uuid = "189a3867-3050-52da-a836-e630ba90ab69"
 version = "1.2.2"
 
+[[deps.RelocatableFolders]]
+deps = ["SHA", "Scratch"]
+git-tree-sha1 = "ffdaf70d81cf6ff22c2b6e733c900c3321cab864"
+uuid = "05181044-ff0b-4ac5-8273-598c1e38db00"
+version = "1.0.1"
+
 [[deps.Requires]]
 deps = ["UUIDs"]
 git-tree-sha1 = "838a3a4188e2ded87a4f9f184b4b0d78a1e91cb7"
@@ -1101,6 +1519,18 @@ git-tree-sha1 = "a8e18eb383b5ecf1b5e6fc237eb39255044fd92b"
 uuid = "30f210dd-8aff-4c5f-94ba-8e64358c1161"
 version = "3.0.0"
 
+[[deps.Scratch]]
+deps = ["Dates"]
+git-tree-sha1 = "3bac05bc7e74a75fd9cba4295cde4045d9fe2386"
+uuid = "6c6a2e73-6563-6170-7368-637461726353"
+version = "1.2.1"
+
+[[deps.SentinelArrays]]
+deps = ["Dates", "Random"]
+git-tree-sha1 = "0e7508ff27ba32f26cd459474ca2ede1bc10991f"
+uuid = "91c51154-3ec4-41a3-a24f-3f23e20d615c"
+version = "1.4.1"
+
 [[deps.Serialization]]
 uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
 
@@ -1114,6 +1544,17 @@ version = "1.1.1"
 deps = ["Distributed", "Mmap", "Random", "Serialization"]
 uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
 
+[[deps.Showoff]]
+deps = ["Dates", "Grisu"]
+git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
+uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
+version = "1.0.3"
+
+[[deps.SimpleBufferStream]]
+git-tree-sha1 = "874e8867b33a00e784c8a7e4b60afe9e037b74e1"
+uuid = "777ac1f9-54b0-4bf8-805c-2214025038e7"
+version = "1.1.0"
+
 [[deps.SimpleUnPack]]
 git-tree-sha1 = "58e6353e72cde29b90a69527e56df1b5c3d8c437"
 uuid = "ce78b400-467f-4804-87d8-8f486da07d0a"
@@ -1205,6 +1646,12 @@ weakdeps = ["ChainRulesCore", "InverseFunctions"]
     StatsFunsChainRulesCoreExt = "ChainRulesCore"
     StatsFunsInverseFunctionsExt = "InverseFunctions"
 
+[[deps.StatsPlots]]
+deps = ["AbstractFFTs", "Clustering", "DataStructures", "Distributions", "Interpolations", "KernelDensity", "LinearAlgebra", "MultivariateStats", "NaNMath", "Observables", "Plots", "RecipesBase", "RecipesPipeline", "Reexport", "StatsBase", "TableOperations", "Tables", "Widgets"]
+git-tree-sha1 = "9115a29e6c2cf66cf213ccc17ffd61e27e743b24"
+uuid = "f3b207a7-027a-5e70-b257-86293d7955fd"
+version = "0.15.6"
+
 [[deps.StringManipulation]]
 deps = ["PrecompileTools"]
 git-tree-sha1 = "a04cabe79c5f01f4d723cc6704070ada0b9d46d5"
@@ -1236,6 +1683,12 @@ deps = ["Dates"]
 uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
 version = "1.0.3"
 
+[[deps.TableOperations]]
+deps = ["SentinelArrays", "Tables", "Test"]
+git-tree-sha1 = "e383c87cf2a1dc41fa30c093b2a19877c83e1bc1"
+uuid = "ab02a1b2-a7df-11e8-156e-fb1833f50b87"
+version = "1.2.0"
+
 [[deps.TableTraits]]
 deps = ["IteratorInterfaceExtensions"]
 git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
@@ -1253,6 +1706,12 @@ deps = ["ArgTools", "SHA"]
 uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
 version = "1.10.0"
 
+[[deps.TensorCore]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
+uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
+version = "0.1.1"
+
 [[deps.TerminalLoggers]]
 deps = ["LeftChildRightSiblingTrees", "Logging", "Markdown", "Printf", "ProgressLogging", "UUIDs"]
 git-tree-sha1 = "f133fab380933d042f6796eda4e130272ba520ca"
@@ -1284,6 +1743,15 @@ weakdeps = ["PDMats"]
     [deps.Tracker.extensions]
     TrackerPDMatsExt = "PDMats"
 
+[[deps.TranscodingStreams]]
+git-tree-sha1 = "54194d92959d8ebaa8e26227dbe3cdefcdcd594f"
+uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
+version = "0.10.3"
+weakdeps = ["Random", "Test"]
+
+    [deps.TranscodingStreams.extensions]
+    TestExt = ["Test", "Random"]
+
 [[deps.Transducers]]
 deps = ["Adapt", "ArgCheck", "BangBang", "Baselet", "CompositionsBase", "ConstructionBase", "DefineSingletons", "Distributed", "InitialValues", "Logging", "Markdown", "MicroCollections", "Requires", "Setfield", "SplittablesBase", "Tables"]
 git-tree-sha1 = "3064e780dbb8a9296ebb3af8f440f787bb5332af"
@@ -1329,6 +1797,11 @@ version = "0.30.4"
     DynamicHMC = "bbc10e6e-7c05-544b-b16e-64fede858acb"
     Optim = "429524aa-4258-5aef-a3af-852621145aeb"
 
+[[deps.URIs]]
+git-tree-sha1 = "67db6cc7b3821e19ebe75791a9dd19c9b1188f2b"
+uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
+version = "1.5.1"
+
 [[deps.UUIDs]]
 deps = ["Random", "SHA"]
 uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
@@ -1336,6 +1809,29 @@ uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 [[deps.Unicode]]
 uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
 
+[[deps.UnicodeFun]]
+deps = ["REPL"]
+git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
+uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
+version = "0.4.1"
+
+[[deps.Unitful]]
+deps = ["Dates", "LinearAlgebra", "Random"]
+git-tree-sha1 = "3c793be6df9dd77a0cf49d80984ef9ff996948fa"
+uuid = "1986cc42-f94f-5a68-af5c-568840ba703d"
+version = "1.19.0"
+weakdeps = ["ConstructionBase", "InverseFunctions"]
+
+    [deps.Unitful.extensions]
+    ConstructionBaseUnitfulExt = "ConstructionBase"
+    InverseFunctionsUnitfulExt = "InverseFunctions"
+
+[[deps.UnitfulLatexify]]
+deps = ["LaTeXStrings", "Latexify", "Unitful"]
+git-tree-sha1 = "e2d817cc500e960fdbafcf988ac8436ba3208bfd"
+uuid = "45397f5d-5981-4c77-b2b3-fc36d6e9b728"
+version = "1.6.3"
+
 [[deps.UnsafeAtomics]]
 git-tree-sha1 = "6331ac3440856ea1988316b46045303bef658278"
 uuid = "013be700-e6cd-48c3-b4a1-df204f14c38f"
@@ -1347,28 +1843,291 @@ git-tree-sha1 = "323e3d0acf5e78a56dfae7bd8928c989b4f3083e"
 uuid = "d80eeb9a-aca5-4d75-85e5-170c8b632249"
 version = "0.1.3"
 
+[[deps.Unzip]]
+git-tree-sha1 = "ca0969166a028236229f63514992fc073799bb78"
+uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
+version = "0.2.0"
+
+[[deps.Vulkan_Loader_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Wayland_jll", "Xorg_libX11_jll", "Xorg_libXrandr_jll", "xkbcommon_jll"]
+git-tree-sha1 = "2f0486047a07670caad3a81a075d2e518acc5c59"
+uuid = "a44049a8-05dd-5a78-86c9-5fde0876e88c"
+version = "1.3.243+0"
+
+[[deps.Wayland_jll]]
+deps = ["Artifacts", "EpollShim_jll", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
+git-tree-sha1 = "7558e29847e99bc3f04d6569e82d0f5c54460703"
+uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
+version = "1.21.0+1"
+
+[[deps.Wayland_protocols_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "93f43ab61b16ddfb2fd3bb13b3ce241cafb0e6c9"
+uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
+version = "1.31.0+0"
+
+[[deps.Widgets]]
+deps = ["Colors", "Dates", "Observables", "OrderedCollections"]
+git-tree-sha1 = "fcdae142c1cfc7d89de2d11e08721d0f2f86c98a"
+uuid = "cc8bc4a8-27d6-5769-a93b-9d913e69aa62"
+version = "0.6.6"
+
 [[deps.WoodburyMatrices]]
 deps = ["LinearAlgebra", "SparseArrays"]
-git-tree-sha1 = "c1a7aa6219628fcd757dede0ca95e245c5cd9511"
+git-tree-sha1 = "5f24e158cf4cee437052371455fe361f526da062"
 uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
-version = "1.0.0"
+version = "0.5.6"
+
+[[deps.XML2_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Zlib_jll"]
+git-tree-sha1 = "801cbe47eae69adc50f36c3caec4758d2650741b"
+uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
+version = "2.12.2+0"
+
+[[deps.XSLT_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
+git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
+uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
+version = "1.1.34+0"
+
+[[deps.XZ_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "522b8414d40c4cbbab8dee346ac3a09f9768f25d"
+uuid = "ffd25f8a-64ca-5728-b0f7-c24cf3aae800"
+version = "5.4.5+0"
+
+[[deps.Xorg_libICE_jll]]
+deps = ["Libdl", "Pkg"]
+git-tree-sha1 = "e5becd4411063bdcac16be8b66fc2f9f6f1e8fe5"
+uuid = "f67eecfb-183a-506d-b269-f58e52b52d7c"
+version = "1.0.10+1"
+
+[[deps.Xorg_libSM_jll]]
+deps = ["Libdl", "Pkg", "Xorg_libICE_jll"]
+git-tree-sha1 = "4a9d9e4c180e1e8119b5ffc224a7b59d3a7f7e18"
+uuid = "c834827a-8449-5923-a945-d239c165b7dd"
+version = "1.2.3+0"
+
+[[deps.Xorg_libX11_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
+git-tree-sha1 = "afead5aba5aa507ad5a3bf01f58f82c8d1403495"
+uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
+version = "1.8.6+0"
+
+[[deps.Xorg_libXau_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "6035850dcc70518ca32f012e46015b9beeda49d8"
+uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
+version = "1.0.11+0"
+
+[[deps.Xorg_libXcursor_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
+git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
+uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
+version = "1.2.0+4"
+
+[[deps.Xorg_libXdmcp_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "34d526d318358a859d7de23da945578e8e8727b7"
+uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
+version = "1.1.4+0"
+
+[[deps.Xorg_libXext_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
+git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
+uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
+version = "1.3.4+4"
+
+[[deps.Xorg_libXfixes_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
+git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
+uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
+version = "5.0.3+4"
+
+[[deps.Xorg_libXi_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
+git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
+uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
+version = "1.7.10+4"
+
+[[deps.Xorg_libXinerama_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
+git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
+uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
+version = "1.1.4+4"
+
+[[deps.Xorg_libXrandr_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
+git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
+uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
+version = "1.5.2+4"
+
+[[deps.Xorg_libXrender_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
+git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
+uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
+version = "0.9.10+4"
+
+[[deps.Xorg_libpthread_stubs_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "8fdda4c692503d44d04a0603d9ac0982054635f9"
+uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
+version = "0.1.1+0"
+
+[[deps.Xorg_libxcb_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
+git-tree-sha1 = "b4bfde5d5b652e22b9c790ad00af08b6d042b97d"
+uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
+version = "1.15.0+0"
+
+[[deps.Xorg_libxkbfile_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
+git-tree-sha1 = "730eeca102434283c50ccf7d1ecdadf521a765a4"
+uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
+version = "1.1.2+0"
+
+[[deps.Xorg_xcb_util_cursor_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_jll", "Xorg_xcb_util_renderutil_jll"]
+git-tree-sha1 = "04341cb870f29dcd5e39055f895c39d016e18ccd"
+uuid = "e920d4aa-a673-5f3a-b3d7-f755a4d47c43"
+version = "0.1.4+0"
+
+[[deps.Xorg_xcb_util_image_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
+uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
+version = "0.4.0+1"
+
+[[deps.Xorg_xcb_util_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
+git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
+uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
+version = "0.4.0+1"
+
+[[deps.Xorg_xcb_util_keysyms_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
+uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
+version = "0.4.0+1"
+
+[[deps.Xorg_xcb_util_renderutil_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
+uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
+version = "0.3.9+1"
+
+[[deps.Xorg_xcb_util_wm_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
+uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
+version = "0.4.1+1"
+
+[[deps.Xorg_xkbcomp_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxkbfile_jll"]
+git-tree-sha1 = "330f955bc41bb8f5270a369c473fc4a5a4e4d3cb"
+uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
+version = "1.4.6+0"
+
+[[deps.Xorg_xkeyboard_config_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xkbcomp_jll"]
+git-tree-sha1 = "691634e5453ad362044e2ad653e79f3ee3bb98c3"
+uuid = "33bec58e-1273-512f-9401-5d533626f822"
+version = "2.39.0+0"
+
+[[deps.Xorg_xtrans_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "e92a1a012a10506618f10b7047e478403a046c77"
+uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
+version = "1.5.0+0"
 
 [[deps.Zlib_jll]]
 deps = ["Libdl"]
 uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
 version = "1.2.13+1"
 
+[[deps.Zstd_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "49ce682769cd5de6c72dcf1b94ed7790cd08974c"
+uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
+version = "1.5.5+0"
+
 [[deps.ZygoteRules]]
 deps = ["ChainRulesCore", "MacroTools"]
 git-tree-sha1 = "27798139afc0a2afa7b1824c206d5e87ea587a00"
 uuid = "700de1a5-db45-46bc-99cf-38207098b444"
 version = "0.2.5"
 
+[[deps.eudev_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "gperf_jll"]
+git-tree-sha1 = "431b678a28ebb559d224c0b6b6d01afce87c51ba"
+uuid = "35ca27e7-8b34-5b7f-bca9-bdc33f59eb06"
+version = "3.2.9+0"
+
+[[deps.fzf_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "a68c9655fbe6dfcab3d972808f1aafec151ce3f8"
+uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
+version = "0.43.0+0"
+
+[[deps.gperf_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "3516a5630f741c9eecb3720b1ec9d8edc3ecc033"
+uuid = "1a1c6b14-54f6-533d-8383-74cd7377aa70"
+version = "3.1.1+0"
+
+[[deps.libaom_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4"
+uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
+version = "3.4.0+0"
+
+[[deps.libass_jll]]
+deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
+uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
+version = "0.15.1+0"
+
 [[deps.libblastrampoline_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
 version = "5.8.0+1"
 
+[[deps.libevdev_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "141fe65dc3efabb0b1d5ba74e91f6ad26f84cc22"
+uuid = "2db6ffa8-e38f-5e21-84af-90c45d0032cc"
+version = "1.11.0+0"
+
+[[deps.libfdk_aac_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
+uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
+version = "2.0.2+0"
+
+[[deps.libinput_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "eudev_jll", "libevdev_jll", "mtdev_jll"]
+git-tree-sha1 = "ad50e5b90f222cfe78aa3d5183a20a12de1322ce"
+uuid = "36db933b-70db-51c0-b978-0f229ee0e533"
+version = "1.18.0+0"
+
+[[deps.libpng_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
+git-tree-sha1 = "93284c28274d9e75218a416c65ec49d0e0fcdf3d"
+uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
+version = "1.6.40+0"
+
+[[deps.libvorbis_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
+git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
+uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
+version = "1.3.7+1"
+
+[[deps.mtdev_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "814e154bdb7be91d78b6802843f76b6ece642f11"
+uuid = "009596ad-96f7-51b1-9f1b-5ce2d5e8a71e"
+version = "1.1.6+0"
+
 [[deps.nghttp2_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
@@ -1378,3 +2137,21 @@ version = "1.52.0+1"
 deps = ["Artifacts", "Libdl"]
 uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
 version = "17.4.0+2"
+
+[[deps.x264_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
+uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
+version = "2021.5.5+0"
+
+[[deps.x265_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
+uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
+version = "3.5.0+0"
+
+[[deps.xkbcommon_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
+git-tree-sha1 = "9c304562909ab2bab0262639bd4f444d7bc2be37"
+uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
+version = "1.4.1+1"
diff --git a/EpiAware/test/Project.toml b/EpiAware/test/Project.toml
index 96861b1d0..4d508af14 100644
--- a/EpiAware/test/Project.toml
+++ b/EpiAware/test/Project.toml
@@ -3,6 +3,7 @@ Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 DynamicPPL = "366bfd00-2699-11ea-058f-f148b4cae6d8"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+StatsPlots = "f3b207a7-027a-5e70-b257-86293d7955fd"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 TestItemRunner = "f8b46487-2199-4994-9208-9a1283c18c0a"
 TestItems = "1c621080-faea-4a02-84b6-bbd5e436b8fe"
diff --git a/EpiAware/test/predictive_checking/toy_model_log_infs_RW.jl b/EpiAware/test/predictive_checking/toy_model_log_infs_RW.jl
new file mode 100644
index 000000000..259adfc4c
--- /dev/null
+++ b/EpiAware/test/predictive_checking/toy_model_log_infs_RW.jl
@@ -0,0 +1,123 @@
+using Pkg: generate
+#=
+# Toy model for running analysis:
+
+This is a toy model for demonstrating current functionality of EpiAware package.
+
+## Generative Model without data
+
+### Latent Process
+
+The latent process is a random walk defined by a Turing model `random_walk` of specified length `n`.
+
+_Unfixed parameters_:
+- `σ²_RW`: The variance of the random walk process. Current defauly prior is
+- `init_rw_value`: The initial value of the random walk process.
+- `ϵ_t`: The random noise vector.
+
+```math
+\begin{align}
+X(t) &= X(0) + \sigma_{RW} \sum_{t= 1}^n \epsilon_t \\
+X(0) &\sim \mathcal{N}(0, 1) \\
+\epsilon_t &\sim \mathcal{N}(0, 1) \\
+\sigma_{RW} &\sim \text{HalfNormal}(0.05).
+\end{align}
+```
+
+### Log-Infections Model
+
+The log-infections model is defined by a Turing model `log_infections` that takes the observed data `y_t` (or `missing` value),
+an `EpiModel` object `epimodel`, and a `latent_process` model. In this case the latent process is a random walk model.
+
+It also accepts optional arguments for the `latent_process_priors`, `transform_function`, `pos_shift`, `neg_bin_cluster_factor`, and `neg_bin_cluster_factor_prior`.
+
+```math
+\log I_t = \exp(X(t)).
+```
+
+### Observation model
+
+The observation model is a negative binomial distribution with mean `μ` and cluster factor `r`. Delays are implemented
+as the action of a sparse kernel on the infections $I(t)$. The delay kernel is contained in an `EpiModel` struct.
+
+```math
+\begin{align}
+y_t &\sim \text{NegBinomial}(\mu = \sum_s\geq 0 K[t, t-s] I(s), r),
+r &\sim \text{Gamma}(3, 0.05/3).
+\end{align}
+```
+
+## Load dependencies in `TestEnv`
+
+=#
+
+split(pwd(), "/")[end] != "EpiAware" && begin
+    cd("./EpiAware")
+    using Pkg
+    Pkg.activate(".")
+
+    using TestEnv
+    TestEnv.activate()
+end
+
+using EpiAware
+using Turing
+using Distributions
+using StatsPlots
+using Random
+using DynamicPPL
+Random.seed!(0)
+
+#=
+## Create an `EpiModel` struct
+Somewhat randomly chosen parameters for the `EpiModel` struct.
+
+=#
+
+truth_GI = Gamma(1, 2)
+truth_delay = Uniform(0.0, 5.0)
+neg_bin_cluster_factor = 0.05
+time_horizon = 100
+
+epimodel = EpiModel(
+    truth_GI,
+    truth_delay,
+    neg_bin_cluster_factor,
+    time_horizon,
+    D_gen = 10.0,
+    D_delay = 10.0,
+)
+
+#=
+## Define a log-infections model
+The log-infections model is defined by a Turing model `log_infections`.
+
+In this case we don't have observed data, so we use `missing` value for `y_t`.
+=#
+toy_log_infs = log_infections(
+    missing,
+    epimodel,
+    random_walk;
+    latent_process_priors = EpiAware.STANDARD_RW_PRIORS,
+)
+
+#=
+## Sample from the model
+I define a fixed version of the model with initial infections set to 10 and variance of the random walk process set to 0.1.
+We can sample from the model using the `rand` function, and plot the generated infections against generated cases.
+=#
+cond_toy = fix(toy_log_infs, (init_rw_value = log(10.0), σ²_RW = 0.1))
+random_epidemic = rand(cond_toy)
+
+# We can get the generated infections using `generated_quantities` function. Because the observed
+# cases are "defined" with a `~` operator they can be accessed directly from the randomly sampled
+# process.
+gen = generated_quantities(cond_toy, random_epidemic)
+plot(
+    gen.I_t,
+    label = "I_t",
+    xlabel = "Time",
+    ylabel = "Infections",
+    title = "Generated Infections",
+)
+scatter!(X.y_t, lab = "generated cases")
diff --git a/EpiAware/test/test_latent-processes.jl b/EpiAware/test/test_latent-processes.jl
index e47941d5d..856a26243 100644
--- a/EpiAware/test/test_latent-processes.jl
+++ b/EpiAware/test/test_latent-processes.jl
@@ -3,7 +3,7 @@
     using DynamicPPL, Turing
     n = 5
     model = random_walk(n)
-    fixed_model = fix(model, (σ²_RW = 1.0,)) #Fixing the standard deviation of the random walk process
+    fixed_model = fix(model, (σ²_RW = 1.0, init_rw_value = 0.0)) #Fixing the standard deviation of the random walk process
     n_samples = 1000
     samples_day_5 =
         sample(fixed_model, Prior(), n_samples) |>
diff --git a/EpiAware/test/test_models.jl b/EpiAware/test/test_models.jl
new file mode 100644
index 000000000..ed4fc11bd
--- /dev/null
+++ b/EpiAware/test/test_models.jl
@@ -0,0 +1,40 @@
+
+@testitem "`log_infections` with RW latent process" begin
+    using Distributions, Turing, DynamicPPL
+    # Define test inputs
+    y_t = missing # Data will be generated from the model
+    epimodel = EpiModel([0.2, 0.3, 0.5], [0.1, 0.4, 0.5], 0.8, 10)
+    latent_process_priors = EpiAware.STANDARD_RW_PRIORS
+    transform_function = exp
+    n_generate_ahead = 0
+    pos_shift = 1e-6
+    neg_bin_cluster_factor = 0.5
+    neg_bin_cluster_factor_prior = Gamma(3, 0.05 / 3)
+
+    # Call the function
+    test_mdl = log_infections(
+        y_t,
+        epimodel,
+        random_walk;
+        latent_process_priors,
+        transform_function,
+        pos_shift,
+        neg_bin_cluster_factor,
+        neg_bin_cluster_factor_prior,
+    )
+
+    # Define expected outputs for a conditional model
+    # Underlying log-infections are const value 1 for all time steps and
+    # any other unfixed parameters
+
+    fixed_test_mdl = fix(
+        test_mdl,
+        (init_rw_value = log(1.0), σ²_RW = 0.0, neg_bin_cluster_factor = 0.05),
+    )
+    X = rand(fixed_test_mdl)
+    expected_I_t = [1.0 for _ = 1:epimodel.time_horizon]
+    gen = generated_quantities(fixed_test_mdl, rand(fixed_test_mdl))
+
+    # Perform tests
+    @test gen.I_t ≈ expected_I_t
+end