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posterior_plots.jl
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posterior_plots.jl
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using Distributions, StatsBase, StatsPlots
using LinearAlgebra, RecursiveArrayTools
using OrdinaryDiffEq, ApproxBayes, CSV, DataFrames
using JLD2, MCMCChains
using MonkeypoxUK
## Grab UK data and setup model
include("mpxv_datawrangling_inff.jl");
include("setup_model.jl");
## Comment out to use latest data rather than reterospective data
colname = "seqn_fit5"
inferred_prop_na_msm = past_mpxv_data_inferred[:, colname] |> x -> x[.~ismissing.(x)]
mpxv_wkly =
Matrix(past_mpxv_data_inferred[1:size(inferred_prop_na_msm, 1), ["gbmsm", "nongbmsm"]]) .+
Vector(past_mpxv_data_inferred[1:size(inferred_prop_na_msm, 1), "na_gbmsm"]) .*
hcat(inferred_prop_na_msm, 1.0 .- inferred_prop_na_msm)
wks = Date.(past_mpxv_data_inferred.week[1:size(mpxv_wkly, 1)], DateFormat("dd/mm/yyyy"))
##Load posterior draws and structure
smc = MonkeypoxUK.load_smc("posteriors/smc_posterior_draws_2022-09-12.jld2")
param_draws = load("posteriors/posterior_param_draws_2022-09-26.jld2")["param_draws"]
## Create size distribution plot for the meta population sizes
n_metapop = 50
α_metapop_draws = [θ[1] for θ in param_draws]
size_distribution = α_metapop_draws .|> α -> rand(DirichletMultinomial(N_msm, α * ones(n_cliques))) |> x -> sort(x, rev = true)
size_distribution_mat = [size_distribution[i][j] for i = 1:length(size_distribution), j = 1:length(size_distribution[1])]
mean_sizes = mean(size_distribution_mat, dims=1)[:] #mean(size_distribution_mat,dims = 1)[:]
lb = mean_sizes .- [quantile(size_distribution_mat[:,metapop],0.025) for metapop = 1:size(size_distribution_mat,2)]
ub = [quantile(size_distribution_mat[:, metapop], 0.975) for metapop = 1:size(size_distribution_mat, 2)] .- mean_sizes
plt_grp_size = bar(mean_sizes ./ N_msm,
yerrors=(lb, ub) ./ N_msm,
lab="Posterior mean group size",
title="Ordered metapopulation clique sizes",
xlabel="Clique size rank",
ylabel="Proportion of GBMSM in clique",
xticks=[1; 5:5:50],
size=(800, 600),dpi = 250,
left_margin=5mm,
guidefont=16,
tickfont=13,
titlefont=24,
legendfont=16,
right_margin=5mm)
savefig(plt_grp_size,"plots/clique_size.png")
##Create transformations to more interpetable parameters
param_names = [:metapop_size_dispersion, :prob_detect, :mean_inf_period, :prob_transmission,
:R0_other, :detect_dispersion, :init_infs, :chg_pnt, :sex_trans_red, :other_trans_red,:sex_trans_red_post_WHO, :other_trans_red_post_WHO]
transformations = [fill(x -> x, 2)
# x -> 1 + mean(Geometric(1 / (1 + x))) # Translate the infectious period parameter into mean infectious period
x -> x
fill(x -> x, 2)
x -> 1 / (x + 1) #Translate "effective sample size" for Beta-Binomial on sampling to overdispersion parameter
fill(x -> x, 4);
fill(x -> x, 2)]
function col_transformations(X, f_vect)
for j = 1:size(X, 2)
X[:, j] = f_vect[j].(X[:, j])
end
return X
end
param_mat = [p[j] for p in param_draws, j = 1:length(param_names)]
# val_mat = smc.parameters |> X -> col_transformations(X, transformations) |> X -> hcat(X[:,1:10],X[:,11].*X[:,4],X[:,12].*X[:,5]) |> X -> [X[i, j] for i = 1:size(X, 1), j = 1:size(X, 2), k = 1:1]
# val_mat = smc.parameters |> X -> col_transformations(X, transformations) |> X -> [X[i, j] for i = 1:size(X, 1), j = 1:size(X, 2), k = 1:1]
val_mat = param_mat|> X -> col_transformations(X, transformations) |> X -> [X[i, j] for i = 1:size(X, 1), j = 1:size(X, 2), k = 1:1]
chn = Chains(val_mat, param_names)
CSV.write("posteriors/posterior_chain_" * string(wks[end]) * ".csv", DataFrame(chn))
##Calculate orignal R₀ and latest R(t)
"""
function construct_next_gen_mat(params, constants, susceptible_prop, vac_rates; vac_eff::Union{Nothing,Number} = nothing)
Construct the next generation matrix `G` in orientation:
> `G_ij = E[# Infected people in group j due to one in group i]`
Returns `(Real(eigvals(G)[end]), G)`. NB: `Real(eigvals(G)[end])` is the leading eignvalue of `G` i.e. the reproductive number.
"""
function construct_next_gen_mat(params, constants, susceptible_prop, vac_rates; vac_eff::Union{Nothing,Number} = nothing)
#Get parameters
α_choose, p_detect, mean_inf_period, p_trans, R0_other, M, init_scale, chp_t, trans_red, trans_red_other, scale_trans_red2, scale_red_other2 = params
#Get constant data
N_total, N_msm, ps, ms, ingroup, ts, α_incubation, n_cliques, wkly_vaccinations, vac_effectiveness, chp_t2 = copy(constants)
if ~isnothing(vac_eff)
vac_effectiveness = vac_eff
end
#Calculate next gen matrix G_ij = E[#Infections in group j due to a single infected person in group i]
_A = (ms .* (susceptible_prop .+ (vac_rates .* (1.0 .- vac_effectiveness)))') .* (mean_inf_period .* p_trans ./ length(ms) ) #Sexual transmission within MSM
A = _A .+ (R0_other/N_uk) .* repeat(ps' .* N_msm,10) #Other routes of transmission MSM -> MSM
B = (R0_other*(N_uk - N_msm)/N_total) .* ones(10) # MSM transmission to non MSM
C = (R0_other/N_uk) .* ps' .* N_msm #Non-msm transmission to MSM
D = [ (R0_other*(N_uk - N_msm)/N_total) ]# Non-MSM transmission to non-MSM
G = [A B;C D]
return Real(eigvals(G)[end]), G
end
## Calculate the original R0 with next gen matrix method and lastest R(t)
R0s = map(θ -> construct_next_gen_mat(θ,constants, [ones(10); zeros(0)], [zeros(10);fill(1.0,0)])[1],param_draws )
@show round(mean(R0s),digits = 2),round.(quantile(R0s,[0.1,0.9]),digits = 2)
##
prior_tuple = smc.setup.prior.distribution
prior_val_mat = Matrix{Float64}(undef, 10_000, length(prior_tuple))
for j = 1:length(prior_tuple)
prior_val_mat[:, j] .= rand(prior_tuple[j], 10_000)
end
prior_val_mat = col_transformations(prior_val_mat, transformations)
# prior_val_mat[:,11] .= prior_val_mat[:,11].*prior_val_mat[:,4]
# prior_val_mat[:,12] .= prior_val_mat[:,12].*prior_val_mat[:,5]
##
pretty_parameter_names = ["Metapop. size dispersion",
"Prob. of detection",
"Mean dur. infectious",
"Prob. trans. per sexual contact",
"Non-sexual R0",
"Prob. of detect. dispersion",
"Init. Infs scale",
"Timing: 1st change point",
"Sex. trans. reduction: 1st cng pnt",
"Other trans. reduction: 1st cng pnt",
"Sex. trans. reduction: WHO cng pnt",
"Other. trans. reduction: WHO cng pnt"]
post_plt = plot(; layout=(6, 2),
size=(800, 2000), dpi=250,
left_margin=10mm,
right_margin=10mm)
for j = 1:length(prior_tuple)
histogram!(post_plt[j], val_mat[:, j],
norm=:pdf,
fillalpha=0.5,
nbins=100,
lw=0.5,
alpha=0.1,
lab="",
color=1,
title=string(pretty_parameter_names[j]))
histogram!(post_plt[j], prior_val_mat[:, j],
norm=:pdf,
fillalpha=0.5,
alpha=0.1,
color=2,
nbins=100,
lab="")
density!(post_plt[j], val_mat[:, j],
lw=3,
color=1,
lab="Posterior")
density!(post_plt[j], prior_val_mat[:, j],
lw=3,
color=2,
lab="Prior")
end
display(post_plt)
savefig(post_plt, "posteriors/post_plot" * string(wks[end]) * ".png")
##
crn_plt = corner(chn,
size=(2000, 2000),
left_margin=5mm, right_margin=5mm)
savefig(crn_plt, "posteriors/post_crnplot" * string(wks[end]) * ".pdf")
##