Example for the ns.jl file, modify later

nestedsampexample.jl

julia> using NestedSamplers
julia> using Distributions

# eggbox likelihood function
tmax = 3π
julia> function logl(x)
       t = @. 2*tmax*x - tmax
       return 2 + cos(t[1]/2)*cos(t[2]/2)^5
       end
logl (generic function with 1 method)

# prior constrined to line in the range (0, 20)
julia> prior = [
           Uniform(0, 20),
           Uniform(0, 20)
       ]
2-element Array{Uniform{Float64},1}:
 Uniform{Float64}(a=0.0, b=20.0)
 Uniform{Float64}(a=0.0, b=20.0)

# creating the model
julia> model = NestedModel(logl, prior)
NestedModel{typeof(logl),Uniform{Float64}}(logl, Uniform{Float64}[Uniform{Float64}(a=0.0, b=20.0), Uniform{Float64}(a=0.0, b=20.0)])

julia> using StatsBase: sample, Weights
julia> using MCMCChains: Chains

# creating the sampler
# 2 parameters, 100 active points, multi-ellipsoid

julia> spl = Nested(2, 100; bounds = Bounds.MultiEllipsoid)
Nested(ndims=2, nactive=100, enlarge=1.25, update_interval=150)
  bounds=MultiEllipsoid{Float64}(ndims=2)
  proposal=NestedSamplers.Proposals.Uniform
  logz=-1.0e300
  log_vol=-4.610166019324897
  H=0.0

julia> spl = Nested(2, 100; bounds = Bounds.MultiEllipsoid)
Nested(ndims=2, nactive=100, enlarge=1.25, update_interval=150)
  bounds=MultiEllipsoid{Float64}(ndims=2)
  proposal=NestedSamplers.Proposals.Uniform
  logz=-1.0e300
  log_vol=-4.610166019324897
  H=0.0

julia> chain = sample(model, spl;
                      dlogz = 0.2,
                      param_names = ["x", "y"],
                      chain_type = Chains)
Object of type Chains, with data of type 358×3×1 Array{Float64,3}

Log evidence      = 2.086139406693275
Iterations        = 1:358
Thinning interval = 1
Chains            = 1
Samples per chain = 358
internals         = weights
parameters        = x, y

2-element Array{MCMCChains.ChainDataFrame,1}

Summary Statistics
  parameters     mean     std  naive_se    mcse       ess   r_hat
  ──────────  ───────  ──────  ────────  ──────  ────────  ──────
           x   9.9468  5.7734    0.3051  0.5474  315.7439  1.0017
           y  10.0991  5.5946    0.2957  0.2016  396.0076  0.9995

Quantiles
  parameters    2.5%   25.0%   50.0%    75.0%    97.5%
  ──────────  ──────  ──────  ──────  ───────  ───────
           x  0.4682  5.2563  9.5599  14.9525  19.3789
           y  0.5608  5.4179  9.8601  14.8477  19.2020