SaranjeetKaur
commented
4 years ago """ Nested sampling algorithm.
Example
#Note-to-self: set a seed here
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
"""
mileslucas
mvsoom
yebai
torfjelde
ParadaCarleton
NestedSamplers is an independent sampler library at the moment and lacks an interface for models specified by the domain-specific language (DSL) in Turing. However, since NestedSampler supports the
AbstractMCMCinterface, it should be a relatively lightweight task to add such an interface. A good starting point is the elliptical slice sampler (ESS) interface, which can be found at