Report on a Gravity.jl execution

Version 1.6.5 (2025-12-02)

Best Results

• RMS = 0.45

• log-likelihood = -476.2

• log-posterior = -512.6

• χ²(x) = 47.63

• Best fit parameters:

  • aᵣ = 6.534

  • σᵣ = 300.7

  • s₁ = 18.06

  • ε₁ = 0.622

  • θ₁ = -38.9

  • σ₁ = 1145.0

  • σ₂ = 216.5

  • x₁[1] = 1.451

  • x₁[2] = -0.8353

  • x₂[1] = -47.92

  • x₂[2] = 27.88

  • Ωₘ = 0.2224

  • w₀ = -1.079

Best-fit model plot

Pair plot

MCMC diagnostics

Chain Properties

• Iterations: 5001:10:19991

• Number of chains: 100

• Samples per chain: 1500

Summary Statistics

Quantiles

MCMC Execution Report

• System Information:

  • Hostname: MacBook-Pro.local

  • CPU(s): 1 x Apple M4 Max

  • CPU target: apple-m4

  • Cores: 16 (16 CPU-threads)

  • Core kinds: 12 performance cores, 4 efficiency cores

  • NUMA domain(s): 1

• CPU Time: 10m 19.51s

• Wall Time: 1m 1.08s

• Compute Time: 1m 1.08s

Gravity Model

Source: examples/RXJ2248/RXJ2248.yml
Source timestamp: 2025-12-09T11:21:16.760
Config timestamp: 2025-12-09T12:44:09.280

Model Configuration

(fixed, free, linked, & implicit parameters)

Lenses

dm1. LensTool-NIE @z=0.348: x, s, ε, σ, θ
dm2. LensTool-NIS @z=0.348: x, σ, s
gas1. LensTool-JaffeEll @z=0.348: x, σ, s, ε, θ, a
gas2. LensTool-JaffeEll @z=0.348: x, σ, s, ε, θ, a
gas3. LensTool-JaffeEll @z=0.348: x, σ, s, ε, θ, a
1809-10394. 222 × LensTool-JaffeSph @z=0.348: x, σ, s, a

Sources

2. Point{3} @z=1.229: x
3. Point{2} @z=1.26: x
4. Point{3} @z=1.398: x
6. Point{3} @z=1.429: x
7. Point{3} @z=1.035: x
8. Point{3} @z=1.837: x
13. Point{2} @z=1.2582: x
14. Point{5} @z=6.112: x
18. Point{2} @z=4.113: x
20. Point{3} @z=3.118: x
23. Point{2} @z=0.7301: x
24. Point{3} @z=2.978: x
25. Point{2} @z=5.2373: x
26. Point{2} @z=5.051: x
27. Point{3} @z=3.286: x
28. Point{3} @z=3.169: x
29. Point{2} @z=5.894: x
30. Point{3} @z=3.4519: x
31. Point{3} @z=3.7131: x
33. Point{3} @z=3.6045: x

Cosmological model

Ωₘ: cosmology_Ωₘ ~ 0.0 .. 1.0
h₀: 0.7
w₀: cosmology_w₀ ~ -2.0 .. 0.0
Ωᵣ: 0.0

Sampling options

scheme: simplified-imageplane
algorithm: emcee
iterations: 20000
warmup: 5000
thinning: 10
random-seed: 1
threads: auto

Likelihood options

bayesianfactor: true
matches: all
duplicates: true
missedpredictionspenalty: true

Algorithm options

points: 100
stretch-scale: Exponential(5.0)

Preamble

pixelscale: 1
α: 0.27
β: 0.66
αₑ: log(10) * 0.4 * α
βₑ: log(10) * 0.4 * β
wcs_origin: (342.18321, -44.530878)
aᵣ: 5.7 .. 15
σᵣ: 310 ± 15
s₁: 10 .. 25
ε₁: 0.4 .. 0.9
θ₁: -50 .. -30
σ₁: 1000 .. 1300
σ₂: 180 .. 500
x₁: (-5, -5) .. (5, 5)
x₂: (-100, 0) .. (0, 50)
cosmology_Ωₘ: 0.0 .. 1.0
cosmology_w₀: -2.0 .. 0.0

Parameters

The model has 13 free parameters and 40 implicitly fit source parameters. The model includes 110 constraints from point-like images.

Benchmarks

A single call to logposterior takes 252.916 μs (738 allocs: 60.859 KiB) and returns Float64.

Input YAML file

# Model from Bergamini et al. (2023) [2023A&A...674A..79B]
parameters:
    pixelscale: 1
    α: 0.27
    β: 0.66
    αₑ: log(10) * 0.4 * α
    βₑ: log(10) * 0.4 * β
    wcs_origin: (342.18321, -44.530878)
    aᵣ: 5.7 .. 15
    σᵣ: 310 ± 15
    s₁: 10 .. 25
    ε₁: 0.4 .. 0.9
    θ₁: -50 .. -30
    σ₁: 1000 .. 1300
    σ₂: 180 .. 500
    x₁: (-5, -5) .. (5, 5)
    x₂: (-100, 0) .. (0, 50)
cosmology:
    Ωₘ: 0.0 .. 1.0
    h₀: 0.7
    w₀: -2.0 .. 0.0
    Ωᵣ: 0.0
sampling:
    scheme: simplified-imageplane
    likelihood-options:
        bayesianfactor: true
        matches: all
        duplicates: true
        missedpredictionspenalty: true
    algorithm: emcee
    iterations: 20000
    warmup: 5000
    thinning: 10
    algorithm-options:
        points: 100
        stretch-scale: Exponential(5.0)
    random-seed: 1
    threads: auto
lenses:
    - LensTool-NIE:
        name: dm1
        z: 0.348
        x: x₁
        s: s₁
        ε: ε₁
        σ: σ₁
        θ: θ₁
    - LensTool-NIS:
        name: dm2
        z: 0.348
        x: x₂
        σ: σ₂
        s: 0.05
    - LensTool-JaffeEll:
        name: gas1
        z: 0.348
        x: (18.898, -73.357)
        σ: 335.93
        s: 188.4
        ε: 0.805
        θ: -162.05
        a: 189.24
    - LensTool-JaffeEll:
        name: gas2
        z: 0.348
        x: (-18.05, 13.47)
        σ: 442.2
        s: 36.32
        ε: 0.13
        θ: -27.80
        a: 339.16
    - LensTool-JaffeEll:
        name: gas3
        z: 0.348
        x: (0.20, -1.24)
        σ: 249.7
        s: 14.43
        ε: 0.34
        θ: -15.49
        a: 356.50
    - loop:
        lens: members.csv
        LensTool-JaffeSph:
            name: lens.id
            z: 0.348
            x: wcsmap(lens.ra, lens.dec)
            σ: σᵣ * exp(αₑ * (16.176 - lens.mag))
            s: 0.01
            a: aᵣ * exp(βₑ * (16.176 - lens.mag))
sources:
    - loop:
        img: sources.csv
        group-by: id
        Point:
            name: img.id
            z: img.z
            x: (0.0, 0.0) ± 1000.0
            images's:
                Point:
                    name: img.img
                    x: wcsmap(img.ra, img.dec) ± img.err