Table 1 An overview on which priors were used and on how the data was created
From: Comprehensive benchmarking of Markov chain Monte Carlo methods for dynamical systems
θ | θ min | θ max | θ true | |
|---|---|---|---|---|
(M1a) | log10(t 0) | −2 | 1 | - |
log10(k TL m 0) | −5 | 5 | - | |
log10(β) | −5 | 5 | - | |
n t =150 | log10(δ) | −5 | 5 | - |
t∈ [ 2,27] | log10(σ) | −2 | 2 | - |
(M1b) | log10(t 0) | −2 | 1 | log10(2) |
log10(k TL m 0) | −5 | 5 | log10(5) | |
log10(β) | −5 | 5 | log10(0.8) | |
n t =51 | log10(δ) | −5 | 5 | log10(0.2) |
t∈ [ 0,10] | log10(σ) | −2 | 2 | −1 |
(M2) | k 1 | 2 | 20 | 8 |
k 2 | 0 | 5 | 1 | |
k 3 | 0 | 5 | 1 | |
k 4 | 0 | 5 | 1 | |
x 0,1 | −3 | 3 | 2 | |
x 0,2 | −3 | 3 | 0.25 | |
n t =101 | \(\sigma _{1}^{0}\) | 10−3 | 1 | 0.3 |
t∈ [ 0,200] | \(\sigma _{2}^{0}\) | 10−3 | 1 | 0.3 |
(M3) | b 1 | 0 | 5 | 1 |
n t =101 | b 2 | 0 | 5 | 0.2 |
t∈ [ 0,2.5] | σ 1 | 10−3 | 102 | 0.03 |
(M4) | κ | 1 | 5 | 3.8 |
k 2 | 0.8 | 1.2 | 1 | |
k 3 | 0.8 | 1.2 | 1 | |
k 4 | 0.8 | 1.2 | 1 | |
k 5 | 0.8 | 1.2 | 1 | |
x 0,1 | 0 | 2 | 1 | |
x 0,2 | 0 | 2 | 1 | |
x 0,3 | 0 | 2 | 1 | |
σ 1 | 10−2 | 2 | 0.75 | |
n t =101 | σ 2 | 10−2 | 2 | 0.32 |
t∈ [ 0,200] | σ 3 | 10−2 | 2 | 0.46 |
(M5) | a | 2 | 8 | 5 |
d | 2 | 8 | 5 | |
ω | 2 | 8 | 2.464 | |
x 0,1 | −1 | 3 | 0 | |
x 0,2 | −1 | 3 | 0 | |
x 0,3 | −1 | 3 | 1 | |
σ 1 | 10−2 | 2 | 0.2 | |
n t =101 | σ 2 | 10−2 | 2 | 0.8 |
t∈ [ 0,200] | σ 3 | 10−2 | 2 | 0.2 |
(M6) | α | 0 | 20 | 10 |
β | 0 | 10 | \(\frac {8}{3}\) | |
ρ | 10 | 30 | 28 | |
x 0,1 | 0 | 35 | 26.61 | |
x 0,2 | −10 | 10 | −2.74 | |
x 0,3 | −5 | 5 | 0.95 | |
σ 1 | 10−4 | 102 | 1 | |
n t =101 | σ 2 | 10−4 | 102 | 1 |
t∈ [ 0,200] | σ 3 | 10−4 | 102 | 1 |