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Table 2

Results from the benchmarking of the estimation algorithms.

l n Input Median Mode MAP

0 14 2074.60 2074.39 ± 0.39
0 15 2208.52 2208.11 ± 0.18
0 16 2341.62 2341.98 ± 0.42
0 17 2473.77 2473.56 ± 0.33
0 18 2606.07 2606.10 ± 0.08
0 19 2739.37 2738.57 ± 0.16
0 20 2872.82 2872.38 ± 0.13
0 21 3006.50 3005.58 ± 0.26
0 22 3140.17 3140.86 ± 1.18
0 23 3273.89 3274.67 ± 0.73
0 24 3408.19 3407.34 ± 0.28
0 25 3542.70 3540.86 ± 1.27
0 26 3677.54 3675.50 ± 1.88
1 13 2002.44 2001.96 ± 0.26
1 14 2137.33 2137.33 ± 0.43
1 15 2271.23 2271.37 ± 0.35
1 16 2403.73 2403.89 ± 0.39
1 17 2536.27 2536.61 ± 0.16
1 18 2669.12 2669.92 ± 0.21
1 19 2802.69 2803.04 ± 0.18
1 20 2936.64 2937.02 ± 0.18
1 21 3070.29 3074.67 ± 0.54
1 22 3204.20 3203.02 ± 0.51
1 23 3338.27 3339.05 ± 0.31
1 24 3472.67 3472.51 ± 1.13
1 25 3607.63 3605.10 ± 2.22
2 13 2063.21 2064.18 ± 0.43
2 14 2197.53 2197.01 ± 0.14
2 15 2331.10 2330.55 ± 0.34
2 16 2463.53 2463.76 ± 0.53
2 17 2596.15 2596.00 ± 0.08
2 18 2729.73 2727.57 ± 0.17
2 19 2863.47 2863.65 ± 0.15
2 20 2997.50 2997.59 ± 0.24
2 21 3131.46 3131.55 ± 0.39
2 22 3265.46 3264.55 ± 0.52
2 23 3400.03 3399.34 ± 0.46
2 24 3534.80 3531.10 ± 2.02
2 25 3669.86 3665.32 ± 2.00
3 12 1983.00 1983.74 ± 0.48
3 13 2118.42 2118.57 ± 0.38
3 14 2252.78 2254.28 ± 0.68
3 15 2385.91 2386.54 ± 0.82
3 16 2518.85 2519.77 ± 0.18
3 17 2652.01 2650.13 ± 0.22
3 18 2786.05 2787.33 ± 0.23
3 19 2920.37 2921.05 ± 0.47
3 20 3054.48 3057.32 ± 0.62
3 21 3188.85 3184.63 ± 1.26
3 22 3323.28 3322.36 ± 0.46
3 23 3458.15 3456.01 ± 1.20
3 24 3593.50 3587.87 ± 2.49

Notes. For the right and left tables, Cols. 1 and 2 give the orders and degrees of the simulated modes. Column 3 gives the input frequencies to the time series simulator (Jiménez-Reyes et al. 2008, only the frequencies we effectively searched for are displayed, more modes with lower amplitude were included in the simulated time series). Columns 4 and 5 display the frequencies obtained from our MCMC algorithm using the posterior median (Col. 4) and the mode (Col. 5) estimates alongside with the upper and lower limits of the corresponding credible interval. Column 6 shows the frequencies estimated with the MAP direct-optimization methodology, alongside uncertainties derived by inversing the Hessian matrix.

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