Sampling-path diagnostic report

14OI

Estimated trajectory

TipHow to read this trajectory

The dark line connects the marginal median location for each STAP. Pale lines are a deterministic subset of posterior trajectories and reveal route alternatives. Orange points are sampled long STAPs; green diamonds are fixed locations and are not assessed for MCMC convergence.

Run definition

setting value
Saved iterations per chain 400
Sampled STAPs 90
Excluded known STAPs 0
Likelihood map map_light
Movement kernel gamma
Movement shape 1.412246
Movement scale 8.909248
Component weights (light, movement, route) 1, 1, 1
Route detour multiplier 1
Long periods sampled from light only TRUE
Requested iterations 500
Chains 4
Warmup 100
Thinning 1
Block iteration interval 2
Likelihood support 0.99
Maximum radius (km/day) 2000
Progress update interval 10
Workers 1
Seed 1
Light-only long periods 3
Iterations requiring path repair 3
Daily sites repaired 3
Maximum sites repaired in one iteration 1
Movement approximation epsilon 1e-06

Computational support

These diagnostics are computed after sampling, but inspect the pre-sampling state space fixed before the chains ran: the map extent, retained likelihood support, and maximum daily movement radius. They do not test convergence and are not pass/fail criteria. In particular, daily STAPs with little twilight information commonly place their likelihood mode or mass on the map edge; this is expected evidence of weak light information, not automatically a reason to widen the map. Likewise, a long move near the configured radius can be biologically plausible. Use these counts to decide whether the chosen bounds visibly constrain an important part of the trajectory.

NoteReview computational support in context

These observations are prompts for inspection, not failed diagnostics.

  • Sampled locations: 0 of 144000 were outside retained likelihood support; 0 of 144000 were on the map boundary.
  • STAP likelihood maps: 5 STAP modes were on the map edge; 24 STAPs placed more than 1% of likelihood mass on that edge.
  • Moves: 201 of 64524 non-zero moves reached at least 90% of the configured maximum radius (2000 km/day).

Trace behaviour

Trace plots ask whether chains explore the same range repeatedly rather than remaining in different parts of the trajectory space.

TipWhat good traces look like

Colours represent independent chains. For bird trajectories, exact path repetition is not expected. Look for overlapping, stationary bands without persistent chain-specific levels or long directional trends.

Total trajectory length

Coordinates of the worst-mixing STAP (21)

R-hat: agreement among chains

TipWhat R-hat measures

For each coordinate and path summary, R-hat compares variation within independent chains with variation between them after splitting each chain in half and rank-normalising the draws. A value near 1 means the chains give compatible marginal distributions; values above 1.05 need attention. It assesses sampling agreement, not location accuracy or biological uncertainty.

WarningSome chain disagreement remains

6 sampled STAPs and 0 path-level summaries have R-hat above 1.05.

Effective sample size: sampling precision

TipWhat effective sample size measures

ESS estimates how many independent draws would provide the same Monte Carlo precision as the autocorrelated saved draws. It is computed from within-chain autocorrelation and agreement across chains. Bulk ESS concerns typical locations and central summaries; tail ESS concerns uncertainty limits. The plot shows the smaller latitude/longitude value for each STAP, with a target of roughly 100 effective draws per chain.

WarningMonte Carlo precision is limited

53 sampled STAPs fall below the bulk-ESS target and 36 fall below the tail-ESS target of 400.

Monte Carlo error in location

TipWhat Monte Carlo error means for a trajectory

The MCSE is the estimated standard error of the posterior mean location caused by using a finite, autocorrelated sample. It is computed separately for latitude and longitude from the saved chains, then converted approximately to kilometres and shown as the larger coordinate error. Compare it with the posterior location uncertainty: a small MCSE means the estimated posterior mean is numerically stable, not that the bird’s location is known precisely.

Spatial agreement among chains

TipWhat these spatial values represent

Geographic separation is the largest great-circle distance between the mean locations of any two chains at a STAP. A large value can reveal chains occupying different broad regions, but it also increases naturally when the posterior is diffuse or multimodal. Occupancy overlap is the mean shared probability mass of the chain-specific distributions over exact grid cells: 1 means identical occupancy and 0 means no shared cells. Fine grids and broad uncertainty can lower overlap even when chains agree geographically. Use both plots to investigate a high R-hat or visibly separated traces; neither has a universal threshold or replaces R-hat.

Geographic separation

Occupancy overlap

TipWhy add spatial diagnostics?

On a high-resolution discrete grid, chains can visit different exact cells while occupying the same geographic region. Centroid separation expresses disagreement in kilometres. Exact-cell overlap remains useful, but it should not be treated as a universal pass/fail threshold.

Did more iterations help?

TipHow to use the iteration trend

The diagnostic is recomputed after 25%, 50%, 75%, and 100% of saved iterations per chain. The full run should already have R-hat at or below 1.05. A sustained downward trend while R-hat remains high suggests that a longer run is worth testing. A flat, high trend instead suggests poor mixing that needs a change to initialization or the update strategy; simply adding iterations is unlikely to solve it.

WarningA longer run may help

The worst daily-STAP R-hat fell by at least 0.02 from the first checkpoint to the full run. Test a longer run, then confirm that R-hat reaches 1.05 or below.

Detailed results

Path-level MCMC diagnostics
metric rhat ess_bulk ess_tail mcse_mean
n_stays 1.01 190.61 482.91 0.28
n_unique_cells 1.01 208.64 670.95 0.25
path_length_km 1.01 439.90 973.84 33.35
STAPs ordered by the largest R-hat
stap_id stap_type maximum_rhat minimum_bulk_ess minimum_tail_ess maximum_mcse_km maximum_chain_centroid_separation_km mean_pairwise_overlap
21 daily 1.09 40.64 134.55 62.33 290.01 0.74
20 daily 1.08 39.26 121.54 55.79 268.59 0.76
22 daily 1.08 42.62 256.58 64.61 300.32 0.76
19 daily 1.06 66.63 82.00 37.02 176.66 0.76
23 daily 1.06 78.72 151.29 66.44 249.14 0.74
18 daily 1.05 131.61 142.47 29.73 115.96 0.78
24 daily 1.05 98.76 137.95 68.65 202.36 0.70
25 daily 1.04 102.09 138.03 74.90 245.85 0.67
17 daily 1.04 150.08 48.52 24.99 95.67 0.80
16 daily 1.04 133.78 66.11 20.49 108.90 0.81
15 daily 1.04 141.21 83.29 19.01 100.90 0.81
12 daily 1.04 135.50 103.16 19.35 98.56 0.81
14 daily 1.04 112.02 95.29 19.11 95.64 0.82
13 daily 1.04 108.80 95.29 19.48 95.67 0.82
64 daily 1.04 130.98 192.79 14.23 96.64 0.78
Show the complete per-STAP diagnostic table
stap_id stap_type lat_rhat lon_rhat lat_ess_bulk lon_ess_bulk lat_ess_tail lon_ess_tail lat_mcse_km lon_mcse_km maximum_chain_centroid_separation_km mean_pairwise_overlap n_distinct_chain_modes
21 daily 1.087 1.003 40.643 541.310 134.548 438.228 62.327 2.153 290.008 0.741 2
20 daily 1.085 1.009 39.264 428.917 121.540 393.353 55.794 2.321 268.593 0.756 2
22 daily 1.082 1.002 42.624 652.354 256.577 607.254 64.612 2.379 300.317 0.759 1
19 daily 1.059 1.042 66.632 92.484 81.998 NA 37.020 5.698 176.662 0.763 2
23 daily 1.056 1.001 78.715 1304.239 151.287 798.076 66.445 2.752 249.141 0.737 2
18 daily 1.051 1.037 131.610 134.245 142.475 NA 29.730 4.129 115.956 0.779 2
24 daily 1.048 1.000 98.763 1196.836 137.954 1209.955 68.653 2.660 202.362 0.701 3
25 daily 1.042 1.003 102.095 1294.999 138.034 1183.440 74.899 2.911 245.853 0.667 3
17 daily 1.041 1.027 150.080 201.677 48.517 NA 24.995 3.508 95.669 0.800 2
16 daily 1.040 1.020 133.777 364.419 66.113 317.563 20.491 2.370 108.898 0.812 3
15 daily 1.039 1.032 141.213 149.149 83.288 149.163 19.009 3.608 100.895 0.807 2
12 daily 1.039 1.033 150.647 135.495 103.157 119.470 19.349 3.978 98.563 0.809 2
14 daily 1.037 1.031 142.321 112.024 95.291 148.822 19.113 3.955 95.641 0.820 2
13 daily 1.037 1.031 144.521 108.798 95.291 148.301 19.480 4.107 95.669 0.817 2
64 daily 1.037 1.011 130.985 237.940 677.542 192.790 14.234 4.286 96.645 0.784 2
11 daily 1.036 1.024 165.537 187.572 136.329 175.164 16.731 3.212 91.084 0.812 2
26 daily 1.034 1.000 111.659 1288.503 135.016 1189.678 75.769 2.164 321.760 0.702 4
10 daily 1.033 1.022 210.169 209.588 212.441 192.693 14.140 3.116 79.325 0.801 3
41 daily 1.019 1.032 224.018 906.076 281.549 529.611 12.355 2.542 49.925 0.857 2
27 daily 1.031 1.002 126.899 1030.580 176.781 980.290 69.977 2.376 327.593 0.681 4
28 daily 1.028 1.001 157.746 664.201 229.837 1368.259 62.244 3.980 352.155 0.647 3
9 daily 1.027 1.016 242.197 307.529 236.776 250.294 13.781 2.868 72.804 0.798 3
63 daily 1.027 1.008 220.233 498.625 699.772 903.810 11.055 3.044 79.343 0.798 1
50 daily 1.026 1.007 224.282 315.333 428.016 260.386 10.593 1.995 82.105 0.856 1
65 daily 1.025 1.010 158.480 235.375 746.284 862.852 13.268 4.903 82.456 0.786 2
42 daily 1.013 1.021 245.782 777.357 353.926 511.631 11.242 1.692 45.920 0.868 2
51 daily 1.020 1.004 220.328 524.249 529.531 374.916 11.679 1.683 76.864 0.852 1
49 daily 1.018 1.008 316.711 432.096 530.661 303.478 8.875 1.677 66.576 0.868 1
43 daily 1.009 1.017 363.088 913.110 487.571 363.477 8.912 1.754 49.843 0.863 2
40 daily 1.016 1.010 238.316 763.349 414.517 445.820 12.382 2.854 58.599 0.845 3
29 daily 1.014 1.003 216.652 1280.030 402.473 1426.308 51.626 2.272 311.549 0.703 4
8 daily 1.014 1.006 413.277 737.052 319.282 606.680 14.382 3.990 78.423 0.779 3
88 daily 1.009 1.013 443.418 743.175 503.758 818.948 4.747 3.042 18.706 0.832 2
38 daily 1.013 1.004 303.454 1103.874 570.437 1319.795 16.098 2.473 109.666 0.819 1
48 daily 1.012 1.003 357.237 413.767 477.932 365.313 8.489 1.573 57.370 0.881 1
66 daily 1.011 1.002 696.016 958.286 657.457 625.209 4.841 1.867 17.869 0.865 1
62 daily 1.011 1.006 336.991 694.066 613.918 908.458 8.993 2.971 35.420 0.816 1
30 daily 1.011 0.999 267.442 1166.611 549.968 1146.409 38.263 2.488 243.269 0.726 3
39 daily 1.010 1.002 332.617 1376.296 695.582 1460.125 13.676 2.559 91.188 0.815 3
47 daily 1.010 1.002 352.880 522.096 478.709 423.692 8.552 1.360 53.869 0.884 1
52 daily 1.010 1.002 187.964 398.881 389.692 388.021 16.377 3.200 49.586 0.858 1
35 daily 1.009 1.003 338.297 800.721 427.084 1075.916 13.526 3.548 38.587 0.790 2
6 daily 1.009 1.002 291.349 776.947 531.929 813.866 10.309 2.005 38.572 0.827 2
37 daily 1.009 1.004 344.243 1334.101 523.743 1337.427 16.727 2.339 105.344 0.788 3
87 daily 1.009 1.007 455.706 734.533 514.145 699.170 4.190 2.549 15.835 0.840 2
69 daily 1.008 1.006 568.659 618.388 657.346 621.846 3.271 1.734 17.325 0.905 2
73 daily 1.008 1.003 519.581 480.739 658.995 439.264 3.678 2.532 5.792 0.907 1
67 daily 1.008 1.005 615.404 535.480 729.407 553.930 3.247 1.982 19.845 0.898 2
5 daily 1.008 1.006 287.268 737.618 367.105 729.948 10.659 2.046 34.976 0.825 1
68 daily 1.008 1.007 591.166 691.754 679.666 616.014 3.200 1.636 15.591 0.900 2
77 daily 1.005 1.008 520.253 586.369 701.452 569.271 4.212 2.876 23.964 0.872 2
46 daily 1.008 1.003 366.245 633.282 432.062 580.362 8.393 1.112 49.266 0.887 2
72 daily 1.007 1.004 507.577 346.056 644.842 354.291 3.466 2.696 7.362 0.903 2
34 daily 1.007 0.999 357.852 855.467 527.966 806.638 11.448 2.489 23.063 0.845 1
31 daily 1.007 1.003 485.449 1239.136 733.513 1296.486 22.438 2.214 149.093 0.785 1
70 daily 1.006 1.005 562.260 622.312 712.791 594.440 3.288 1.760 15.663 0.907 2
75 daily 1.006 1.003 854.907 922.346 905.733 1209.712 6.979 4.238 52.524 0.852 2
33 daily 1.006 1.002 524.545 1014.860 827.927 942.123 8.065 2.027 10.206 0.866 1
4 daily 1.006 1.004 313.771 742.182 422.892 626.624 10.816 2.313 38.528 0.813 2
45 daily 1.006 1.004 374.579 637.811 450.882 558.813 8.319 1.117 47.867 0.878 2
71 daily 1.006 1.005 565.287 484.532 674.920 487.220 3.273 2.150 13.931 0.904 2
86 daily 1.006 1.002 373.582 637.651 456.736 645.879 3.757 2.118 11.721 0.866 2
61 daily 1.005 1.005 393.403 546.357 569.713 698.753 8.432 3.473 25.310 0.830 3
76 daily 1.004 1.005 584.940 574.475 647.295 587.725 3.984 2.897 22.084 0.870 1
44 daily 1.005 1.003 378.960 696.753 472.456 530.041 8.315 1.167 44.263 0.885 2
81 daily 1.005 1.001 726.562 890.104 1326.965 1340.702 5.191 2.661 11.717 0.833 1
36 daily 1.005 1.001 324.318 1408.838 589.360 989.131 17.334 2.418 58.239 0.807 3
89 daily 1.005 1.005 591.833 1105.516 625.075 1115.265 4.266 2.701 15.664 0.847 1
56 daily 1.005 1.001 807.299 1348.214 1204.085 1323.176 8.985 2.102 43.974 0.820 2
78 daily 1.005 1.002 627.178 748.162 754.950 745.704 4.029 2.549 15.205 0.875 1
82 daily 1.004 1.005 736.402 803.987 755.093 949.932 2.938 2.127 12.013 0.899 1
7 daily 1.004 1.004 467.693 693.450 678.772 807.167 8.118 2.829 28.265 0.817 1
3 daily 1.004 1.002 430.107 685.881 786.932 624.319 11.008 3.461 47.123 0.776 2
54 daily 1.004 1.002 275.554 379.323 544.447 917.371 29.303 6.310 83.392 0.793 2
85 daily 1.004 1.001 499.296 711.124 394.895 678.351 3.086 1.958 9.742 0.866 2
55 daily 1.004 1.002 580.997 1058.688 793.842 1329.959 11.590 2.392 52.796 0.783 3
57 daily 1.004 1.000 673.467 1160.167 856.950 1109.778 9.033 2.312 45.380 0.853 2
32 long 1.004 1.000 1510.746 1422.689 1329.642 NA 2.434 0.327 9.466 0.931 1
80 daily 1.000 1.004 1101.593 1295.246 1184.731 1401.667 5.591 2.585 21.164 0.816 2
53 daily 1.004 1.002 230.665 276.215 358.681 839.176 25.078 7.489 59.280 0.800 2
79 daily 1.002 1.001 691.214 1151.349 991.003 1188.327 6.149 2.417 33.681 0.848 2
59 daily 1.001 1.002 584.530 1008.761 956.480 1303.465 8.948 2.552 28.457 0.835 3
2 daily 1.000 1.002 743.702 1076.276 1027.746 1376.675 10.621 5.967 22.975 0.704 2
60 daily 1.002 1.001 750.081 843.457 875.553 884.434 8.048 3.017 14.926 0.823 3
58 daily 1.000 1.001 642.455 1219.604 1055.448 1042.227 9.032 2.658 31.688 0.812 1
1 long 1.001 1.000 1609.503 1522.304 NA NA 1.638 0.970 6.401 0.926 1
74 daily 1.001 1.001 792.730 752.805 844.557 649.405 4.788 3.850 16.561 0.859 1
83 daily 1.000 1.000 471.440 790.211 357.383 722.348 3.222 1.872 8.789 0.877 2
84 daily 1.000 1.000 467.427 735.953 362.048 730.546 3.230 1.896 10.006 0.868 2
90 long 1.000 0.999 1621.936 1687.751 NA 1549.103 1.381 1.122 3.241 0.949 2

Overall assessment

NoteComputational support

Some observations reached a configured support boundary. Review them in the context of the available twilight information and route.

WarningAgreement among chains

6 sampled STAPs and 0 path-level summaries have R-hat above 1.05.

WarningMonte Carlo precision

53 sampled STAPs fall below the bulk-ESS target and 36 fall below the tail-ESS target of 400.

CautionRecommended next action

Review the affected STAP likelihood maps and moves alongside the trajectory. Change map or movement support only when those bounds appear to exclude scientifically plausible alternatives.

TipFinal interpretation

Convergence means that independent chains provide compatible Monte Carlo descriptions of the posterior trajectory under the chosen likelihood, movement model, grid, and computational support. It does not establish that those scientific choices are correct. Once sampling is adequate, comparing plausible movement and likelihood specifications is usually more valuable than pursuing unnecessarily precise Monte Carlo estimates.