StressPy 0.0.9 โ synthetic worked example
Local geometric diagnostics ยท Residual = observed โ predicted
Summary
All scalar results and calculation status; settings and arrays follow in detail.
| category | quantity | value | interpretation |
|---|---|---|---|
| Analysis | stresspy_version | 0.0.9 | |
| Analysis | python_version | 3.12.14 | |
| Analysis | numpy_version | 2.3.5 | |
| Analysis | n_observations | 5 | |
| Analysis | n_parameters | 2 | |
| Analysis | metric | sigma | |
| Analysis | jacobian_method | central | |
| Analysis | rank_rtol | 1.1102230246251565e-15 | |
| Analysis | rank_atol | 0.0 | |
| Analysis | rank_threshold | 1.7554167342926843e-14 | |
| Fit | rmse_original | 0.6648308055437864 | Original observation units; not a noise-calibrated statistic |
| Geometry | total_stress | 55.25 | |
| Geometry | tangent_stress | 43.35000000022918 | |
| Geometry | normal_stress | 11.899999999770822 | |
| Geometry | normal_fraction | 0.21538461538046735 | |
| Geometry | normal_fraction_pct | 21.538461538046736 | |
| Geometry | rank | 2 | |
| Geometry | condition_number | 1.4142135623717986 | Retained singular spectrum |
| Geometry | repair_norm | 0.5283937925425799 | Supplied parameter coordinates |
| Geometry | full_column_condition_number | 1.4142135623717986 | Infinite if full column rank is not retained |
| Settings | sigma_floor | Not applied | Requested absolute uncertainty floor; None means not applied |
| Settings | sigma_floor_quantile | Not applied | Requested quantile floor; None means not applied |
| Settings | applied_sigma_floor | Not applied | Effective floor value; None means not applied |
| Optional analyses | nonlinear_repair | Included | |
| Optional analyses | calibration | Included | |
| Optional analyses | rank_sensitivity | Included | |
| Optional analyses | weighting_sensitivity | Included | |
| Optional analyses | parameter_diagnostics | Included | |
| Optional analyses | joint_compatibility | Not calculated | |
| Optional analyses | bounded_repair | Not calculated | |
| Optional analyses | deletion_influence | Not calculated | |
| Nonlinear repair | baseline_total_stress | 55.25 | |
| Nonlinear repair | best_alpha | 1.0 | |
| Nonlinear repair | best_stress | 11.899999999999999 | |
| Nonlinear repair | actual_reduction | 43.35 | |
| Nonlinear repair | scaled_repair_norm | 0.5283937925425799 | |
| Calibration | method | fixed_geometry_monte_carlo | |
| Calibration | noise_model | independent zero-mean Gaussian | |
| Calibration | observed_stress | 11.899999999770822 | |
| Calibration | reference_mean | 2.9671898839174653 | |
| Calibration | n_resamples | 999 | |
| Calibration | exceedances | 5 | |
| Calibration | p_value | 0.006 | |
| Calibration | confidence_level | 0.95 | |
| Calibration | tail_probability_interval | [0.0021396770441084265, 0.01166256327907405] |
Observations
Original observation coordinates; components add to residual. Stress attribution appears here only for known diagonal metrics.
| index | label | observed | predicted | residual | tangent_component | normal_component | group | tangent_stress_contribution | normal_stress_contribution | normal_share | leverage |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | x=-2 | 0.2 | 0.0 | 0.2 | -0.05999999999622331 | 0.2599999999962233 | left | 0.08999999998866992 | 1.6899999999509028 | 0.14201680672129832 | 0.6000000000022 |
| 1 | x=-1 | 0.7 | 0.5 | 0.19999999999999996 | 0.2000000000017786 | -1.778621694370486e-12 | left | 1.0000000000177858 | 7.908737829213344e-23 | 6.645998175937526e-24 | 0.2999999999990832 |
| 2 | x=0 | 1.1 | 1.0 | 0.10000000000000009 | 0.45999999999739655 | -0.35999999999739646 | centre | 5.28999999994012 | 3.239999999953136 | 0.2722689075643306 | 0.19999999999706652 |
| 3 | x=1 | 1.9 | 1.5 | 0.3999999999999999 | 0.719999999999615 | -0.31999999999961504 | right | 12.959999999986136 | 2.55999999999384 | 0.21512605042379346 | 0.2999999999979831 |
| 4 | x=2 | 3.4 | 2.0 | 1.4 | 0.9800000000060504 | 0.41999999999394966 | right | 24.01000000029647 | 4.409999999872943 | 0.3705882352905776 | 0.6000000000036669 |
Whitened Coordinates
Whitened-coordinate contributions sum to tangent/normal stress; dense whitening mixes original observations.
| coordinate | weighted_residual | weighted_tangent_component | weighted_normal_component | tangent_stress_contribution | normal_stress_contribution | leverage |
|---|---|---|---|---|---|---|
| 0 | 1.0 | -0.29999999998111654 | 1.2999999999811165 | 0.08999999998866992 | 1.6899999999509028 | 0.6000000000022 |
| 1 | 0.9999999999999998 | 1.0000000000088929 | -8.893108471852429e-12 | 1.0000000000177858 | 7.908737829213344e-23 | 0.2999999999990832 |
| 2 | 0.5000000000000004 | 2.2999999999869827 | -1.7999999999869822 | 5.28999999994012 | 3.239999999953136 | 0.19999999999706652 |
| 3 | 1.9999999999999996 | 3.5999999999980745 | -1.599999999998075 | 12.959999999986136 | 2.55999999999384 | 0.2999999999979831 |
| 4 | 7.0 | 4.900000000030252 | 2.0999999999697483 | 24.01000000029647 | 4.409999999872943 | 0.6000000000036669 |
Parameters
Values may be unavailable for residual-only analyses. Participation is in the retained/discarded numerical parameter subspaces; it is not a probability or uncertainty.
| index | label | value | local_repair | retained_participation | discarded_participation | jacobian_step | tested_repair | best_parameters |
|---|---|---|---|---|---|---|---|---|
| 0 | intercept | 1.0 | 0.4599999999992127 | 1.0 | 0.0 | 6.055454452393343e-06 | 0.4599999999992127 | 1.4599999999992126 |
| 1 | slope | 0.5 | 0.25999999999664464 | 1.0 | 0.0 | 6.055454452393343e-06 | 0.25999999999664464 | 0.7599999999966447 |
Singular Values
| index | singular_value | retained | rank_threshold |
|---|---|---|---|
| 0 | 15.811388300880932 | True | 1.7554167342926843e-14 |
| 1 | 11.1803398875368 | True | 1.7554167342926843e-14 |
Tangent Basis
Retained left singular vectors in whitened observation coordinates.
| whitened_coordinate | direction_0 | direction_1 |
|---|---|---|
| 0 | -0.6324555320272983 | 0.44721359551143686 |
| 1 | -0.31622776600959057 | 0.44721359550405765 |
| 2 | 5.218020152720572e-12 | 0.4472135954966782 |
| 3 | 0.3162277660229255 | 0.44721359549339845 |
| 4 | 0.6324555320406332 | 0.44721359549421846 |
Parameter Basis
Retained right singular vectors in supplied parameter coordinates.
| parameter_index | direction_0 | direction_1 |
|---|---|---|
| 0 | 1.6500868289262163e-11 | 1.0 |
| 1 | 1.0 | -1.6500868289262163e-11 |
Jacobian
Prediction Jacobian in supplied coordinates.
| observation_index | parameter_0 | parameter_1 |
|---|---|---|
| 0 | 0.9999999999960519 | -2.000000000001271 |
| 1 | 0.9999999999960519 | -0.9999999999960519 |
| 2 | 0.9999999999960519 | 0.0 |
| 3 | 1.000000000005219 | 1.000000000005219 |
| 4 | 1.0000000000235534 | 2.000000000010438 |
Settings
Copied inputs and effective metric/rank settings. Null settings were not applied.
| setting | index | value |
|---|---|---|
| metric | Not calculated | sigma |
| sigma | 0 | 0.2 |
| sigma | 1 | 0.2 |
| sigma | 2 | 0.2 |
| sigma | 3 | 0.2 |
| sigma | 4 | 0.2 |
| covariance | Not calculated | Not calculated |
| whitener | Not calculated | Not calculated |
| rank_rtol | Not calculated | 1.1102230246251565e-15 |
| rank_atol | Not calculated | 0.0 |
| weights | Not calculated | Not calculated |
| sigma_input | 0 | 0.2 |
| sigma_input | 1 | 0.2 |
| sigma_input | 2 | 0.2 |
| sigma_input | 3 | 0.2 |
| sigma_input | 4 | 0.2 |
| sigma_floor | Not calculated | Not calculated |
| sigma_floor_quantile | Not calculated | Not calculated |
| applied_sigma_floor | Not calculated | Not calculated |
Groups
Additive contributions under the analysis metric; these do not identify a causal defective mechanism.
| group | count | tangent_stress | normal_stress |
|---|---|---|---|
| left | 2 | 1.0900000000064556 | 1.6899999999509028 |
| centre | 1 | 5.28999999994012 | 3.239999999953136 |
| right | 2 | 36.9700000002826 | 6.969999999866783 |
Repair Steps
All attempted nonlinear steps, including rejected bounds and model errors.
| alpha | parameters | status | total_stress | fixed_tangent_stress | fixed_normal_stress | predicted_reduction | actual_reduction | efficiency_ratio |
|---|---|---|---|---|---|---|---|---|
| 1.0 | [1.4599999999992126, 0.7599999999966447] | linear_agreement | 11.899999999999999 | 4.0165672698976646e-21 | 11.899999999999999 | 43.35000000022918 | 43.35 | 0.9999999999947133 |
| 0.5 | [1.2299999999996063, 0.6299999999983223] | linear_agreement | 22.737500000131668 | 10.837500000246264 | 11.8999999998854 | 32.51250000017188 | 32.51249999986833 | 0.9999999999906636 |
| 0.1 | [1.0459999999999212, 0.5259999999996645] | linear_agreement | 47.013500000047394 | 35.11350000025366 | 11.899999999793733 | 8.236500000043545 | 8.236499999952606 | 0.999999999988959 |
Calibration Quantiles
| quantile | reference_stress |
|---|---|
| 0.025 | 0.1910405409369134 |
| 0.5 | 2.3469913662423414 |
| 0.95 | 7.731293950276721 |
| 0.975 | 8.957501952888789 |
Calibration Reference
| replicate | normal_stress | rank |
|---|---|---|
| 0 | 5.590104082604839 | 2 |
| 1 | 1.3688715603531187 | 2 |
| 2 | 0.6476136454160536 | 2 |
| 3 | 2.037858171424092 | 2 |
| 4 | 2.189409811297154 | 2 |
| 5 | 0.30170713699656454 | 2 |
| 6 | 4.649414868576239 | 2 |
| 7 | 2.8184789078002903 | 2 |
| 8 | 0.9251293800926449 | 2 |
| 9 | 0.4493327572340022 | 2 |
| 10 | 1.9667205042242037 | 2 |
| 11 | 3.6242056438294195 | 2 |
| 12 | 0.4984033284408267 | 2 |
| 13 | 1.595116818035664 | 2 |
| 14 | 0.5834745599706389 | 2 |
| 15 | 0.9729277535903496 | 2 |
| 16 | 0.5183900467151318 | 2 |
| 17 | 0.6292811155559414 | 2 |
| 18 | 0.7614625667012463 | 2 |
| 19 | 1.3793616897272696 | 2 |
| 20 | 3.066541638513716 | 2 |
| 21 | 3.458020278299145 | 2 |
| 22 | 1.7786307775149999 | 2 |
| 23 | 2.3414446130654607 | 2 |
| 24 | 0.7816731646717495 | 2 |
| 25 | 2.5939392715942766 | 2 |
| 26 | 2.9663579706613348 | 2 |
| 27 | 0.11076444980998958 | 2 |
| 28 | 4.170068723635331 | 2 |
| 29 | 0.9305140167232139 | 2 |
| 30 | 1.7597381279194155 | 2 |
| 31 | 1.2042545737464108 | 2 |
| 32 | 6.091331930857692 | 2 |
| 33 | 1.807677192337213 | 2 |
| 34 | 1.1122270621671289 | 2 |
| 35 | 1.563895539745626 | 2 |
| 36 | 1.8510946051042803 | 2 |
| 37 | 8.193515132300185 | 2 |
| 38 | 4.435781600757979 | 2 |
| 39 | 1.1978748582380099 | 2 |
| 40 | 3.6160595686672368 | 2 |
| 41 | 0.8364992553669641 | 2 |
| 42 | 2.386313930126573 | 2 |
| 43 | 1.0966920253629597 | 2 |
| 44 | 1.1478547333066453 | 2 |
| 45 | 6.3604608025316045 | 2 |
| 46 | 3.1912317792770124 | 2 |
| 47 | 2.1448702046338317 | 2 |
| 48 | 7.546652101955017 | 2 |
| 49 | 13.972906583536913 | 2 |
| 50 | 4.113381496449681 | 2 |
| 51 | 0.3778241998699702 | 2 |
| 52 | 0.5591563494788664 | 2 |
| 53 | 0.22871366987212582 | 2 |
| 54 | 1.4314484383904922 | 2 |
| 55 | 3.164468232993633 | 2 |
| 56 | 5.280138439195151 | 2 |
| 57 | 0.3267420870868253 | 2 |
| 58 | 7.763036656583226 | 2 |
| 59 | 2.7917913745599625 | 2 |
| 60 | 5.542610861802084 | 2 |
| 61 | 1.0496651687946843 | 2 |
| 62 | 1.167238208748055 | 2 |
| 63 | 2.6266601751385434 | 2 |
| 64 | 1.2303851563267594 | 2 |
| 65 | 2.8614010548198214 | 2 |
| 66 | 2.0399902710565323 | 2 |
| 67 | 0.7261790391847288 | 2 |
| 68 | 1.8488149603859065 | 2 |
| 69 | 4.9881771575381535 | 2 |
| 70 | 1.5188598055566112 | 2 |
| 71 | 0.5890335038323661 | 2 |
| 72 | 2.1132337869808206 | 2 |
| 73 | 3.9816610662643277 | 2 |
| 74 | 0.8981814645663526 | 2 |
| 75 | 10.522242946917201 | 2 |
| 76 | 3.0034597027256367 | 2 |
| 77 | 2.7878246419858956 | 2 |
| 78 | 1.6418987541851655 | 2 |
| 79 | 0.8782842682770968 | 2 |
| 80 | 0.9188258606040307 | 2 |
| 81 | 3.258911985761849 | 2 |
| 82 | 2.4976225703145216 | 2 |
| 83 | 1.6515844364244336 | 2 |
| 84 | 0.6155403115984889 | 2 |
| 85 | 5.475858182480517 | 2 |
| 86 | 4.761128867099062 | 2 |
| 87 | 0.8422745547003382 | 2 |
| 88 | 1.6519427019647477 | 2 |
| 89 | 3.2850265229465916 | 2 |
| 90 | 4.086719683862636 | 2 |
| 91 | 1.78888259434965 | 2 |
| 92 | 1.5660516141872503 | 2 |
| 93 | 5.829265530694476 | 2 |
| 94 | 0.6138373415688444 | 2 |
| 95 | 6.022820628464029 | 2 |
| 96 | 1.221127571575466 | 2 |
| 97 | 1.6343747316415658 | 2 |
| 98 | 0.6225609164326681 | 2 |
| 99 | 3.5691461771580992 | 2 |
| 100 | 0.29093340555608044 | 2 |
| 101 | 5.7963417485102395 | 2 |
| 102 | 0.5299723410160286 | 2 |
| 103 | 2.089842458463308 | 2 |
| 104 | 2.4614723126760922 | 2 |
| 105 | 2.2908209310665546 | 2 |
| 106 | 2.129571023025799 | 2 |
| 107 | 5.4046218416189475 | 2 |
| 108 | 0.994796643311599 | 2 |
| 109 | 1.5287485771485152 | 2 |
| 110 | 2.6363319404173824 | 2 |
| 111 | 0.2205898251892129 | 2 |
| 112 | 1.4044683282701176 | 2 |
| 113 | 1.2310585301512926 | 2 |
| 114 | 1.6470246256666838 | 2 |
| 115 | 4.928131621660872 | 2 |
| 116 | 1.3225583346067527 | 2 |
| 117 | 8.015548744912085 | 2 |
| 118 | 7.966152296500817 | 2 |
| 119 | 3.3887500755225575 | 2 |
| 120 | 2.4678428105363515 | 2 |
| 121 | 3.530721615995853 | 2 |
| 122 | 2.6231331537765827 | 2 |
| 123 | 2.9301246399729743 | 2 |
| 124 | 0.7195554133527295 | 2 |
| 125 | 5.446800285810189 | 2 |
| 126 | 5.714322788993313 | 2 |
| 127 | 1.3498290679363427 | 2 |
| 128 | 6.521147156827649 | 2 |
| 129 | 3.0434369992952344 | 2 |
| 130 | 5.002835601487785 | 2 |
| 131 | 2.347191015451291 | 2 |
| 132 | 1.1192920352476048 | 2 |
| 133 | 5.53887447885398 | 2 |
| 134 | 3.4074101396322347 | 2 |
| 135 | 2.961714047003381 | 2 |
| 136 | 1.1498778775590601 | 2 |
| 137 | 3.1891510260539864 | 2 |
| 138 | 4.133891274884021 | 2 |
| 139 | 1.7713916646698236 | 2 |
| 140 | 3.3274163319124668 | 2 |
| 141 | 0.8500488202738958 | 2 |
| 142 | 1.4207687552727137 | 2 |
| 143 | 2.9015980702586064 | 2 |
| 144 | 5.053432777421884 | 2 |
| 145 | 1.0092241294903457 | 2 |
| 146 | 0.3210335230497613 | 2 |
| 147 | 2.8567791264175613 | 2 |
| 148 | 4.499426931670469 | 2 |
| 149 | 1.132198828750028 | 2 |
| 150 | 3.7474053584872054 | 2 |
| 151 | 2.54503324102248 | 2 |
| 152 | 0.10894730684996036 | 2 |
| 153 | 4.176907425065468 | 2 |
| 154 | 1.1118163357144188 | 2 |
| 155 | 2.1473933877102835 | 2 |
| 156 | 2.5957838304830934 | 2 |
| 157 | 0.6669494873569877 | 2 |
| 158 | 4.047771472375681 | 2 |
| 159 | 1.373408419374106 | 2 |
| 160 | 0.5262806182497866 | 2 |
| 161 | 2.5147028126821716 | 2 |
| 162 | 0.4761239961727925 | 2 |
| 163 | 1.0937897004333654 | 2 |
| 164 | 4.105943944512528 | 2 |
| 165 | 6.392786697788604 | 2 |
| 166 | 2.7626426035113423 | 2 |
| 167 | 4.7730429898739395 | 2 |
| 168 | 2.5941940148942213 | 2 |
| 169 | 7.346630717853092 | 2 |
| 170 | 0.9234192105984648 | 2 |
| 171 | 4.34748748876525 | 2 |
| 172 | 1.1812063856848596 | 2 |
| 173 | 2.4220915097243405 | 2 |
| 174 | 3.4593803997560832 | 2 |
| 175 | 1.3956325893989587 | 2 |
| 176 | 1.5182609406498153 | 2 |
| 177 | 3.076480382090944 | 2 |
| 178 | 0.14296936182262612 | 2 |
| 179 | 2.7992683548057644 | 2 |
| 180 | 2.7212500671221376 | 2 |
| 181 | 3.4760529192455225 | 2 |
| 182 | 1.7246845594353593 | 2 |
| 183 | 3.939694806262524 | 2 |
| 184 | 0.5348804966676957 | 2 |
| 185 | 1.6754459342981383 | 2 |
| 186 | 1.4839776056830414 | 2 |
| 187 | 2.3469913662423414 | 2 |
| 188 | 0.6784006307218992 | 2 |
| 189 | 10.282486628087813 | 2 |
| 190 | 3.819707965236242 | 2 |
| 191 | 4.601641437753739 | 2 |
| 192 | 2.320183504661107 | 2 |
| 193 | 1.3571633898127713 | 2 |
| 194 | 1.4101607480697393 | 2 |
| 195 | 4.309786640168048 | 2 |
| 196 | 2.8407891162791405 | 2 |
| 197 | 2.377472796281296 | 2 |
| 198 | 1.7321170496078149 | 2 |
| 199 | 0.44960313448443145 | 2 |
| 200 | 0.8235706831968492 | 2 |
| 201 | 0.7910557392710659 | 2 |
| 202 | 5.156452427132284 | 2 |
| 203 | 0.5968231266478758 | 2 |
| 204 | 3.0582165654165423 | 2 |
| 205 | 3.0542482788786924 | 2 |
| 206 | 1.0810095219409486 | 2 |
| 207 | 1.5233427657734202 | 2 |
| 208 | 2.915242101240052 | 2 |
| 209 | 1.5764032772288354 | 2 |
| 210 | 8.891353909483282 | 2 |
| 211 | 0.7870105356341132 | 2 |
| 212 | 3.5188656641690703 | 2 |
| 213 | 2.742304465033466 | 2 |
| 214 | 1.0643980624584786 | 2 |
| 215 | 6.6451547900806895 | 2 |
| 216 | 0.18788663701623154 | 2 |
| 217 | 2.703402200557111 | 2 |
| 218 | 1.435579719817943 | 2 |
| 219 | 0.6152256355671413 | 2 |
| 220 | 0.7938819146015842 | 2 |
| 221 | 4.406127387291576 | 2 |
| 222 | 2.9304512697051393 | 2 |
| 223 | 1.6632529695347622 | 2 |
| 224 | 0.5245244057310338 | 2 |
| 225 | 4.288218334843543 | 2 |
| 226 | 2.2340027628250154 | 2 |
| 227 | 0.5942146419308291 | 2 |
| 228 | 10.409270236573569 | 2 |
| 229 | 1.1973857429148347 | 2 |
| 230 | 1.3284333952173848 | 2 |
| 231 | 6.120725665572445 | 2 |
| 232 | 1.1001224580632092 | 2 |
| 233 | 8.600535172600372 | 2 |
| 234 | 1.4303888105113876 | 2 |
| 235 | 0.3966253693903597 | 2 |
| 236 | 2.8572659552704325 | 2 |
| 237 | 1.2212555361226511 | 2 |
| 238 | 2.766328826774807 | 2 |
| 239 | 8.4187652906434 | 2 |
| 240 | 1.38011773212525 | 2 |
| 241 | 4.572472059721714 | 2 |
| 242 | 1.2808143329143107 | 2 |
| 243 | 4.160991403046945 | 2 |
| 244 | 2.293634440592305 | 2 |
| 245 | 1.1217499800891324 | 2 |
| 246 | 1.0080295682511995 | 2 |
| 247 | 0.1766652358232397 | 2 |
| 248 | 5.618102760919088 | 2 |
| 249 | 1.979616139968962 | 2 |
| 250 | 2.0531690004815264 | 2 |
| 251 | 3.7244899940360177 | 2 |
| 252 | 0.7559659709478943 | 2 |
| 253 | 0.9001038903087674 | 2 |
| 254 | 1.1035815468943446 | 2 |
| 255 | 2.8586721218254776 | 2 |
| 256 | 9.869432218530093 | 2 |
| 257 | 3.9136626976872226 | 2 |
| 258 | 3.4620859530909223 | 2 |
| 259 | 2.410109615773074 | 2 |
| 260 | 4.692345322511977 | 2 |
| 261 | 10.120588572338125 | 2 |
| 262 | 2.022122789155186 | 2 |
| 263 | 5.926351732267698 | 2 |
| 264 | 1.858980767166864 | 2 |
| 265 | 4.020268459379481 | 2 |
| 266 | 1.7939326744120512 | 2 |
| 267 | 5.128869680888428 | 2 |
| 268 | 1.7088219715144288 | 2 |
| 269 | 3.553874472653572 | 2 |
| 270 | 3.8044265280503433 | 2 |
| 271 | 0.3975972821255437 | 2 |
| 272 | 4.771746851274117 | 2 |
| 273 | 2.8482659949020896 | 2 |
| 274 | 4.963563560832189 | 2 |
| 275 | 0.7093047745209723 | 2 |
| 276 | 8.858679428465809 | 2 |
| 277 | 2.8200428387664904 | 2 |
| 278 | 5.215525123670104 | 2 |
| 279 | 1.4458090164294968 | 2 |
| 280 | 0.7243647226590314 | 2 |
| 281 | 0.30922614655548897 | 2 |
| 282 | 8.738778229443389 | 2 |
| 283 | 5.331747772703281 | 2 |
| 284 | 1.1817927462948647 | 2 |
| 285 | 1.3563156705087263 | 2 |
| 286 | 2.0080037800680373 | 2 |
| 287 | 8.891947892476688 | 2 |
| 288 | 4.115223072701889 | 2 |
| 289 | 4.214077346881405 | 2 |
| 290 | 1.7024897302861834 | 2 |
| 291 | 4.700953890176089 | 2 |
| 292 | 3.07845186877927 | 2 |
| 293 | 0.52613113419971 | 2 |
| 294 | 4.532364918532654 | 2 |
| 295 | 8.807414798972943 | 2 |
| 296 | 0.22924319085240327 | 2 |
| 297 | 3.120456153948348 | 2 |
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| 777 | 0.578385096167973 | 2 |
| 778 | 2.9979360966627815 | 2 |
| 779 | 5.60860947641545 | 2 |
| 780 | 2.05483308343448 | 2 |
| 781 | 6.078975284301158 | 2 |
| 782 | 2.7293242315178983 | 2 |
| 783 | 0.38827762503736235 | 2 |
| 784 | 1.8136957568146168 | 2 |
| 785 | 2.2769537943233544 | 2 |
| 786 | 1.6410410248970335 | 2 |
| 787 | 1.3521399729100796 | 2 |
| 788 | 1.6086600989058708 | 2 |
| 789 | 5.287995989115207 | 2 |
| 790 | 5.925026695566475 | 2 |
| 791 | 3.9276111355212806 | 2 |
| 792 | 0.4260574639403669 | 2 |
| 793 | 0.13595261008324017 | 2 |
| 794 | 4.8158456302978845 | 2 |
| 795 | 0.5089560350079066 | 2 |
| 796 | 0.4692620985885129 | 2 |
| 797 | 3.5874558212764067 | 2 |
| 798 | 1.7236014329161187 | 2 |
| 799 | 2.088175218754551 | 2 |
| 800 | 1.4479151228211036 | 2 |
| 801 | 1.883545468320623 | 2 |
| 802 | 1.5015978345332113 | 2 |
| 803 | 2.2359795047000426 | 2 |
| 804 | 1.4341553192336822 | 2 |
| 805 | 0.8536547533926299 | 2 |
| 806 | 2.2113950938413742 | 2 |
| 807 | 3.6669699765997086 | 2 |
| 808 | 0.6388139044154988 | 2 |
| 809 | 0.18979850389801897 | 2 |
| 810 | 1.1672263822703886 | 2 |
| 811 | 0.41005513534280735 | 2 |
| 812 | 1.7044404655052243 | 2 |
| 813 | 2.160470446495701 | 2 |
| 814 | 3.541346318717052 | 2 |
| 815 | 2.6886262290413376 | 2 |
| 816 | 1.509844479645005 | 2 |
| 817 | 3.0044875470128485 | 2 |
| 818 | 5.099351196240804 | 2 |
| 819 | 3.431952809020303 | 2 |
| 820 | 4.074922797062937 | 2 |
| 821 | 9.40878163749595 | 2 |
| 822 | 1.227328534676546 | 2 |
| 823 | 3.1932133533450737 | 2 |
| 824 | 2.0509735389341985 | 2 |
| 825 | 1.1544101809578342 | 2 |
| 826 | 1.6165285596504149 | 2 |
| 827 | 3.389149111566049 | 2 |
| 828 | 9.853165425256938 | 2 |
| 829 | 9.880742955338695 | 2 |
| 830 | 2.760587775163068 | 2 |
| 831 | 1.406238804480673 | 2 |
| 832 | 2.4664796913558673 | 2 |
| 833 | 2.07074745660254 | 2 |
| 834 | 0.04698403153819881 | 2 |
| 835 | 3.2288284725855454 | 2 |
| 836 | 8.04976749907127 | 2 |
| 837 | 4.266728409578703 | 2 |
| 838 | 3.0580536125271434 | 2 |
| 839 | 4.669028918126355 | 2 |
| 840 | 3.7796465568276463 | 2 |
| 841 | 1.7409357970061463 | 2 |
| 842 | 0.29458366018218163 | 2 |
| 843 | 1.9146498900828701 | 2 |
| 844 | 8.953531171369113 | 2 |
| 845 | 3.5976999529826577 | 2 |
| 846 | 3.683507420141205 | 2 |
| 847 | 0.3582121497215908 | 2 |
| 848 | 1.2644613318348674 | 2 |
| 849 | 1.9138692812653209 | 2 |
| 850 | 2.2705996389707 | 2 |
| 851 | 7.168420515690166 | 2 |
| 852 | 2.024586352311738 | 2 |
| 853 | 1.7115884354281587 | 2 |
| 854 | 2.5695921235857755 | 2 |
| 855 | 1.0459806917247605 | 2 |
| 856 | 8.915939668608127 | 2 |
| 857 | 3.567684588114889 | 2 |
| 858 | 3.0917899290274926 | 2 |
| 859 | 3.3049015400009916 | 2 |
| 860 | 2.126745275136722 | 2 |
| 861 | 8.001242349863913 | 2 |
| 862 | 0.06781775332328156 | 2 |
| 863 | 7.727766982909335 | 2 |
| 864 | 1.9116568309704498 | 2 |
| 865 | 3.985434570955976 | 2 |
| 866 | 5.652505089361419 | 2 |
| 867 | 0.531433068021606 | 2 |
| 868 | 4.952843977717582 | 2 |
| 869 | 5.490110742591029 | 2 |
| 870 | 1.3636477646952834 | 2 |
| 871 | 3.4258189364634553 | 2 |
| 872 | 0.6847902788058499 | 2 |
| 873 | 0.9471085000600187 | 2 |
| 874 | 2.6650583733651145 | 2 |
| 875 | 1.9805740280278041 | 2 |
| 876 | 2.3897240094037517 | 2 |
| 877 | 5.12020323886083 | 2 |
| 878 | 2.0629529640533035 | 2 |
| 879 | 0.0431049300560536 | 2 |
| 880 | 2.6970882851405045 | 2 |
| 881 | 1.7447394450124147 | 2 |
| 882 | 1.50970957203079 | 2 |
| 883 | 1.9154775666925068 | 2 |
| 884 | 1.805578967123893 | 2 |
| 885 | 1.507082312202184 | 2 |
| 886 | 3.014273776591058 | 2 |
| 887 | 2.085408150912184 | 2 |
| 888 | 4.229095096543895 | 2 |
| 889 | 2.1943186363130587 | 2 |
| 890 | 1.4639326067236265 | 2 |
| 891 | 4.63974016908687 | 2 |
| 892 | 2.003779955279223 | 2 |
| 893 | 6.27476683247954 | 2 |
| 894 | 4.601262032546967 | 2 |
| 895 | 0.9233513752451527 | 2 |
| 896 | 0.13042414928275675 | 2 |
| 897 | 4.6271364792448635 | 2 |
| 898 | 4.579356979707283 | 2 |
| 899 | 2.8116245441902645 | 2 |
| 900 | 5.543078568516074 | 2 |
| 901 | 3.7992860585972563 | 2 |
| 902 | 2.276635321434937 | 2 |
| 903 | 0.457116259279607 | 2 |
| 904 | 0.7519845980718757 | 2 |
| 905 | 1.7196625756001975 | 2 |
| 906 | 4.622247847037217 | 2 |
| 907 | 2.65355179362432 | 2 |
| 908 | 5.2133777994399475 | 2 |
| 909 | 8.467569497816559 | 2 |
| 910 | 3.917865606861904 | 2 |
| 911 | 1.5612669216373782 | 2 |
| 912 | 1.3028387566983497 | 2 |
| 913 | 7.620422520117171 | 2 |
| 914 | 1.7460259992454383 | 2 |
| 915 | 6.094673123507409 | 2 |
| 916 | 1.993229129085144 | 2 |
| 917 | 4.180841814127165 | 2 |
| 918 | 1.4970754267824788 | 2 |
| 919 | 1.618148623497065 | 2 |
| 920 | 0.45977352757401385 | 2 |
| 921 | 3.8868798192056593 | 2 |
| 922 | 3.2955870042751116 | 2 |
| 923 | 18.042717803535684 | 2 |
| 924 | 0.21837831641039226 | 2 |
| 925 | 1.4757125279772783 | 2 |
| 926 | 0.6068945761811223 | 2 |
| 927 | 3.1530312522268686 | 2 |
| 928 | 2.2283801261416656 | 2 |
| 929 | 0.5722982067229668 | 2 |
| 930 | 2.219610375651955 | 2 |
| 931 | 0.628085631086837 | 2 |
| 932 | 3.5643811734021598 | 2 |
| 933 | 3.106059166237632 | 2 |
| 934 | 2.4180684245778714 | 2 |
| 935 | 0.7806430949149676 | 2 |
| 936 | 1.0501036814602538 | 2 |
| 937 | 0.951181746009044 | 2 |
| 938 | 0.6007087265906794 | 2 |
| 939 | 0.947548088072918 | 2 |
| 940 | 4.660083687535421 | 2 |
| 941 | 1.3921253288209456 | 2 |
| 942 | 2.2504869449013256 | 2 |
| 943 | 1.0699552004003199 | 2 |
| 944 | 1.3729539603509606 | 2 |
| 945 | 2.1839164217100895 | 2 |
| 946 | 9.584941299213453 | 2 |
| 947 | 1.7016125350248648 | 2 |
| 948 | 0.020667728949907156 | 2 |
| 949 | 1.1064153568797892 | 2 |
| 950 | 5.5135805037210135 | 2 |
| 951 | 2.044762865671598 | 2 |
| 952 | 4.693654429747006 | 2 |
| 953 | 6.602632194371077 | 2 |
| 954 | 5.945928866826845 | 2 |
| 955 | 2.472253931812453 | 2 |
| 956 | 2.418904593680291 | 2 |
| 957 | 2.6718240266772946 | 2 |
| 958 | 4.978887137574222 | 2 |
| 959 | 1.9326035193625937 | 2 |
| 960 | 1.2007721751192857 | 2 |
| 961 | 6.296372345954184 | 2 |
| 962 | 0.14672661887742117 | 2 |
| 963 | 10.905994724428375 | 2 |
| 964 | 3.054534653558444 | 2 |
| 965 | 5.088801151884991 | 2 |
| 966 | 0.7575895228403144 | 2 |
| 967 | 3.2879873527721553 | 2 |
| 968 | 2.1665867848975617 | 2 |
| 969 | 0.8332814231377949 | 2 |
| 970 | 7.21435613934723 | 2 |
| 971 | 3.4429444212625775 | 2 |
| 972 | 4.078270163959651 | 2 |
| 973 | 4.38680165701483 | 2 |
| 974 | 1.4432168431673809 | 2 |
| 975 | 2.545051964521767 | 2 |
| 976 | 0.7259213043995536 | 2 |
| 977 | 2.1956494285384047 | 2 |
| 978 | 1.8886346382191113 | 2 |
| 979 | 1.612246660422779 | 2 |
| 980 | 1.5858647499067136 | 2 |
| 981 | 1.7363651204150827 | 2 |
| 982 | 3.033712170587012 | 2 |
| 983 | 2.5850381902935444 | 2 |
| 984 | 1.8762105207289488 | 2 |
| 985 | 0.7504866685834322 | 2 |
| 986 | 4.137099301395242 | 2 |
| 987 | 3.6103770912853923 | 2 |
| 988 | 0.5538500602931423 | 2 |
| 989 | 1.1449890056060186 | 2 |
| 990 | 6.405797394825508 | 2 |
| 991 | 7.033213770042238 | 2 |
| 992 | 1.2702105927500396 | 2 |
| 993 | 1.2302727461739893 | 2 |
| 994 | 7.492295806630473 | 2 |
| 995 | 2.385311999134176 | 2 |
| 996 | 8.399861895321536 | 2 |
| 997 | 0.9304849137874841 | 2 |
| 998 | 1.0767091219319416 | 2 |
Rank Sensitivity
Explicit rank cutoff sweep; no p-values are inferred.
| rank_rtol | rank | normal_stress | normal_fraction | repair_norm |
|---|---|---|---|---|
| 1e-12 | 2 | 11.899999999770822 | 0.21538461538046735 | 0.5283937925425799 |
| 1e-08 | 2 | 11.899999999770822 | 0.21538461538046735 | 0.5283937925425799 |
| 0.0001 | 2 | 11.899999999770822 | 0.21538461538046735 | 0.5283937925425799 |
Weighting Sensitivity
Absolute stresses under different metrics are not directly comparable.
| scheme | rank | total_stress | tangent_stress | normal_stress | normal_fraction | repair_norm | analysis_settings |
|---|---|---|---|---|---|---|---|
| equal | 2 | 2.2099999999999995 | 1.7340000000091669 | 0.4759999999908328 | 0.21538461538046738 | 0.5283937925425799 | {"metric": "euclidean", "sigma": null, "covariance": null, "whitener": null, "rank_rtol": 1.1102230246251565e-15, "rank_atol": 0.0, "weights": null, "sigma_input": null, "sigma_floor": null, "sigma_floor_quantile": null, "applied_sigma_floor": null} |
| sigma_0.2 | 2 | 55.25 | 43.35000000022918 | 11.899999999770822 | 0.21538461538046735 | 0.5283937925425799 | {"metric": "sigma", "sigma": [0.2, 0.2, 0.2, 0.2, 0.2], "covariance": null, "whitener": null, "rank_rtol": 1.1102230246251565e-15, "rank_atol": 0.0, "weights": null, "sigma_input": [0.2, 0.2, 0.2, 0.2, 0.2], "sigma_floor": null, "sigma_floor_quantile": null, "applied_sigma_floor": null} |
Parameter Diagnostics
Separately supplied diagnostics; scale and truncation may differ from the main result. Retained variance factors are not full uncertainties.
| index | label | parameter_scale | identifiable_participation | null_participation | retained_variance_factor | has_null_component |
|---|---|---|---|---|---|---|
| 0 | intercept | 1.0 | 1.0 | 0.0 | 0.007999999999945832 | False |
| 1 | slope | 1.0 | 1.0 | 0.0 | 0.003999999999980249 | False |
Parameter Diagnostic Settings
| quantity | value |
|---|---|
| rank | 2 |
| singular_values | [15.811388300880932, 11.1803398875368] |
| retained_directions | [[1.6500868289262163e-11, 1.0], [1.0, -1.6500868289262163e-11]] |
| retained_condition_number | 1.4142135623717986 |
| full_column_condition_number | 1.4142135623717986 |
| condition_indices | [1.0, 1.4142135623717986] |
Metadata
User-supplied provenance; not independently inferred or verified.
| key | value |
|---|---|
| data | Synthetic demonstration, not experimental evidence |
| model | intercept + slope * x |
| x | [-2.0, -1.0, 0.0, 1.0, 2.0] |
| parameter_coordinates | raw; dimensionless example |
| units | dimensionless synthetic observations |
| fit_protocol | supplied baseline; not fitted to these observations |
| calibration_seed | 42 |
| calibration_resamples | 999 |
| calibration_noise | independent zero-mean Gaussian, sigma=0.2 |
| calibration_scope | conditional fixed-geometry reference, not refitting |
Interpretation and provenance
- Stress is the squared norm in the selected observation metric. RMSE uses original observation units; mixed units require care.
- Normal stress is local to the supplied parameter point, Jacobian, metric and retained rank. It can contain noise and does not prove global model failure.
- Repair magnitude and parameter participation depend on parameter coordinates. Retained variance factors are not full parameter uncertainties.
- Missing optional analyses are marked Not calculated. No fit, calibration or sensitivity calculation is run by make_report.
- CSV/JSON retain full numerical precision. NaN means undefined; Infinity is retained. JSON encodes both as strings.
- Model code, dataset identifiers, solver/fitting settings, units and RNG state are not inferred; record them with metadata for reproducibility.
- Repair trial tangent/normal stresses use the fixed baseline tangent space. An improving trial is not a global optimisation certificate.
- The tail interval describes Monte Carlo exceedance uncertainty, not structural error. The p-value is conditional on the specified null; plug-in bootstrap calibration is approximate.