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Last edited by Moritz Huebner
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15D_Gaussian

The 15-D analytical Gaussian is being implemented on this branch.

To do:

  • Add bimodal Gaussian

Unimodal distribution:

09:27 bilby INFO    : Analytic log evidence: -34.53877639491069
09:27 bilby INFO    : Sampled log evidence:  -34.28736207565682 +/- 0.19721688249742667
09:27 bilby INFO    : x0
09:27 bilby INFO    : Expected posterior standard deviation: 0.21445714241587377
09:27 bilby INFO    : Sampled posterior standard deviation:  0.217231388383747
09:27 bilby INFO    : x1
09:27 bilby INFO    : Expected posterior standard deviation: 0.23406495738756009
09:27 bilby INFO    : Sampled posterior standard deviation:  0.23561448955248837
09:27 bilby INFO    : x2
09:27 bilby INFO    : Expected posterior standard deviation: 0.21053433070089667
09:27 bilby INFO    : Sampled posterior standard deviation:  0.209899237086974
09:27 bilby INFO    : x3
09:27 bilby INFO    : Expected posterior standard deviation: 0.17280434626400767
09:27 bilby INFO    : Sampled posterior standard deviation:  0.17274250124134846
09:27 bilby INFO    : x4
09:27 bilby INFO    : Expected posterior standard deviation: 0.2320352145346266
09:27 bilby INFO    : Sampled posterior standard deviation:  0.23213131111342167
09:27 bilby INFO    : x5
09:27 bilby INFO    : Expected posterior standard deviation: 0.2091567812284964
09:27 bilby INFO    : Sampled posterior standard deviation:  0.20621315975499444
09:27 bilby INFO    : x6
09:27 bilby INFO    : Expected posterior standard deviation: 0.19143099949672157
09:27 bilby INFO    : Sampled posterior standard deviation:  0.19260546804828244
09:27 bilby INFO    : x7
09:27 bilby INFO    : Expected posterior standard deviation: 0.24027956023783628
09:27 bilby INFO    : Sampled posterior standard deviation:  0.23705379247129021
09:27 bilby INFO    : x8
09:27 bilby INFO    : Expected posterior standard deviation: 0.2147247079161986
09:27 bilby INFO    : Sampled posterior standard deviation:  0.21572375066501234
09:27 bilby INFO    : x9
09:27 bilby INFO    : Expected posterior standard deviation: 0.2430869196930184
09:27 bilby INFO    : Sampled posterior standard deviation:  0.2461813842165372
09:27 bilby INFO    : x10
09:27 bilby INFO    : Expected posterior standard deviation: 0.15626169000243328
09:27 bilby INFO    : Sampled posterior standard deviation:  0.15464607798704444
09:27 bilby INFO    : x11
09:27 bilby INFO    : Expected posterior standard deviation: 0.21822850109015837
09:27 bilby INFO    : Sampled posterior standard deviation:  0.21956694664810278
09:27 bilby INFO    : x12
09:27 bilby INFO    : Expected posterior standard deviation: 0.20649445141804712
09:27 bilby INFO    : Sampled posterior standard deviation:  0.20982444391260122
09:27 bilby INFO    : x13
09:27 bilby INFO    : Expected posterior standard deviation: 0.2290174707003685
09:27 bilby INFO    : Sampled posterior standard deviation:  0.22789820117469411
09:27 bilby INFO    : x14
09:27 bilby INFO    : Expected posterior standard deviation: 0.23196955226413352
09:27 bilby INFO    : Sampled posterior standard deviation:  0.23451333745242517
09:27 bilby INFO    : Analytic log evidence: -34.53877639491069
09:27 bilby INFO    : Sampled log evidence:  -34.13251361133434 +/- 0.1952942381908463

Bimodal distribution:

09:27 bilby INFO    : x0
09:27 bilby INFO    : Expected posterior standard deviation both modes: 0.21445714241587377
09:27 bilby INFO    : Sampled posterior standard deviation first mode:  0.21970334771506136
09:27 bilby INFO    : Sampled posterior standard deviation second mode:  0.21497526076962373
09:27 bilby INFO    : x1
09:27 bilby INFO    : Expected posterior standard deviation both modes: 0.23406495738756009
09:27 bilby INFO    : Sampled posterior standard deviation first mode:  0.2359553010597719
09:27 bilby INFO    : Sampled posterior standard deviation second mode:  0.23260647731460615
09:27 bilby INFO    : x2
09:27 bilby INFO    : Expected posterior standard deviation both modes: 0.21053433070089667
09:27 bilby INFO    : Sampled posterior standard deviation first mode:  0.21450461528002307
09:27 bilby INFO    : Sampled posterior standard deviation second mode:  0.20933004788552784
09:27 bilby INFO    : x3
09:27 bilby INFO    : Expected posterior standard deviation both modes: 0.17280434626400767
09:27 bilby INFO    : Sampled posterior standard deviation first mode:  0.17320985350478724
09:27 bilby INFO    : Sampled posterior standard deviation second mode:  0.17213427526298586
09:27 bilby INFO    : x4
09:27 bilby INFO    : Expected posterior standard deviation both modes: 0.2320352145346266
09:27 bilby INFO    : Sampled posterior standard deviation first mode:  0.2351962728603326
09:27 bilby INFO    : Sampled posterior standard deviation second mode:  0.22635522117055756
09:27 bilby INFO    : x5
09:27 bilby INFO    : Expected posterior standard deviation both modes: 0.2091567812284964
09:27 bilby INFO    : Sampled posterior standard deviation first mode:  0.2113918325612163
09:27 bilby INFO    : Sampled posterior standard deviation second mode:  0.207233765320099
09:27 bilby INFO    : x6
09:27 bilby INFO    : Expected posterior standard deviation both modes: 0.19143099949672157
09:27 bilby INFO    : Sampled posterior standard deviation first mode:  0.19584762993869573
09:27 bilby INFO    : Sampled posterior standard deviation second mode:  0.18755053736151464
09:27 bilby INFO    : x7
09:27 bilby INFO    : Expected posterior standard deviation both modes: 0.24027956023783628
09:27 bilby INFO    : Sampled posterior standard deviation first mode:  0.24426901012534488
09:27 bilby INFO    : Sampled posterior standard deviation second mode:  0.2393038814432799
09:27 bilby INFO    : x8
09:27 bilby INFO    : Expected posterior standard deviation both modes: 0.2147247079161986
09:27 bilby INFO    : Sampled posterior standard deviation first mode:  0.21892066011255445
09:27 bilby INFO    : Sampled posterior standard deviation second mode:  0.21395785796286826
09:27 bilby INFO    : x9
09:27 bilby INFO    : Expected posterior standard deviation both modes: 0.2430869196930184
09:27 bilby INFO    : Sampled posterior standard deviation first mode:  0.248508592621802
09:27 bilby INFO    : Sampled posterior standard deviation second mode:  0.2397239188618564
09:27 bilby INFO    : x10
09:27 bilby INFO    : Expected posterior standard deviation both modes: 0.15626169000243328
09:27 bilby INFO    : Sampled posterior standard deviation first mode:  0.15732222654745634
09:27 bilby INFO    : Sampled posterior standard deviation second mode:  0.1562944828170343
09:27 bilby INFO    : x11
09:27 bilby INFO    : Expected posterior standard deviation both modes: 0.21822850109015837
09:27 bilby INFO    : Sampled posterior standard deviation first mode:  0.22645320807218292
09:27 bilby INFO    : Sampled posterior standard deviation second mode:  0.2189360815005306
09:27 bilby INFO    : x12
09:27 bilby INFO    : Expected posterior standard deviation both modes: 0.20649445141804712
09:27 bilby INFO    : Sampled posterior standard deviation first mode:  0.2115837168583208
09:27 bilby INFO    : Sampled posterior standard deviation second mode:  0.20622644598149525
09:27 bilby INFO    : x13
09:27 bilby INFO    : Expected posterior standard deviation both modes: 0.2290174707003685
09:27 bilby INFO    : Sampled posterior standard deviation first mode:  0.2309004777267608
09:27 bilby INFO    : Sampled posterior standard deviation second mode:  0.22888508049824224
09:27 bilby INFO    : x14
09:27 bilby INFO    : Expected posterior standard deviation both modes: 0.23196955226413352
09:27 bilby INFO    : Sampled posterior standard deviation first mode:  0.23387124929542796
09:27 bilby INFO    : Sampled posterior standard deviation second mode:  0.22648891183830994

Edit by Moritz Huebner (September 24, 2019) It was pointed out that the combined log evidence for the bimodal distribution was not quoted here. I went back to the original data and calculated the log evidence using ResultList.combine(). The log evidence and log evidence error are now quoted below.

log evidence analytic: -34.53877639491069
log evidence combined runs: -34.251042697350414
log_evidence_err: 0.3914408337283419

Unimodal distribution

Corner plot

multidim_gaussian_unimodal_corner

Bimodal distribution

Corner plot - 128 runs combined

combined_corner_compressed