Narrow Posterior Distributions and Low Acceptance Rates in pocoMC

[phelipedarc]

Hello everyone,

I am currently using pocoMC to estimate physical properties from observational data, specifically related to GRBs (Gamma-Ray Bursts). While the sampling is progressing, I am facing two major challenges:

1. Narrow posterior distributions for the parameters of interest.
2. An acceptance rate (acc) that drops below 0.2 during certain epochs, which might indicate that the target distribution is not being explored efficiently.

prior_best = pc.Prior([
    uniform(loc=50.0, scale=10.0),  # Uniform [50, 60]: loc=50, scale=60-50=10
    uniform(loc=-6.0, scale=8.0),  # Uniform [-6, 2]: loc=-6, scale=2-(-6)=8
    uniform(loc=-2.0, scale=1.5),  # Uniform [-2, -0.5]: loc=-2, scale=-0.5-(-2)=1.5
    uniform(loc=-6.0, scale=5.7),  # Uniform [-6, -0.3]: loc=-6, scale=-0.3-(-6)=5.7
    uniform(loc=-6.0, scale=5.7),  
    norm(loc=2.46, scale=0.20),   
    uniform(loc=-5.0, scale=5.0), 
])


sampler = pc.Sampler(
    prior=prior_best,
    likelihood=log_likelihood,
    vectorize=False,
    random_state=0, 
    n_effective=1024, 
    n_active=512,dynamic=True,sample='tpcn',pool=80,flow='nsf6',
)
from time import time
t_i = time()

sampler.run(n_total=4096,
            n_evidence=4096,
            progress=True,
           )

Are there recommended adjustments to address these issues? Any advice or insights would be greatly appreciated. Thank you for your time and help!

[minaskar]

Thanks for posting this. Could you provide some additional information? Does the efficiency (sampler.results["efficiency"] or simply eff in the progress bar) drop during the run?

A few things to try is to increase n_steps (by default it its equal to n_dim//2, so 7//2=3 in your case). Another is to try using another normalizing flow (e.g. flow='maf6').

Finally, would it be easy to reproduce this problem in a Google colab or something similar?

[phelipedarc]

Hi, thanks for addressing this issue so promptly! I'll implement the suggested changes and provide an update in a few days (it typically takes 24–48 hours to converge).

Unfortunately, I can't share the data (only the code) with you since it's not publicly available. However, I can share my training details, which might help us identify the problem.

Here is my training information:

{'u': array([[[ 0.1064493 ,  0.74896178, -0.4375979 , ..., -0.00368688,
           2.60067613, -1.31063546],
         [ 0.53980911, -1.37279647,  0.41213216, ..., -1.2991477 ,
          -0.35398613, -0.06045457],
         [ 0.24040125,  1.97074151, -0.13488945, ...,  0.49144723,
          -0.12180953, -0.36825216],
         ...,
         [-0.14436214,  0.07876778, -0.45255656, ...,  1.45599729,
           0.44513688, -0.26894539],
         [-1.23293202, -0.06082701,  1.49387614, ...,  0.77781374,
           0.25209125, -0.05930918],
         [-0.39120077, -2.16849361,  1.81131094, ...,  0.15728196,
          -0.93723665, -0.02269975]],
 
        [[ 0.61272817,  0.53818484, -1.26422234, ...,  0.76050689,
          -0.04427506,  0.30629399],
         [ 0.44314494,  1.08724855,  0.67880633, ...,  0.30672261,
          -0.19309107, -0.93741648],
         [ 0.29019796, -0.67051712,  0.45293491, ..., -2.52617608,
          -0.16834574, -1.33688809],
         ...,
         [ 0.28538259, -0.21893644, -0.55823814, ...,  0.11139586,
           1.60264358,  0.40229105],
         [ 0.33460829, -1.33710947, -1.57284997, ...,  0.24019657,
           0.88192042, -0.06060899],
         [ 1.57208335,  0.13992627, -0.46722153, ...,  0.12154096,
           0.94261701,  0.91953087]],
 
        [[ 0.7320025 , -0.1021707 , -1.66348941, ..., -2.79788726,
           0.35434264, -0.82987985],
         [ 0.9875588 , -0.65344134, -0.13748825, ...,  0.74374775,
          -0.57704191,  1.24986818],
         [-0.03609139,  1.25175329, -0.72160391, ...,  1.2855137 ,
          -1.0064122 ,  0.51709143],
         ...,
         [-1.4197647 , -0.96926798, -0.56121167, ...,  0.79279054,
          -0.44328344,  0.63474267],
         [-0.03475987, -1.65451865,  0.83838857, ..., -0.36622818,
           1.05860379,  0.17159645],
         [ 0.54660904, -0.86185488, -0.80848325, ...,  0.11347605,
          -0.92355884, -0.91921787]],
 
        ...,
 
        [[-0.45304069,  3.03793406, -2.81392956, ...,  1.4053365 ,
           2.25484395,  0.27372742],
         [-0.46699008,  2.79258704, -2.3308568 , ...,  1.47770798,
           2.18134451,  0.29077095],
         [-0.46318915,  3.21324134, -2.37628222, ...,  1.37465596,
           2.23236275,  0.27197495],
         ...,
         [-0.47406244,  2.61439991, -2.1214242 , ...,  1.45756888,
           2.27540708,  0.28573409],
         [-0.46274561,  2.92753267, -2.4007659 , ...,  1.33416295,
           2.32941961,  0.26467353],
         [-0.46094638,  3.0458014 , -2.35363007, ...,  1.44226408,
           2.19673371,  0.29174143]],
 
        [[-0.46439266,  2.5308013 , -2.69422626, ...,  1.37757349,
           2.2510798 ,  0.28444052],
         [-0.46037126,  2.68924522, -2.46339893, ...,  1.72653103,
           2.2144959 ,  0.30559665],
         [-0.46623287,  2.64327359, -2.27541614, ...,  1.34991682,
           2.24970794,  0.27784497],
         ...,
         [-0.46339041,  3.28372312, -2.39596081, ...,  1.37418795,
           2.3155787 ,  0.27407858],
         [-0.46753705,  3.13220143, -2.28208375, ...,  1.44522762,
           2.2386446 ,  0.27935523],
         [-0.45933351,  3.3560164 , -2.5597291 , ...,  1.26456714,
           2.38354063,  0.26306325]],
 
        [[-0.46275881,  2.60944009, -2.55735302, ...,  1.32951951,
           2.32321572,  0.2736994 ],
         [-0.4633128 ,  2.89953756, -2.42153835, ...,  1.49342823,
           2.22810483,  0.29661804],
         [-0.4698683 ,  2.94930911, -2.20106602, ...,  1.49877143,
           2.19497848,  0.29341918],
         ...,
         [-0.4694097 ,  3.03520727, -1.84939933, ...,  1.74355769,
           2.16293645,  0.29818988],
         [-0.46663186,  2.63074231, -2.29277802, ...,  1.71815097,
           2.27208662,  0.31732017],
         [-0.46406293,  2.75043607, -2.57900953, ...,  1.44930601,
           2.26768374,  0.29911333]]]),
 'x': array([[[55.48813504,  0.15199138, -1.52255863, ..., -3.16510147,
           2.96846692, -4.56580694],
         [57.15189366, -5.33468183, -1.03571908, ..., -5.45098938,
           2.38417132, -2.70744728],
         [56.02763376,  1.79819538, -1.35344799, ..., -2.08126588,
           2.43008511, -3.30188077],
         ...,
         [54.46135513, -1.7894271 , -1.53043179, ..., -0.71606133,
           2.54220091, -3.11562289],
         [51.04627889, -2.23414276, -0.61375696, ..., -1.5487723 ,
           2.5040254 , -2.70516369],
         [53.48475989, -5.88267343, -0.5604906 , ..., -2.80024993,
           2.26883133, -2.63204774]],
 
        [[57.40097526, -0.39836985, -1.85175411, ..., -1.57812299,
           2.44541785, -1.97876482],
         [56.80514481,  0.86782055, -0.89687918, ..., -2.46934229,
           2.41598892, -4.18897782],
         [56.22384429, -4.02034251, -1.01335597, ..., -5.9675416 ,
           2.4208824 , -4.58629171],
         ...,
         [56.204999  , -2.73192706, -1.584376  , ..., -2.90374446,
           2.77110222, -1.79558091],
         [56.39622243, -5.28993612, -1.9165993 , ..., -2.61523595,
           2.6285765 , -2.70775515],
         [59.48540301, -1.59536865, -1.53809562, ..., -2.88081047,
           2.64057948, -0.94634674]],
 
        [[57.78276167, -2.36537019, -1.93061228, ..., -5.98554351,
           2.524246  , -4.04929333],
         [58.4834527 , -3.9769609 , -1.35495939, ..., -1.6069144 ,
           2.34006119, -0.5632595 ],
         [54.90419908,  1.13690668, -1.66130013, ..., -0.86827605,
           2.2551516 , -1.58485805],
         ...,
         [50.73826282, -4.69356431, -1.5858489 , ..., -1.52368894,
           2.36651244, -1.38059345],
         [54.90966386, -5.6167769 , -0.82356819, ..., -3.97125184,
           2.6635163 , -2.24339568],
         [57.175595  , -4.47078818, -1.69868292, ..., -2.89903986,
           2.27153616, -4.1663281 ]],
 
        ...,
 
        [[53.25247696,  1.98996388, -1.9963712 , ..., -0.75761667,
           2.9000773 , -2.04206403],
         [53.20096635,  1.97806466, -1.98557091, ..., -0.69916301,
           2.88554251, -2.00887261],
         [53.21496816,  1.99445278, -1.98721502, ..., -0.78426509,
           2.89563156, -2.04548451],
         ...,
         [53.17498149,  1.96261664, -1.97537952, ..., -0.71482   ,
           2.90414374, -2.01866737],
         [53.21660376,  1.98563319, -1.9880311 , ..., -0.8211954 ,
           2.91482492, -2.05975027],
         [53.22324199,  1.9902214 , -1.98641692, ..., -0.72702982,
           2.88858578, -2.0069868 ]],
 
        [[53.21053194,  1.95247095, -1.99479124, ..., -0.78168201,
           2.89933293, -2.02118482],
         [53.22536511,  1.9700108 , -1.98991382, ..., -0.54113988,
           2.89209832, -1.98011473],
         [53.20375375,  1.96564279, -1.98331627, ..., -0.80658696,
           2.89906164, -2.03403288],
         ...,
         [53.21422614,  1.99566444, -1.98787465, ..., -0.78468042,
           2.91208783, -2.0413788 ],
         [53.19895356,  1.99267764, -1.98360272, ..., -0.72464442,
           2.89687382, -2.03108911],
         [53.22919749,  1.99664906, -1.9923005 , ..., -0.88947735,
           2.92552756, -2.06289965]],
 
        [[53.21655507,  1.96207352, -1.99224828, ..., -0.82556025,
           2.91359808, -2.0421187 ],
         [53.21451226,  1.98429322, -1.98868719, ..., -0.68726056,
           2.89478954, -1.99751773],
         [53.19038062,  1.98660267, -1.97981565, ..., -0.68327801,
           2.88823868, -2.00372774],
         ...,
         [53.1920663 ,  1.98987318, -1.95344129, ..., -0.53251075,
           2.88190225, -1.99446816],
         [53.20228488,  1.96435741, -1.98405321, ..., -0.54548106,
           2.90348711, -1.95745379],
         [53.21174711,  1.97505078, -1.99271278, ..., -0.7213783 ,
           2.90261642, -1.9926771 ]]]),
 'logdetj': array([[ 1.16324988, -0.17232041, -1.15430797, ...,  1.00382215,
          0.32119229, -1.59390341],
        [ 0.83027389,  0.6324779 , -1.75981841, ...,  2.18521689,
          0.38952175,  0.61187391],
        [-3.68901289,  0.62638536,  0.75075855, ...,  0.53633783,
         -0.19662943,  1.40988136],
        ...,
        [-8.91381743, -7.2692475 , -8.39685142, ..., -6.35134553,
         -7.55363377, -7.90709209],
        [-7.40218813, -7.59117344, -6.54242069, ..., -8.72091431,
         -8.05550436, -9.21015633],
        [-7.14827926, -7.84339981, -7.43873538, ..., -7.02488426,
         -7.17953477, -7.87793157]]),
 'logl': array([[-1.65560592e+05, -5.09498045e+05, -8.16073134e+05, ...,
         -3.90907286e+05, -2.38041572e+04, -6.70582796e+04],
        [-1.12734616e+04, -3.52415962e+05, -5.73250172e+04, ...,
         -8.50995544e+05, -3.35940721e+04, -1.13345134e+06],
        [-1.24282821e+05, -4.96076313e+06, -6.38447000e+03, ...,
         -2.58049210e+06, -1.10239115e+06, -5.01486655e+05],
        ...,
        [-9.54238198e+02, -9.53441039e+02, -9.53272079e+02, ...,
         -9.55116170e+02, -9.57260583e+02, -9.54595719e+02],
        [-9.56364376e+02, -9.54307605e+02, -9.54802842e+02, ...,
         -9.52113472e+02, -9.52683396e+02, -9.55015855e+02],
        [-9.55005451e+02, -9.53978840e+02, -9.54172106e+02, ...,
         -9.57952561e+02, -9.53928267e+02, -9.52440467e+02]]),
 'logp': array([[-12.41909524,  -9.25923749,  -9.19854888, ...,  -9.27182499,
          -9.21159058,  -9.64418089],
        [ -9.19002061,  -9.21157481,  -9.20648995, ..., -10.39717001,
          -9.54258806,  -9.59497447],
        [ -9.23895699,  -9.36717909,  -9.71189845, ...,  -9.29661168,
          -9.70509868,  -9.63134534],
        ...,
        [-11.60821302, -11.45094298, -11.55954832, ..., -11.65315837,
         -11.77318398, -11.4834348 ],
        [-11.60003038, -11.52122463, -11.59705163, ..., -11.74215517,
         -11.5730968 , -11.89631144],
        [-11.75925283, -11.55038693, -11.4797172 , ..., -11.41238145,
         -11.64587278, -11.63622881]]),
 'logw': array([-1.64556229e+05, -5.08493143e+05, -8.15068065e+05, ...,
        -8.33724999e+00, -8.18281984e+00, -8.14722393e+00]),
 'blobs': array([None, None, None, None, None, None, None, None, None, None, None,
        None, None, None, None, None, None, None, None, None, None, None,
        None, None, None, None, None, None, None, None, None, None, None,
        None, None, None, None, None, None, None, None, None, None, None,
        None, None, None, None, None, None, None], dtype=object),
 'iter': array([0, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
        3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
        3, 3, 3, 3, 3, 3, 3]),
 'logz': array([    0.        ,     0.        ,     0.        ,     0.        ,
           -1.04877159,    -1.59771556,    -2.17714285,    -2.84427362,
           -3.58941091,    -4.38485668,    -5.23929008,    -6.16810061,
           -7.28857779,    -8.6099475 ,   -10.25154581,   -12.17944308,
          -14.293319  ,   -16.58061848,   -18.89596345,   -21.19301013,
          -23.59700904,   -26.43507592,   -30.18772417,   -35.69626678,
          -43.26608822,   -53.37045099,   -66.45869102,   -82.33027079,
          -99.33050258,  -115.84574633,  -129.3784276 ,  -144.41737023,
         -161.76101338,  -182.05549488,  -208.49978951,  -241.22811188,
         -281.79266317,  -324.44029246,  -374.03732129,  -427.46359017,
         -483.17695794,  -548.0192571 ,  -635.90475299,  -730.69378351,
         -832.49088909,  -945.53009802, -1013.12615979, -1013.02881735,
        -1012.98448544, -1012.95258716, -1012.92557051]),
 'calls': array([   512,   1024,   1536,   2048,   5632,   7168,   9728,  11264,
         12800,  14336,  15872,  17408,  18944,  20480,  22016,  23552,
         25088,  27136,  28672,  30720,  32256,  33792,  35328,  36864,
         38400,  40448,  42496,  44544,  51712,  67072,  82432,  97792,
        113152, 128512, 143872, 159232, 174592, 189952, 205312, 220672,
        236032, 251392, 266752, 282112, 297472, 312832, 328192, 343552,
        358912, 374272, 386560]),
 'steps': array([ 1,  1,  1,  1,  7,  3,  5,  3,  3,  3,  3,  3,  3,  3,  3,  3,  3,
         4,  3,  4,  3,  3,  3,  3,  3,  4,  4,  4, 14, 30, 30, 30, 30, 30,
        30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 24]),
 'efficiency': array([1.        , 1.        , 1.        , 1.        , 1.        ,
        1.        , 1.        , 1.        , 1.        , 1.        ,
        1.        , 1.        , 1.        , 1.        , 1.        ,
        1.        , 1.        , 0.97969377, 1.        , 0.97019737,
        1.        , 1.        , 1.        , 1.        , 1.        ,
        0.98235009, 0.97086184, 0.92170246, 0.72087099, 0.65034014,
        0.63078622, 0.60651485, 0.65956683, 0.66048741, 0.64987427,
        0.70317447, 0.60189469, 0.76727878, 0.77615839, 0.86565184,
        0.95237525, 0.78543856, 0.97713356, 0.95405467, 0.96027784,
        0.91108028, 0.93568182, 0.66418812, 0.84799856, 0.98931089,
        1.        ]),
 'ess': array([1024.        , 1024.        , 1024.        , 1024.        ,
        1029.81835343, 1018.96174169, 1032.24815622, 1028.39376461,
        1028.43473642, 1027.88258244, 1024.29795293, 1029.39490523,
        1023.11156655, 1021.68136038, 1022.97785042, 1028.51313425,
        1015.73992335, 1025.99157038, 1021.13541056, 1028.3854604 ,
        1034.07535623, 1026.02565741, 1017.1165472 , 1023.2976886 ,
        1029.79303704, 1024.92330744, 1023.63062259, 1019.75810784,
        1019.20854509, 1015.78667818, 1030.76893527, 1022.97389026,
        1025.96087889, 1033.3072996 , 1022.98962867, 1024.38205515,
        1014.90041058, 1029.19150054, 1027.93860991, 1016.88364339,
        1026.80309605, 1024.01518202, 1019.24606858, 1021.34207562,
        1027.15613704, 1015.49041012, 1285.52154944, 1886.71090043,
        2483.16636011, 3057.62304602, 3622.30756335]),
 'accept': array([1.        , 1.        , 1.        , 1.        , 0.50524656,
        0.58509568, 0.50069501, 0.45175418, 0.4272028 , 0.35670789,
        0.32591644, 0.31998278, 0.32986111, 0.34853655, 0.31361134,
        0.31389499, 0.28320479, 0.21438247, 0.25147232, 0.20336998,
        0.27276114, 0.26368483, 0.24199637, 0.27387594, 0.26005058,
        0.20904683, 0.20269639, 0.22693649, 0.14989514, 0.17149561,
        0.18673183, 0.20635446, 0.21710249, 0.2217333 , 0.22418812,
        0.16856806, 0.2386103 , 0.17808808, 0.1791395 , 0.17976783,
        0.20011214, 0.17299363, 0.19385441, 0.18326441, 0.18839312,
        0.16182438, 0.16352039, 0.17895175, 0.21399516, 0.21859126,
        0.26512922]),
 'beta': array([0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
        1.54972076e-06, 4.41073928e-06, 1.15632651e-05, 2.96828676e-05,
        6.78287079e-05, 1.32674163e-04, 2.35657324e-04, 3.95836853e-04,
        6.47507212e-04, 1.02872993e-03, 1.60796743e-03, 2.40014860e-03,
        3.37436721e-03, 4.53012203e-03, 5.80605388e-03, 7.14103111e-03,
        8.65601366e-03, 1.05922324e-02, 1.33701106e-02, 1.77058865e-02,
        2.39411519e-02, 3.25197941e-02, 4.38574528e-02, 5.78634471e-02,
        7.30443584e-02, 8.79806553e-02, 1.00449670e-01, 1.14505144e-01,
        1.30935224e-01, 1.50455234e-01, 1.76173874e-01, 2.08354582e-01,
        2.48555326e-01, 2.91117622e-01, 3.40960914e-01, 3.95022714e-01,
        4.51739335e-01, 5.18130275e-01, 6.08480848e-01, 7.06360636e-01,
        8.11887283e-01, 9.29457731e-01, 1.00000000e+00, 1.00000000e+00,
        1.00000000e+00, 1.00000000e+00, 1.00000000e+00])}

[minaskar]

Both the efficiency and the acceptance rate look okay. The reason that the latter drops slightly during some iterations is that there're not enough time to be tuned (due the low number of steps), but that's not an issue to worry since the acceptance rate is not dangerously low.

The only issue that I notice is that during the last iterations, the efficiency is slightly lower than the optimal leading pocoMC to do perform more steps. The problem is that pocoMC saturates the maximum number of steps during these iterations (n_max_steps=10*n_steps by default). To resolve this, you can either increase n_steps or n_max_steps. Increasing n_steps will lead to more steps per iteration throughout the run, whereas increasing n_max_steps will only increase the number of steps during the low-efficiency iterations. Overall, increasing n_steps is more expensive but more robust. As I mentioned before, the default value in your case is just n_dim//2, so perhaps try doubling that?