Low Bulk and Tail ESS for Intercept Only

Modeling
, ,
1

Problem background is similar to :
https://discourse.mc-stan.org/t/problems-converging-using-custom-gamma2-distribution/14684

The data is different, and there is a g_swath parameter instead of g_shape.
2 g_size levels
2 g_noise levels
2 g_swath levels
6 g_interps levels
20 g_reps in each g_sizeg_noises_swath combination with g_interps repeated measures.
When running the model below for 20 g_reps, everything looks great. However, the bulk and tail ess is low for the intercept only.

brms_20red6_gamma_mdl4_1

 Family: gamma 
  Links: mu = log; shape = log 
Formula: y ~ g_size * g_noise * g_swath * g_interps + (1 | g_rep) 
         shape ~ g_size * g_noise * g_swath * g_interps
   Data: t_longSubset20red6_unord (Number of observations: 960) 
Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
         total post-warmup samples = 4000

Group-Level Effects: 
~g_rep (Number of levels: 20) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.04      0.01     0.03     0.06 1.00     1222     1732

Population-Level Effects: 
                                                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept                                             5.31      0.01     5.28     5.33 1.01      842     1677
shape_Intercept                                       7.30      0.22     6.85     7.72 1.00     2638     3213
g_size25                                              0.19      0.05     0.09     0.29 1.00     1602     2034
g_noise19                                             2.94      0.01     2.92     2.96 1.00     1919     2370
g_swathLM                                            -0.03      0.03    -0.10     0.04 1.00     1803     2163
g_interpsEM006                                       -0.57      0.01    -0.58    -0.56 1.00     2239     2205
g_interpsEM018                                       -0.60      0.01    -0.61    -0.59 1.00     2171     2256
g_interpsEM033                                       -0.61      0.01    -0.62    -0.60 1.00     2168     2314
g_interpsEM035                                       -0.61      0.01    -0.62    -0.60 1.00     2145     2238
g_interpsEM037                                       -1.14      0.01    -1.17    -1.12 1.00     4353     3262
g_size25:g_noise19                                   -0.27      0.09    -0.44    -0.10 1.00     1441     2342
g_size25:g_swathLM                                    0.39      0.09     0.21     0.57 1.00     1699     2355
g_noise19:g_swathLM                                  -0.03      0.04    -0.11     0.06 1.00     1827     2135
g_size25:g_interpsEM006                               0.57      0.07     0.44     0.70 1.00     2212     2479
g_size25:g_interpsEM018                               0.59      0.06     0.46     0.72 1.00     1823     2666
g_size25:g_interpsEM033                               0.60      0.07     0.47     0.73 1.00     2247     2545
g_size25:g_interpsEM035                               0.59      0.06     0.47     0.72 1.00     2153     2632
g_size25:g_interpsEM037                               0.70      0.08     0.54     0.85 1.00     2887     2782
g_noise19:g_interpsEM006                             -0.00      0.01    -0.02     0.02 1.00     2008     2385
g_noise19:g_interpsEM018                             -0.01      0.01    -0.03     0.01 1.00     1985     2299
g_noise19:g_interpsEM033                             -0.01      0.01    -0.02     0.01 1.00     1962     2385
g_noise19:g_interpsEM035                             -0.01      0.01    -0.03     0.01 1.00     1923     2447
g_noise19:g_interpsEM037                             -1.39      0.05    -1.50    -1.29 1.00     4944     3052
g_swathLM:g_interpsEM006                              0.34      0.05     0.24     0.45 1.00     2367     3128
g_swathLM:g_interpsEM018                              0.35      0.05     0.25     0.46 1.00     2430     2436
g_swathLM:g_interpsEM033                              0.36      0.05     0.26     0.47 1.00     2474     2568
g_swathLM:g_interpsEM035                              0.36      0.05     0.26     0.46 1.00     2370     2578
g_swathLM:g_interpsEM037                              0.46      0.08     0.30     0.63 1.00     3394     3370
g_size25:g_noise19:g_swathLM                         -0.12      0.15    -0.42     0.19 1.00     1409     2089
g_size25:g_noise19:g_interpsEM006                     0.00      0.12    -0.23     0.24 1.00     2274     2963
g_size25:g_noise19:g_interpsEM018                     0.01      0.12    -0.22     0.25 1.00     2041     2533
g_size25:g_noise19:g_interpsEM033                     0.00      0.12    -0.22     0.23 1.00     2149     2942
g_size25:g_noise19:g_interpsEM035                    -0.02      0.12    -0.25     0.20 1.00     2043     2238
g_size25:g_noise19:g_interpsEM037                     1.08      0.17     0.74     1.44 1.00     3333     3215
g_size25:g_swathLM:g_interpsEM006                    -0.34      0.13    -0.58    -0.09 1.00     2358     2972
g_size25:g_swathLM:g_interpsEM018                    -0.34      0.13    -0.60    -0.08 1.00     2032     3038
g_size25:g_swathLM:g_interpsEM033                    -0.36      0.13    -0.61    -0.10 1.00     2335     2976
g_size25:g_swathLM:g_interpsEM035                    -0.34      0.13    -0.59    -0.09 1.00     2490     2848
g_size25:g_swathLM:g_interpsEM037                    -0.25      0.15    -0.56     0.06 1.00     2726     3142
g_noise19:g_swathLM:g_interpsEM006                   -0.01      0.07    -0.14     0.12 1.00     2696     3207
g_noise19:g_swathLM:g_interpsEM018                   -0.01      0.07    -0.15     0.13 1.00     2538     2829
g_noise19:g_swathLM:g_interpsEM033                   -0.01      0.07    -0.15     0.12 1.00     2464     2962
g_noise19:g_swathLM:g_interpsEM035                   -0.01      0.07    -0.15     0.12 1.00     2519     2997
g_noise19:g_swathLM:g_interpsEM037                    0.95      0.16     0.63     1.28 1.00     3580     2884
g_size25:g_noise19:g_swathLM:g_interpsEM006           0.01      0.22    -0.42     0.44 1.00     2172     2934
g_size25:g_noise19:g_swathLM:g_interpsEM018           0.01      0.22    -0.40     0.45 1.00     1846     3116
g_size25:g_noise19:g_swathLM:g_interpsEM033           0.01      0.22    -0.43     0.46 1.00     2417     2605
g_size25:g_noise19:g_swathLM:g_interpsEM035           0.03      0.22    -0.40     0.47 1.00     2478     2924
g_size25:g_noise19:g_swathLM:g_interpsEM037          -0.85      0.31    -1.47    -0.26 1.00     2855     3236
shape_g_size25                                       -4.29      0.35    -5.00    -3.64 1.00     2141     2405
shape_g_noise19                                      -0.44      0.33    -1.10     0.19 1.00     2579     2881
shape_g_swathLM                                      -3.45      0.36    -4.14    -2.75 1.00     2256     2717
shape_g_interpsEM006                                  1.88      0.40     1.09     2.64 1.00     2859     2587
shape_g_interpsEM018                                  2.57      0.43     1.71     3.40 1.00     2852     2964
shape_g_interpsEM033                                  3.42      0.47     2.52     4.34 1.00     2621     3104
shape_g_interpsEM035                                  3.43      0.48     2.49     4.37 1.00     2580     3078
shape_g_interpsEM037                                 -1.51      0.37    -2.23    -0.82 1.00     2713     3159
shape_g_size25:g_noise19                             -0.27      0.46    -1.18     0.62 1.00     2060     2526
shape_g_size25:g_swathLM                              2.89      0.47     1.95     3.80 1.00     2351     2754
shape_g_noise19:g_swathLM                             0.88      0.47    -0.07     1.83 1.00     2506     2812
shape_g_size25:g_interpsEM006                        -1.57      0.54    -2.61    -0.53 1.00     2538     2070
shape_g_size25:g_interpsEM018                        -2.21      0.55    -3.29    -1.12 1.00     2792     2328
shape_g_size25:g_interpsEM033                        -3.05      0.58    -4.19    -1.96 1.00     2711     2489
shape_g_size25:g_interpsEM035                        -3.05      0.58    -4.21    -1.90 1.00     2631     2906
shape_g_size25:g_interpsEM037                         1.09      0.52     0.08     2.11 1.00     2511     2826
shape_g_noise19:g_interpsEM006                        0.30      0.53    -0.73     1.33 1.00     2885     2569
shape_g_noise19:g_interpsEM018                       -0.00      0.53    -1.01     1.05 1.00     2689     3010
shape_g_noise19:g_interpsEM033                        0.42      0.66    -0.85     1.72 1.00     2538     3193
shape_g_noise19:g_interpsEM035                        0.24      0.63    -0.99     1.52 1.00     2157     2343
shape_g_noise19:g_interpsEM037                       -2.30      0.51    -3.26    -1.28 1.00     2448     2741
shape_g_swathLM:g_interpsEM006                       -2.21      0.55    -3.30    -1.14 1.00     2662     2712
shape_g_swathLM:g_interpsEM018                       -2.90      0.55    -3.99    -1.85 1.00     2680     3280
shape_g_swathLM:g_interpsEM033                       -3.73      0.57    -4.86    -2.62 1.00     2533     3272
shape_g_swathLM:g_interpsEM035                       -3.75      0.59    -4.90    -2.61 1.00     2621     2677
shape_g_swathLM:g_interpsEM037                       -0.15      0.52    -1.12     0.89 1.00     2654     2950
shape_g_size25:g_noise19:g_swathLM                   -0.93      0.59    -2.09     0.24 1.00     2476     2676
shape_g_size25:g_noise19:g_interpsEM006              -0.48      0.69    -1.86     0.86 1.00     2926     3394
shape_g_size25:g_noise19:g_interpsEM018              -0.24      0.70    -1.63     1.14 1.00     2465     2977
shape_g_size25:g_noise19:g_interpsEM033              -0.66      0.77    -2.13     0.83 1.00     2698     3206
shape_g_size25:g_noise19:g_interpsEM035              -0.53      0.74    -1.99     0.91 1.00     2278     3046
shape_g_size25:g_noise19:g_interpsEM037               1.50      0.69     0.14     2.86 1.00     2575     2808
shape_g_size25:g_swathLM:g_interpsEM006               1.76      0.71     0.33     3.17 1.00     2749     2930
shape_g_size25:g_swathLM:g_interpsEM018               2.39      0.70     1.04     3.77 1.00     2925     2857
shape_g_size25:g_swathLM:g_interpsEM033               3.18      0.72     1.80     4.61 1.00     2953     2817
shape_g_size25:g_swathLM:g_interpsEM035               3.17      0.72     1.76     4.54 1.00     2912     2837
shape_g_size25:g_swathLM:g_interpsEM037               0.20      0.69    -1.09     1.55 1.00     2775     3037
shape_g_noise19:g_swathLM:g_interpsEM006             -0.56      0.70    -1.90     0.84 1.00     2951     2574
shape_g_noise19:g_swathLM:g_interpsEM018             -0.30      0.69    -1.64     1.06 1.00     2771     3013
shape_g_noise19:g_swathLM:g_interpsEM033             -0.74      0.77    -2.27     0.79 1.00     2637     3319
shape_g_noise19:g_swathLM:g_interpsEM035             -0.56      0.76    -2.06     0.88 1.00     2576     2588
shape_g_noise19:g_swathLM:g_interpsEM037              0.86      0.69    -0.47     2.16 1.00     2588     2979
shape_g_size25:g_noise19:g_swathLM:g_interpsEM006     0.78      0.91    -0.99     2.57 1.00     3241     2942
shape_g_size25:g_noise19:g_swathLM:g_interpsEM018     0.60      0.88    -1.13     2.28 1.00     2869     3194
shape_g_size25:g_noise19:g_swathLM:g_interpsEM033     1.04      0.95    -0.86     2.86 1.00     3242     3245
shape_g_size25:g_noise19:g_swathLM:g_interpsEM035     0.90      0.91    -0.86     2.70 1.00     2797     3074
shape_g_size25:g_noise19:g_swathLM:g_interpsEM037    -0.58      0.88    -2.29     1.13 1.00     2985     2939

Samples were drawn using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

However, when increasing the reps from 20 to 200. I run into problems with bulk and tail ess overall.

brms_200red6_gamma_mdl4_1

 Family: gamma 
  Links: mu = log; shape = log 
Formula: y ~ g_size * g_noise * g_swath * g_interps + (1 | g_rep) 
         shape ~ g_size * g_noise * g_swath * g_interps
   Data: t_longSubset200red6_unord (Number of observations: 9600) 
Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
         total post-warmup samples = 4000

Group-Level Effects: 
~g_rep (Number of levels: 200) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.04      0.00     0.04     0.05 1.08       49       95

Population-Level Effects: 
                                                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept                                             5.30      0.00     5.29     5.30 1.09       33      181
shape_Intercept                                       7.27      0.09     7.07     7.44 1.02      219      637
g_size25                                              0.18      0.02     0.14     0.21 1.01      349      694
g_noise19                                             2.94      0.00     2.93     2.95 1.01      645     1143
g_swathLM                                            -0.03      0.01    -0.04    -0.01 1.01      619     1377
g_interpsEM006                                       -0.57      0.00    -0.58    -0.57 1.00      728     1463
g_interpsEM018                                       -0.60      0.00    -0.61    -0.60 1.00      687     1537
g_interpsEM033                                       -0.61      0.00    -0.61    -0.60 1.00      688     1392
g_interpsEM035                                       -0.61      0.00    -0.62    -0.61 1.00      694     1651
g_interpsEM037                                       -1.12      0.00    -1.13    -1.11 1.00     1447     2164
g_size25:g_noise19                                   -0.17      0.02    -0.22    -0.12 1.01      343      746
g_size25:g_swathLM                                    0.37      0.03     0.32     0.43 1.00      355      730
g_noise19:g_swathLM                                  -0.04      0.01    -0.06    -0.02 1.01      534     1323
g_size25:g_interpsEM006                               0.57      0.02     0.53     0.62 1.01      463     1028
g_size25:g_interpsEM018                               0.59      0.02     0.55     0.64 1.00      468      953
g_size25:g_interpsEM033                               0.60      0.02     0.56     0.65 1.00      493     1182
g_size25:g_interpsEM035                               0.60      0.02     0.55     0.64 1.01      461      767
g_size25:g_interpsEM037                               0.66      0.03     0.60     0.71 1.00      576     1188
g_noise19:g_interpsEM006                             -0.00      0.00    -0.01     0.00 1.01      622     1233
g_noise19:g_interpsEM018                             -0.01      0.00    -0.02    -0.01 1.01      713     1260
g_noise19:g_interpsEM033                             -0.01      0.00    -0.01    -0.00 1.01      673     1200
g_noise19:g_interpsEM035                             -0.01      0.00    -0.01    -0.00 1.01      682     1251
g_noise19:g_interpsEM037                             -1.41      0.02    -1.45    -1.37 1.00     1187     1675
g_swathLM:g_interpsEM006                              0.35      0.01     0.32     0.38 1.01      795     1463
g_swathLM:g_interpsEM018                              0.36      0.01     0.33     0.38 1.00      921     1914
g_swathLM:g_interpsEM033                              0.37      0.01     0.34     0.39 1.01      919     1920
g_swathLM:g_interpsEM035                              0.37      0.01     0.34     0.39 1.01      945     1930
g_swathLM:g_interpsEM037                              0.43      0.02     0.39     0.47 1.01      869     1605
g_size25:g_noise19:g_swathLM                         -0.26      0.04    -0.35    -0.18 1.01      376      612
g_size25:g_noise19:g_interpsEM006                     0.00      0.03    -0.06     0.06 1.01      445     1260
g_size25:g_noise19:g_interpsEM018                     0.01      0.03    -0.05     0.07 1.00      445      862
g_size25:g_noise19:g_interpsEM033                     0.00      0.03    -0.06     0.07 1.00      470     1177
g_size25:g_noise19:g_interpsEM035                    -0.01      0.03    -0.08     0.05 1.00      493     1428
g_size25:g_noise19:g_interpsEM037                     1.18      0.05     1.08     1.27 1.00      713     1310
g_size25:g_swathLM:g_interpsEM006                    -0.35      0.04    -0.43    -0.27 1.00      498     1153
g_size25:g_swathLM:g_interpsEM018                    -0.35      0.04    -0.43    -0.27 1.00      474     1204
g_size25:g_swathLM:g_interpsEM033                    -0.36      0.04    -0.45    -0.28 1.00      522     1099
g_size25:g_swathLM:g_interpsEM035                    -0.35      0.04    -0.43    -0.27 1.00      527     1156
g_size25:g_swathLM:g_interpsEM037                    -0.22      0.05    -0.31    -0.12 1.00      569     1239
g_noise19:g_swathLM:g_interpsEM006                   -0.02      0.02    -0.06     0.01 1.00      790     1599
g_noise19:g_swathLM:g_interpsEM018                   -0.02      0.02    -0.06     0.01 1.00      781     1589
g_noise19:g_swathLM:g_interpsEM033                   -0.03      0.02    -0.06     0.01 1.01      816     1612
g_noise19:g_swathLM:g_interpsEM035                   -0.03      0.02    -0.06     0.01 1.01      848     1457
g_noise19:g_swathLM:g_interpsEM037                    0.94      0.05     0.85     1.04 1.00      977     1747
g_size25:g_noise19:g_swathLM:g_interpsEM006           0.02      0.06    -0.09     0.14 1.00      519      805
g_size25:g_noise19:g_swathLM:g_interpsEM018           0.02      0.06    -0.10     0.14 1.00      471     1076
g_size25:g_noise19:g_swathLM:g_interpsEM033           0.03      0.06    -0.09     0.15 1.00      542     1073
g_size25:g_noise19:g_swathLM:g_interpsEM035           0.04      0.06    -0.08     0.16 1.00      604     1026
g_size25:g_noise19:g_swathLM:g_interpsEM037          -0.96      0.09    -1.13    -0.79 1.00      631     1262
shape_g_size25                                       -4.36      0.13    -4.62    -4.10 1.01      251      543
shape_g_noise19                                      -0.14      0.13    -0.40     0.12 1.01      254      618
shape_g_swathLM                                      -2.76      0.14    -3.02    -2.48 1.02      206      582
shape_g_interpsEM006                                  2.01      0.15     1.72     2.32 1.02      225      634
shape_g_interpsEM018                                  2.11      0.14     1.82     2.37 1.01      416     1024
shape_g_interpsEM033                                  4.02      0.20     3.65     4.43 1.01      260      585
shape_g_interpsEM035                                  4.02      0.19     3.65     4.38 1.02      232      590
shape_g_interpsEM037                                 -1.62      0.14    -1.89    -1.34 1.02      198      448
shape_g_size25:g_noise19                              0.17      0.18    -0.19     0.53 1.01      259      853
shape_g_size25:g_swathLM                              2.19      0.19     1.82     2.53 1.01      261      572
shape_g_noise19:g_swathLM                             0.31      0.19    -0.05     0.67 1.02      245     1062
shape_g_size25:g_interpsEM006                        -1.95      0.20    -2.35    -1.53 1.01      244      632
shape_g_size25:g_interpsEM018                        -2.05      0.19    -2.43    -1.66 1.01      382      751
shape_g_size25:g_interpsEM033                        -3.95      0.23    -4.41    -3.51 1.01      239      551
shape_g_size25:g_interpsEM035                        -3.96      0.23    -4.39    -3.51 1.02      224      923
shape_g_size25:g_interpsEM037                         1.22      0.19     0.84     1.60 1.01      263      471
shape_g_noise19:g_interpsEM006                       -0.06      0.20    -0.44     0.32 1.01      266      846
shape_g_noise19:g_interpsEM018                       -0.26      0.19    -0.62     0.12 1.01      413      863
shape_g_noise19:g_interpsEM033                       -1.11      0.26    -1.64    -0.61 1.01      303      556
shape_g_noise19:g_interpsEM035                       -1.36      0.25    -1.83    -0.88 1.01      226      637
shape_g_noise19:g_interpsEM037                       -3.03      0.19    -3.39    -2.66 1.02      241      709
shape_g_swathLM:g_interpsEM006                       -2.72      0.21    -3.13    -2.32 1.02      211      722
shape_g_swathLM:g_interpsEM018                       -2.86      0.20    -3.25    -2.47 1.01      450     1081
shape_g_swathLM:g_interpsEM033                       -4.76      0.24    -5.23    -4.31 1.01      227      690
shape_g_swathLM:g_interpsEM035                       -4.76      0.23    -5.20    -4.31 1.01      286      890
shape_g_swathLM:g_interpsEM037                       -0.28      0.20    -0.66     0.11 1.02      205      793
shape_g_size25:g_noise19:g_swathLM                   -0.58      0.25    -1.05    -0.08 1.01      271      667
shape_g_size25:g_noise19:g_interpsEM006              -0.01      0.27    -0.57     0.50 1.01      281      661
shape_g_size25:g_noise19:g_interpsEM018               0.18      0.26    -0.34     0.70 1.01      363      793
shape_g_size25:g_noise19:g_interpsEM033               1.02      0.31     0.40     1.65 1.01      255      537
shape_g_size25:g_noise19:g_interpsEM035               1.22      0.30     0.63     1.77 1.02      229      894
shape_g_size25:g_noise19:g_interpsEM037               2.10      0.26     1.57     2.60 1.01      289      698
shape_g_size25:g_swathLM:g_interpsEM006               2.61      0.28     2.07     3.17 1.01      226      544
shape_g_size25:g_swathLM:g_interpsEM018               2.76      0.28     2.21     3.30 1.01      450     1198
shape_g_size25:g_swathLM:g_interpsEM033               4.63      0.29     4.07     5.24 1.01      241      789
shape_g_size25:g_swathLM:g_interpsEM035               4.64      0.29     4.08     5.20 1.01      294      765
shape_g_size25:g_swathLM:g_interpsEM037               0.31      0.26    -0.20     0.82 1.01      296      680
shape_g_noise19:g_swathLM:g_interpsEM006             -0.11      0.27    -0.65     0.42 1.01      263      804
shape_g_noise19:g_swathLM:g_interpsEM018              0.08      0.26    -0.43     0.61 1.01      451     1097
shape_g_noise19:g_swathLM:g_interpsEM033              0.92      0.31     0.32     1.56 1.01      303      754
shape_g_noise19:g_swathLM:g_interpsEM035              1.16      0.30     0.58     1.76 1.01      288      890
shape_g_noise19:g_swathLM:g_interpsEM037              1.63      0.27     1.10     2.13 1.03      224      797
shape_g_size25:g_noise19:g_swathLM:g_interpsEM006     0.23      0.37    -0.48     0.96 1.01      278      440
shape_g_size25:g_noise19:g_swathLM:g_interpsEM018     0.05      0.37    -0.68     0.77 1.00      411     1204
shape_g_size25:g_noise19:g_swathLM:g_interpsEM033    -0.77      0.39    -1.52     0.00 1.01      263      894
shape_g_size25:g_noise19:g_swathLM:g_interpsEM035    -0.99      0.38    -1.72    -0.22 1.01      307      894
shape_g_size25:g_noise19:g_swathLM:g_interpsEM037    -1.31      0.36    -2.01    -0.60 1.02      308     1161

Samples were drawn using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).
Warning message:
Parts of the model have not converged (some Rhats are > 1.05). Be careful when analysing the results! We recommend running more iterations and/or setting stronger priors.
2

Here, I’ve increased the number of iters to 5000 from 2000 for the 200 g_reps. The bulk and tail look better overall but the Bulk is still much lower than the Tail Ess, and they are both still low for the intercept only:

 brms_200red6_gamma_mdl4
 Family: gamma 
  Links: mu = log; shape = log 
Formula: y ~ g_size * g_noise * g_swath * g_interps + (1 | g_rep) 
         shape ~ g_size * g_noise * g_swath * g_interps
   Data: t_longSubset200red6_unord (Number of observations: 9600) 
Samples: 4 chains, each with iter = 5000; warmup = 1000; thin = 1;
         total post-warmup samples = 16000

Group-Level Effects: 
~g_rep (Number of levels: 200) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.04      0.00     0.04     0.05 1.01      306      498

Population-Level Effects: 
                                                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept                                             5.30      0.00     5.29     5.31 1.04      133      222
shape_Intercept                                       7.26      0.09     7.08     7.44 1.00     1408     3341
g_size25                                              0.18      0.02     0.14     0.21 1.00     1444     3278
g_noise19                                             2.94      0.00     2.94     2.95 1.00     2880     6164
g_swathLM                                            -0.03      0.01    -0.04    -0.01 1.00     2260     5354
g_interpsEM006                                       -0.57      0.00    -0.58    -0.57 1.00     3921     7365
g_interpsEM018                                       -0.60      0.00    -0.61    -0.60 1.00     3859     7143
g_interpsEM033                                       -0.61      0.00    -0.61    -0.60 1.00     3749     7295
g_interpsEM035                                       -0.61      0.00    -0.62    -0.61 1.00     3738     7068
g_interpsEM037                                       -1.12      0.00    -1.13    -1.11 1.00     7744    10626
g_size25:g_noise19                                   -0.17      0.02    -0.21    -0.12 1.00     1518     3674
g_size25:g_swathLM                                    0.37      0.03     0.31     0.43 1.00     1549     2844
g_noise19:g_swathLM                                  -0.04      0.01    -0.06    -0.02 1.00     2165     5219
g_size25:g_interpsEM006                               0.57      0.02     0.53     0.62 1.00     2043     5271
g_size25:g_interpsEM018                               0.59      0.02     0.55     0.64 1.00     2062     4181
g_size25:g_interpsEM033                               0.60      0.02     0.56     0.65 1.00     1881     4785
g_size25:g_interpsEM035                               0.60      0.02     0.55     0.64 1.00     1857     4843
g_size25:g_interpsEM037                               0.65      0.03     0.60     0.71 1.00     2278     5870
g_noise19:g_interpsEM006                             -0.00      0.00    -0.01     0.00 1.00     3044     6557
g_noise19:g_interpsEM018                             -0.01      0.00    -0.02    -0.01 1.00     3042     6451
g_noise19:g_interpsEM033                             -0.01      0.00    -0.01    -0.00 1.00     2955     6281
g_noise19:g_interpsEM035                             -0.01      0.00    -0.01    -0.00 1.00     2950     6310
g_noise19:g_interpsEM037                             -1.41      0.02    -1.45    -1.37 1.00     6350     9454
g_swathLM:g_interpsEM006                              0.35      0.01     0.32     0.37 1.00     3376     7473
g_swathLM:g_interpsEM018                              0.36      0.01     0.33     0.38 1.00     3277     7178
g_swathLM:g_interpsEM033                              0.37      0.01     0.34     0.39 1.00     3252     6539
g_swathLM:g_interpsEM035                              0.36      0.01     0.34     0.39 1.00     3881     6604
g_swathLM:g_interpsEM037                              0.43      0.02     0.39     0.47 1.00     4868     8123
g_size25:g_noise19:g_swathLM                         -0.26      0.04    -0.35    -0.18 1.00     1767     3216
g_size25:g_noise19:g_interpsEM006                     0.00      0.03    -0.06     0.07 1.00     2133     5619
g_size25:g_noise19:g_interpsEM018                     0.01      0.03    -0.06     0.07 1.00     2186     4125
g_size25:g_noise19:g_interpsEM033                     0.00      0.03    -0.06     0.07 1.00     2013     5108
g_size25:g_noise19:g_interpsEM035                    -0.01      0.03    -0.08     0.05 1.00     1949     4776
g_size25:g_noise19:g_interpsEM037                     1.18      0.05     1.08     1.28 1.00     2663     6525
g_size25:g_swathLM:g_interpsEM006                    -0.35      0.04    -0.43    -0.27 1.00     2067     5066
g_size25:g_swathLM:g_interpsEM018                    -0.35      0.04    -0.43    -0.27 1.00     2252     4518
g_size25:g_swathLM:g_interpsEM033                    -0.36      0.04    -0.45    -0.28 1.00     2087     4326
g_size25:g_swathLM:g_interpsEM035                    -0.35      0.04    -0.43    -0.27 1.00     2283     4570
g_size25:g_swathLM:g_interpsEM037                    -0.22      0.05    -0.31    -0.12 1.00     2768     5045
g_noise19:g_swathLM:g_interpsEM006                   -0.02      0.02    -0.06     0.01 1.00     3220     6941
g_noise19:g_swathLM:g_interpsEM018                   -0.02      0.02    -0.06     0.01 1.00     3286     7756
g_noise19:g_swathLM:g_interpsEM033                   -0.03      0.02    -0.06     0.01 1.00     3274     6131
g_noise19:g_swathLM:g_interpsEM035                   -0.03      0.02    -0.06     0.01 1.00     3762     6902
g_noise19:g_swathLM:g_interpsEM037                    0.94      0.05     0.85     1.03 1.00     4544     8125
g_size25:g_noise19:g_swathLM:g_interpsEM006           0.02      0.06    -0.09     0.14 1.00     2265     5919
g_size25:g_noise19:g_swathLM:g_interpsEM018           0.02      0.06    -0.09     0.14 1.00     2376     5151
g_size25:g_noise19:g_swathLM:g_interpsEM033           0.03      0.06    -0.09     0.15 1.00     2293     4849
g_size25:g_noise19:g_swathLM:g_interpsEM035           0.04      0.06    -0.08     0.16 1.00     2365     4726
g_size25:g_noise19:g_swathLM:g_interpsEM037          -0.96      0.09    -1.13    -0.79 1.00     2906     6643
shape_g_size25                                       -4.37      0.13    -4.63    -4.11 1.00     1194     2300
shape_g_noise19                                      -0.14      0.13    -0.40     0.12 1.00     1266     3434
shape_g_swathLM                                      -2.75      0.13    -3.02    -2.49 1.00     1261     2868
shape_g_interpsEM006                                  2.01      0.15     1.73     2.30 1.00     1795     5024
shape_g_interpsEM018                                  2.10      0.15     1.81     2.38 1.00     1681     3310
shape_g_interpsEM033                                  4.03      0.21     3.62     4.44 1.00     1204     2470
shape_g_interpsEM035                                  4.01      0.20     3.60     4.41 1.00     1214     2860
shape_g_interpsEM037                                 -1.62      0.14    -1.88    -1.35 1.00     1850     4304
shape_g_size25:g_noise19                              0.18      0.19    -0.19     0.54 1.00     1124     2642
shape_g_size25:g_swathLM                              2.19      0.19     1.83     2.56 1.00     1140     1906
shape_g_noise19:g_swathLM                             0.31      0.19    -0.06     0.67 1.00     1252     3182
shape_g_size25:g_interpsEM006                        -1.94      0.20    -2.33    -1.55 1.00     1612     3622
shape_g_size25:g_interpsEM018                        -2.04      0.20    -2.43    -1.65 1.00     1442     3138
shape_g_size25:g_interpsEM033                        -3.95      0.25    -4.43    -3.47 1.00     1292     3107
shape_g_size25:g_interpsEM035                        -3.94      0.24    -4.40    -3.46 1.00     1255     2989
shape_g_size25:g_interpsEM037                         1.22      0.19     0.85     1.60 1.00     1596     3566
shape_g_noise19:g_interpsEM006                       -0.07      0.20    -0.45     0.32 1.00     1526     4208
shape_g_noise19:g_interpsEM018                       -0.26      0.20    -0.66     0.13 1.00     1395     3155
shape_g_noise19:g_interpsEM033                       -1.12      0.28    -1.65    -0.57 1.00     1106     2291
shape_g_noise19:g_interpsEM035                       -1.35      0.26    -1.86    -0.82 1.00     1119     1861
shape_g_noise19:g_interpsEM037                       -3.03      0.19    -3.40    -2.66 1.00     1646     4652
shape_g_swathLM:g_interpsEM006                       -2.72      0.20    -3.11    -2.33 1.00     1635     3845
shape_g_swathLM:g_interpsEM018                       -2.86      0.20    -3.24    -2.46 1.00     1514     2889
shape_g_swathLM:g_interpsEM033                       -4.77      0.25    -5.25    -4.30 1.00     1301     3232
shape_g_swathLM:g_interpsEM035                       -4.76      0.24    -5.24    -4.28 1.00     1258     2903
shape_g_swathLM:g_interpsEM037                       -0.28      0.19    -0.65     0.10 1.00     1678     3748
shape_g_size25:g_noise19:g_swathLM                   -0.59      0.26    -1.10    -0.10 1.00     1115     2293
shape_g_size25:g_noise19:g_interpsEM006              -0.03      0.27    -0.56     0.50 1.00     1465     3314
shape_g_size25:g_noise19:g_interpsEM018               0.17      0.27    -0.37     0.70 1.00     1354     3467
shape_g_size25:g_noise19:g_interpsEM033               1.00      0.33     0.36     1.64 1.00     1169     2617
shape_g_size25:g_noise19:g_interpsEM035               1.19      0.32     0.57     1.80 1.00     1154     2487
shape_g_size25:g_noise19:g_interpsEM037               2.09      0.27     1.57     2.61 1.00     1613     3333
shape_g_size25:g_swathLM:g_interpsEM006               2.60      0.27     2.07     3.14 1.00     1561     2559
shape_g_size25:g_swathLM:g_interpsEM018               2.75      0.28     2.20     3.29 1.00     1433     2521
shape_g_size25:g_swathLM:g_interpsEM033               4.64      0.31     4.03     5.24 1.00     1325     3038
shape_g_size25:g_swathLM:g_interpsEM035               4.63      0.30     4.04     5.22 1.00     1309     2200
shape_g_size25:g_swathLM:g_interpsEM037               0.31      0.27    -0.22     0.83 1.00     1587     3545
shape_g_noise19:g_swathLM:g_interpsEM006             -0.10      0.27    -0.63     0.44 1.00     1618     4809
shape_g_noise19:g_swathLM:g_interpsEM018              0.09      0.27    -0.46     0.61 1.00     1498     3419
shape_g_noise19:g_swathLM:g_interpsEM033              0.93      0.33     0.27     1.57 1.00     1289     3127
shape_g_noise19:g_swathLM:g_interpsEM035              1.16      0.32     0.53     1.79 1.00     1240     2517
shape_g_noise19:g_swathLM:g_interpsEM037              1.64      0.26     1.13     2.16 1.00     1627     4300
shape_g_size25:g_noise19:g_swathLM:g_interpsEM006     0.24      0.37    -0.49     0.98 1.00     1511     2534
shape_g_size25:g_noise19:g_swathLM:g_interpsEM018     0.05      0.38    -0.67     0.81 1.00     1470     2996
shape_g_size25:g_noise19:g_swathLM:g_interpsEM033    -0.76      0.41    -1.57     0.04 1.00     1283     3018
shape_g_size25:g_noise19:g_swathLM:g_interpsEM035    -0.97      0.40    -1.74    -0.19 1.00     1346     2700
shape_g_size25:g_noise19:g_swathLM:g_interpsEM037    -1.31      0.37    -2.01    -0.58 1.00     1581     3521

Samples were drawn using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

And Here, I tried with adding a varying intercept to the distributional shape parameter but even though it looks good and seems to have an easier time sampling, I don’t believe this is allowed because I have only 1 measurement for each rep in each factor combination. and I’m not certain but I believe this model maybe dependent on the priors set. Either way, the bulk and tail ess are still low for the intercept.

brms_200red6_gamma_mdl5_1a
 Family: gamma 
  Links: mu = log; shape = log 
Formula: y ~ g_size * g_noise * g_swath * g_interps + (1 | g_rep) 
         shape ~ g_size * g_noise * g_swath * g_interps + (1 + g_size || g_rep)
   Data: t_longSubset200red6_unord (Number of observations: 9600) 
Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
         total post-warmup samples = 4000

Group-Level Effects: 
~g_rep (Number of levels: 200) 
                    Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)           0.04      0.00     0.04     0.05 1.01      593      968
sd(shape_Intercept)     0.60      0.04     0.54     0.68 1.00     1751     2751
sd(shape_g_size25)      0.90      0.05     0.81     1.01 1.00     2057     3236

Population-Level Effects: 
                                                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept                                             5.30      0.00     5.29     5.30 1.01      850     1482
shape_Intercept                                       7.30      0.10     7.09     7.50 1.00     2524     3388
g_size25                                              0.18      0.01     0.16     0.21 1.00     2808     2787
g_noise19                                             2.94      0.00     2.94     2.95 1.00     4025     3235
g_swathLM                                            -0.03      0.01    -0.04    -0.02 1.00     2774     2687
g_interpsEM006                                       -0.57      0.00    -0.58    -0.57 1.00     3473     3580
g_interpsEM018                                       -0.60      0.00    -0.60    -0.60 1.00     3658     3533
g_interpsEM033                                       -0.61      0.00    -0.61    -0.60 1.00     3644     3464
g_interpsEM035                                       -0.61      0.00    -0.61    -0.61 1.00     3567     3616
g_interpsEM037                                       -1.12      0.00    -1.13    -1.11 1.00     4295     3349
g_size25:g_noise19                                   -0.16      0.02    -0.19    -0.13 1.00     2732     2718
g_size25:g_swathLM                                    0.34      0.02     0.30     0.38 1.00     2699     2772
g_noise19:g_swathLM                                  -0.04      0.01    -0.06    -0.03 1.00     2867     3101
g_size25:g_interpsEM006                               0.57      0.02     0.54     0.60 1.00     3249     3256
g_size25:g_interpsEM018                               0.59      0.02     0.56     0.63 1.00     3167     2969
g_size25:g_interpsEM033                               0.60      0.02     0.57     0.64 1.00     3291     3355
g_size25:g_interpsEM035                               0.60      0.02     0.56     0.63 1.00     3235     3096
g_size25:g_interpsEM037                               0.67      0.02     0.63     0.72 1.00     3012     3014
g_noise19:g_interpsEM006                             -0.00      0.00    -0.01     0.00 1.00     3947     3301
g_noise19:g_interpsEM018                             -0.01      0.00    -0.02    -0.01 1.00     4217     3478
g_noise19:g_interpsEM033                             -0.01      0.00    -0.01    -0.00 1.00     4001     3146
g_noise19:g_interpsEM035                             -0.01      0.00    -0.01    -0.00 1.00     3948     3334
g_noise19:g_interpsEM037                             -1.40      0.02    -1.44    -1.36 1.00     4439     3058
g_swathLM:g_interpsEM006                              0.35      0.01     0.33     0.37 1.00     3093     3346
g_swathLM:g_interpsEM018                              0.35      0.01     0.33     0.37 1.00     3205     3275
g_swathLM:g_interpsEM033                              0.37      0.01     0.35     0.39 1.00     3510     3351
g_swathLM:g_interpsEM035                              0.36      0.01     0.34     0.38 1.00     3284     3312
g_swathLM:g_interpsEM037                              0.41      0.02     0.38     0.45 1.00     3750     3299
g_size25:g_noise19:g_swathLM                         -0.24      0.03    -0.30    -0.18 1.00     2781     3155
g_size25:g_noise19:g_interpsEM006                     0.00      0.02    -0.04     0.05 1.00     3120     3445
g_size25:g_noise19:g_interpsEM018                     0.01      0.02    -0.04     0.05 1.00     3253     3063
g_size25:g_noise19:g_interpsEM033                     0.00      0.02    -0.04     0.05 1.00     3306     2995
g_size25:g_noise19:g_interpsEM035                    -0.01      0.02    -0.06     0.03 1.00     3118     3446
g_size25:g_noise19:g_interpsEM037                     1.16      0.04     1.08     1.24 1.00     3385     3132
g_size25:g_swathLM:g_interpsEM006                    -0.35      0.03    -0.41    -0.29 1.00     2824     3318
g_size25:g_swathLM:g_interpsEM018                    -0.35      0.03    -0.41    -0.29 1.00     3190     3006
g_size25:g_swathLM:g_interpsEM033                    -0.36      0.03    -0.42    -0.30 1.00     3177     2677
g_size25:g_swathLM:g_interpsEM035                    -0.35      0.03    -0.41    -0.29 1.00     3090     3289
g_size25:g_swathLM:g_interpsEM037                    -0.21      0.04    -0.29    -0.13 1.00     3181     3160
g_noise19:g_swathLM:g_interpsEM006                   -0.02      0.01    -0.05     0.00 1.00     3134     3347
g_noise19:g_swathLM:g_interpsEM018                   -0.02      0.01    -0.05     0.00 1.00     3829     3295
g_noise19:g_swathLM:g_interpsEM033                   -0.03      0.01    -0.05     0.00 1.00     3825     3473
g_noise19:g_swathLM:g_interpsEM035                   -0.03      0.01    -0.06    -0.00 1.00     3577     3449
g_noise19:g_swathLM:g_interpsEM037                    0.92      0.04     0.84     1.01 1.00     4358     3686
g_size25:g_noise19:g_swathLM:g_interpsEM006           0.02      0.04    -0.06     0.11 1.00     2962     3246
g_size25:g_noise19:g_swathLM:g_interpsEM018           0.02      0.04    -0.06     0.11 1.00     3171     2954
g_size25:g_noise19:g_swathLM:g_interpsEM033           0.02      0.04    -0.06     0.11 1.00     3078     3197
g_size25:g_noise19:g_swathLM:g_interpsEM035           0.04      0.04    -0.05     0.13 1.00     3159     3216
g_size25:g_noise19:g_swathLM:g_interpsEM037          -0.94      0.07    -1.08    -0.80 1.00     3397     3319
shape_g_size25                                       -4.06      0.15    -4.35    -3.77 1.00     2492     3037
shape_g_noise19                                      -0.14      0.13    -0.40     0.12 1.00     2042     2175
shape_g_swathLM                                      -2.36      0.14    -2.64    -2.09 1.00     2816     2745
shape_g_interpsEM006                                  2.07      0.15     1.77     2.36 1.00     2844     3010
shape_g_interpsEM018                                  2.21      0.15     1.92     2.50 1.00     2927     2227
shape_g_interpsEM033                                  4.13      0.21     3.72     4.54 1.00     1611     1884
shape_g_interpsEM035                                  4.15      0.21     3.77     4.56 1.00     1362     2447
shape_g_interpsEM037                                 -1.63      0.14    -1.89    -1.36 1.00     2577     2685
shape_g_size25:g_noise19                              0.25      0.19    -0.13     0.63 1.00     2315     2343
shape_g_size25:g_swathLM                              1.70      0.19     1.32     2.06 1.00     2596     2675
shape_g_noise19:g_swathLM                             0.29      0.19    -0.09     0.66 1.00     2494     2344
shape_g_size25:g_interpsEM006                        -1.99      0.20    -2.37    -1.59 1.00     2908     2998
shape_g_size25:g_interpsEM018                        -2.14      0.20    -2.54    -1.74 1.00     2631     2362
shape_g_size25:g_interpsEM033                        -4.04      0.24    -4.52    -3.58 1.00     1594     2303
shape_g_size25:g_interpsEM035                        -4.08      0.25    -4.58    -3.61 1.00     1527     2963
shape_g_size25:g_interpsEM037                         0.86      0.20     0.47     1.24 1.00     2672     3016
shape_g_noise19:g_interpsEM006                       -0.09      0.20    -0.46     0.30 1.00     2644     2962
shape_g_noise19:g_interpsEM018                       -0.22      0.20    -0.61     0.17 1.00     2597     2745
shape_g_noise19:g_interpsEM033                       -1.16      0.27    -1.70    -0.63 1.00     1752     2505
shape_g_noise19:g_interpsEM035                       -1.38      0.27    -1.91    -0.86 1.00     1360     1919
shape_g_noise19:g_interpsEM037                       -3.08      0.19    -3.45    -2.69 1.00     2710     2205
shape_g_swathLM:g_interpsEM006                       -2.81      0.20    -3.19    -2.40 1.00     2961     3397
shape_g_swathLM:g_interpsEM018                       -3.00      0.20    -3.40    -2.62 1.00     2708     2462
shape_g_swathLM:g_interpsEM033                       -4.90      0.25    -5.39    -4.44 1.00     1972     2907
shape_g_swathLM:g_interpsEM035                       -4.93      0.25    -5.42    -4.46 1.00     1764     2195
shape_g_swathLM:g_interpsEM037                       -0.60      0.20    -0.98    -0.23 1.00     2513     2559
shape_g_size25:g_noise19:g_swathLM                   -0.50      0.26    -1.03     0.02 1.00     2492     2373
shape_g_size25:g_noise19:g_interpsEM006              -0.01      0.27    -0.55     0.53 1.00     2644     3002
shape_g_size25:g_noise19:g_interpsEM018               0.12      0.28    -0.42     0.67 1.00     2708     2833
shape_g_size25:g_noise19:g_interpsEM033               1.04      0.33     0.38     1.67 1.00     1818     2463
shape_g_size25:g_noise19:g_interpsEM035               1.23      0.32     0.59     1.86 1.00     1524     2418
shape_g_size25:g_noise19:g_interpsEM037               2.15      0.27     1.62     2.68 1.00     2824     3171
shape_g_size25:g_swathLM:g_interpsEM006               2.68      0.26     2.16     3.19 1.00     2958     2998
shape_g_size25:g_swathLM:g_interpsEM018               2.88      0.27     2.37     3.42 1.00     2543     2869
shape_g_size25:g_swathLM:g_interpsEM033               4.76      0.30     4.18     5.35 1.00     1925     2735
shape_g_size25:g_swathLM:g_interpsEM035               4.80      0.31

My questions are:

  1. Why is intercept having such a hard time? Why is Bulk and Tail ESS remaining low for Intercept only?
  2. Does it matter if the Bulk Ess is larger than the Tail ess? Should they be about the same or should bulk be more or does the only thing that matter is whether there is at least 400 (4x#chains) for each?
  3. Why is it worse when the number of groups increases? To me, this means variability in the reps was not well represented by the the first 20 reps. But how do I fix this? I’ve tried different varying effects and none seem to help.
  4. When I add varying intercept to shape ~ +(1 | g_rep) or even shape ~ + (1 + g_size || g_rep), I get better (easier) sampling overall, but I don’t believe this is allowed since each g_rep is only measured once in each factor combination. Am I correct that this is not allowed? (Either way, sampling improvements are then limited due to overparameterization.)
  5. What would be the next best step?
3

ok so it seems that I need a longer warmup period. It is my understanding that choosing warmup length and iters is mostly trial and error and this can takeup some time for long complex models.
https://discourse.mc-stan.org/t/how-to-choose-warmup-length-for-very-large-models/14531

Increase iters to increase ess.
Increase warmup for better tuned HMC params (step size, mass matrix).
Because my warmup was too short, step size was tuned near 0, which is why sampling is so poor.

I believe I read somewhere that this sampling problem happens when including a large number of varying group-effects, but I couldn’t find the source again so idk…
I did read that according to Mcclearth, having flat priors on sd can cause sampling difficulties. Perhaps, including many group-effects causing the posterior to be too diffused to sample?

4

HI Samantha,

do you have flat priors on sd or on any other parameter? If that is the case then I would strongly recommend you to think about changing that, preferably by doing prior predictive checks (i.e., you have a \log link function so it’s a bit hard to sometimes reason about priors without doing prior predictive checks).

Using proper priors can make a huge difference for any sampling algorithm.

5

Thanks for responding, No, I’ve tried to set weakly informed priors for each general param type. These prior values were selected to cover what is expected possible and eliminate the impossible. The response variable y is RMSE (between an interpolated seafloor depth (m) surface and the truth). The model fits a gamma (log, log). These priors work well when only with a + (1|g_rep). It appears though, now that I look, that this prior may be too strong for the the other varying group-effects, but Idk how that would affect this particular problem. I will try widening the priors to see it helps. From looking at the shinystan for the various models, it seems the step-size is estimate too low near 0, and the energy distributions for the chains are much wider.

 # y ~ Intercept + b
prior(normal(3, 1),class="Intercept"),
prior(normal(0, 3),class="b"),
# v ~ Intercept + b
prior(normal(8, 2),class="Intercept",dpar="shape"),
prior(normal(0, 2),class="b", dpar="shape"),
# y ~ sd
prior(normal(0, 0.03),class='sd')),
6

Hi Samantha,

it’s a bit hard to give general advice on priors since they depend on the likelihood (e.g., link function) and the data at hand. Your \mathrm{Normal}(0,0.03) for sd looks quite tight, that I agree with :) Once again, the only way to sanity check this is to do prior predictive checks. As a start, run brm() with sample_prior="only", and then use pp_check() to see what your priors imply on the outcome space.