si_trunc <- 20
si_distr <- EpiEstim::discr_si(seq(0, si_trunc), 6.48, 3.83)
si_distr <- si_distr / sum(si_distr)
## Default args for iter and chains
jointlyr::jointly_estimate(10, 100, incid, si_distr)
#>
#> SAMPLING FOR MODEL 'rti0_bayesian' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 2.4e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.24 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
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#> Chain 1:
#> Chain 1: Elapsed Time: 0.592 seconds (Warm-up)
#> Chain 1: 0.591 seconds (Sampling)
#> Chain 1: 1.183 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL 'rti0_bayesian' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 2.5e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.25 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2:
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#> Chain 2: Elapsed Time: 0.63 seconds (Warm-up)
#> Chain 2: 0.613 seconds (Sampling)
#> Chain 2: 1.243 seconds (Total)
#> Chain 2:
#>
#> SAMPLING FOR MODEL 'rti0_bayesian' NOW (CHAIN 3).
#> Chain 3:
#> Chain 3: Gradient evaluation took 1.8e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.18 seconds.
#> Chain 3: Adjust your expectations accordingly!
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#> Chain 3:
#>
#> SAMPLING FOR MODEL 'rti0_bayesian' NOW (CHAIN 4).
#> Chain 4:
#> Chain 4: Gradient evaluation took 1.8e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.18 seconds.
#> Chain 4: Adjust your expectations accordingly!
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#> Chain 4: Elapsed Time: 0.631 seconds (Warm-up)
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#> Chain 4: 1.273 seconds (Total)
#> Chain 4:
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Inference for Stan model: rti0_bayesian.
#> 4 chains, each with iter=2000; warmup=1000; thin=1;
#> post-warmup draws per chain=1000, total post-warmup draws=4000.
#>
#> mean se_mean sd 2.5% 25% 50% 75% 97.5%
#> log_i0 4.99 0.08 1.49 2.02 3.95 4.99 6.00 7.89
#> rt_est 1.05 0.01 0.09 0.88 0.99 1.05 1.12 1.24
#> incid_est[1] 420.76 44.68 838.06 7.52 51.91 146.43 403.97 2676.75
#> incid_est[2] 6.86 0.67 12.42 0.16 1.01 2.69 6.97 41.29
#> incid_est[3] 33.80 3.31 61.21 0.81 4.99 13.26 34.35 203.53
#> incid_est[4] 50.49 4.94 91.28 1.22 7.49 19.85 51.37 303.70
#> incid_est[5] 56.88 5.54 102.29 1.40 8.52 22.50 58.04 341.01
#> incid_est[6] 58.97 5.70 105.12 1.49 8.99 23.56 60.49 351.59
#> incid_est[7] 59.41 5.68 104.70 1.56 9.26 24.05 61.33 351.65
#> incid_est[8] 59.23 5.60 103.04 1.63 9.47 24.34 61.59 347.73
#> incid_est[9] 58.84 5.50 100.95 1.69 9.65 24.58 61.62 342.36
#> incid_est[10] 58.38 5.38 98.73 1.75 9.84 24.80 61.57 336.40
#> incid_est[11] 57.91 5.27 96.50 1.82 10.03 25.00 61.50 330.35
#> incid_est[12] 57.43 5.16 94.30 1.89 10.22 25.18 61.40 324.44
#> incid_est[13] 56.97 5.05 92.16 1.96 10.41 25.38 61.34 318.66
#> incid_est[14] 56.51 4.94 90.06 2.03 10.61 25.58 61.29 312.99
#> incid_est[15] 56.07 4.84 88.02 2.11 10.81 25.79 61.19 307.41
#> incid_est[16] 55.64 4.74 86.03 2.19 11.00 26.02 61.16 301.93
#> incid_est[17] 55.23 4.64 84.09 2.27 11.21 26.25 61.07 296.55
#> incid_est[18] 54.82 4.54 82.20 2.35 11.41 26.49 60.99 291.26
#> incid_est[19] 54.43 4.44 80.35 2.44 11.62 26.73 60.89 286.07
#> incid_est[20] 54.04 4.35 78.56 2.53 11.84 26.96 60.84 280.97
#> incid_est[21] 53.67 4.26 76.80 2.63 12.06 27.19 60.76 275.96
#> incid_est[22] 52.63 4.10 73.87 2.71 12.18 27.15 60.01 266.92
#> incid_est[23] 52.45 4.03 72.50 2.82 12.42 27.43 60.13 262.86
#> incid_est[24] 52.14 3.95 70.95 2.93 12.66 27.68 60.11 258.42
#> incid_est[25] 51.78 3.86 69.32 3.03 12.87 27.91 60.00 253.69
#> incid_est[26] 51.41 3.78 67.71 3.15 13.09 28.14 59.89 248.94
#> incid_est[27] 51.05 3.69 66.12 3.26 13.31 28.35 59.81 244.22
#> incid_est[28] 50.70 3.61 64.58 3.38 13.56 28.55 59.65 239.30
#> incid_est[29] 50.36 3.53 63.07 3.50 13.80 28.77 59.53 234.47
#> incid_est[30] 50.03 3.45 61.60 3.62 14.05 28.97 59.42 229.74
#> incid_est[31] 49.72 3.37 60.17 3.75 14.30 29.19 59.30 225.12
#> incid_est[32] 49.41 3.30 58.77 3.89 14.56 29.39 59.19 220.75
#> incid_est[33] 49.11 3.22 57.41 4.03 14.82 29.60 59.07 216.63
#> incid_est[34] 48.83 3.15 56.07 4.18 15.07 29.82 58.95 212.60
#> incid_est[35] 48.55 3.08 54.77 4.34 15.34 30.03 58.83 208.64
#> incid_est[36] 48.28 3.01 53.50 4.50 15.61 30.25 58.69 204.75
#> incid_est[37] 48.03 2.94 52.26 4.67 15.87 30.49 58.57 200.94
#> incid_est[38] 47.78 2.88 51.05 4.85 16.15 30.73 58.44 197.19
#> incid_est[39] 47.54 2.81 49.86 5.03 16.44 30.96 58.30 193.51
#> incid_est[40] 47.31 2.75 48.70 5.22 16.74 31.21 58.15 189.64
#> incid_est[41] 47.10 2.68 47.57 5.39 17.03 31.46 58.06 185.84
#> incid_est[42] 46.89 2.62 46.46 5.58 17.32 31.69 57.99 182.12
#> incid_est[43] 46.69 2.56 45.38 5.77 17.63 31.93 57.92 178.47
#> incid_est[44] 46.49 2.50 44.32 5.99 17.93 32.17 57.78 174.90
#> incid_est[45] 46.31 2.45 43.28 6.21 18.24 32.42 57.72 171.50
#> incid_est[46] 46.14 2.39 42.27 6.44 18.57 32.69 57.63 168.41
#> incid_est[47] 45.97 2.33 41.27 6.68 18.92 32.97 57.52 165.41
#> incid_est[48] 45.82 2.28 40.30 6.91 19.26 33.21 57.43 162.46
#> incid_est[49] 45.67 2.22 39.34 7.17 19.60 33.47 57.34 159.37
#> incid_est[50] 45.53 2.17 38.41 7.43 19.94 33.73 57.22 155.99
#> incid_est[51] 45.40 2.12 37.49 7.69 20.32 34.00 57.14 152.73
#> incid_est[52] 45.28 2.07 36.59 7.97 20.66 34.26 57.00 149.82
#> incid_est[53] 45.17 2.02 35.70 8.26 21.02 34.52 56.88 147.11
#> incid_est[54] 45.07 1.97 34.84 8.56 21.42 34.79 56.77 144.45
#> incid_est[55] 44.97 1.92 33.99 8.87 21.79 35.08 56.76 141.67
#> incid_est[56] 44.88 1.87 33.15 9.18 22.19 35.35 56.69 138.62
#> incid_est[57] 44.80 1.83 32.33 9.50 22.56 35.62 56.58 135.71
#> incid_est[58] 44.73 1.78 31.52 9.84 22.93 35.91 56.43 133.22
#> incid_est[59] 44.67 1.74 30.73 10.18 23.34 36.16 56.32 130.65
#> incid_est[60] 44.62 1.69 29.95 10.56 23.75 36.48 56.28 128.11
#> incid_est[61] 44.57 1.65 29.18 10.94 24.15 36.76 56.17 125.26
#> incid_est[62] 44.54 1.60 28.43 11.34 24.55 37.05 56.05 122.63
#> incid_est[63] 44.51 1.56 27.68 11.76 24.95 37.34 55.93 120.11
#> incid_est[64] 44.49 1.52 26.95 12.20 25.40 37.61 55.73 117.64
#> incid_est[65] 44.48 1.48 26.22 12.65 25.83 37.84 55.61 115.02
#> incid_est[66] 44.47 1.44 25.51 13.12 26.25 38.09 55.56 112.86
#> incid_est[67] 44.48 1.40 24.81 13.60 26.71 38.39 55.44 110.54
#> incid_est[68] 44.49 1.36 24.11 14.09 27.17 38.68 55.33 108.28
#> incid_est[69] 44.51 1.32 23.43 14.59 27.63 38.97 55.21 106.26
#> incid_est[70] 44.54 1.28 22.75 15.12 28.09 39.28 55.11 104.28
#> incid_est[71] 44.58 1.24 22.08 15.66 28.56 39.60 54.99 102.14
#> incid_est[72] 44.63 1.20 21.41 16.22 29.07 39.94 54.86 100.13
#> incid_est[73] 44.69 1.16 20.76 16.80 29.60 40.25 54.72 98.18
#> incid_est[74] 44.75 1.12 20.11 17.41 30.12 40.57 54.64 96.31
#> incid_est[75] 44.82 1.09 19.46 18.03 30.62 40.85 54.52 94.47
#> incid_est[76] 44.91 1.05 18.82 18.65 31.18 41.18 54.44 92.68
#> incid_est[77] 45.00 1.01 18.19 19.26 31.69 41.45 54.30 90.88
#> incid_est[78] 45.10 0.98 17.56 19.90 32.24 41.78 54.21 88.73
#> incid_est[79] 45.20 0.94 16.93 20.65 32.81 42.09 54.10 86.94
#> incid_est[80] 45.32 0.90 16.31 21.43 33.39 42.43 54.02 85.37
#> incid_est[81] 45.45 0.87 15.69 22.21 33.98 42.75 53.92 83.82
#> incid_est[82] 45.59 0.83 15.08 22.98 34.58 43.11 53.84 82.29
#> incid_est[83] 45.73 0.80 14.47 23.76 35.16 43.40 53.79 80.85
#> incid_est[84] 45.89 0.76 13.86 24.63 35.77 43.71 53.72 79.34
#> incid_est[85] 46.05 0.73 13.25 25.53 36.39 44.10 53.67 77.63
#> incid_est[86] 46.22 0.69 12.65 26.41 37.04 44.43 53.56 76.00
#> incid_est[87] 46.41 0.66 12.05 27.31 37.69 44.80 53.50 74.32
#> incid_est[88] 46.60 0.62 11.45 28.25 38.32 45.16 53.47 73.08
#> incid_est[89] 46.80 0.59 10.85 29.17 38.96 45.53 53.37 71.62
#> incid_est[90] 47.02 0.55 10.25 30.08 39.64 45.90 53.30 70.25
#> incid_est[91] 47.24 0.52 9.66 31.12 40.27 46.24 53.24 68.77
#> incid_est[92] 47.47 0.48 9.07 32.17 40.94 46.61 53.05 67.42
#> incid_est[93] 47.72 0.44 8.48 33.26 41.61 46.95 52.97 66.31
#> incid_est[94] 47.97 0.41 7.90 34.29 42.28 47.28 52.89 65.21
#> incid_est[95] 48.24 0.37 7.32 35.52 42.96 47.67 52.86 64.15
#> incid_est[96] 48.52 0.34 6.76 36.63 43.61 48.09 52.83 63.12
#> incid_est[97] 48.81 0.30 6.20 37.82 44.32 48.47 52.80 62.12
#> incid_est[98] 49.11 0.27 5.66 38.95 45.06 48.85 52.76 61.20
#> incid_est[99] 49.42 0.23 5.15 40.15 45.71 49.13 52.77 60.46
#> incid_est[100] 49.74 0.19 4.67 41.25 46.40 49.50 52.80 59.78
#> incid_est[101] 50.08 0.16 4.24 42.31 47.08 49.94 52.86 59.02
#> incid_est[102] 50.42 0.12 3.88 43.18 47.69 50.30 53.03 58.66
#> incid_est[103] 50.78 0.09 3.62 44.08 48.25 50.66 53.19 58.31
#> incid_est[104] 51.15 0.06 3.49 44.77 48.72 51.06 53.41 58.21
#> incid_est[105] 51.54 0.06 3.50 45.11 49.12 51.43 53.79 58.73
#> incid_est[106] 51.94 0.07 3.66 45.10 49.43 51.79 54.29 59.41
#> incid_est[107] 52.35 0.10 3.96 44.99 49.63 52.21 54.82 60.51
#> incid_est[108] 52.78 0.14 4.37 44.63 49.75 52.57 55.46 61.86
#> incid_est[109] 53.22 0.18 4.88 44.12 49.90 52.99 56.21 63.60
#> incid_est[110] 53.67 0.22 5.47 43.66 49.92 53.35 57.01 65.54
#> incid_est[111] 54.14 0.26 6.11 43.07 49.90 53.78 57.98 67.44
#> incid_est[112] 54.62 0.31 6.80 42.44 49.83 54.20 58.84 69.66
#> incid_est[113] 55.12 0.35 7.54 42.01 49.80 54.58 59.81 71.60
#> incid_est[114] 55.63 0.40 8.31 41.19 49.76 54.99 60.73 73.89
#> incid_est[115] 56.16 0.44 9.11 40.51 49.68 55.38 61.77 76.23
#> incid_est[116] 56.71 0.49 9.95 39.91 49.55 55.81 62.80 78.85
#> incid_est[117] 57.27 0.54 10.81 39.16 49.41 56.20 63.83 81.44
#> lp__ 1507.14 0.04 1.03 1504.38 1506.73 1507.46 1507.89 1508.17
#> n_eff Rhat
#> log_i0 333 1.01
#> rt_est 338 1.01
#> incid_est[1] 352 1.02
#> incid_est[2] 342 1.02
#> incid_est[3] 342 1.02
#> incid_est[4] 342 1.02
#> incid_est[5] 341 1.02
#> incid_est[6] 340 1.02
#> incid_est[7] 340 1.02
#> incid_est[8] 338 1.02
#> incid_est[9] 337 1.02
#> incid_est[10] 336 1.02
#> incid_est[11] 335 1.02
#> incid_est[12] 334 1.02
#> incid_est[13] 333 1.02
#> incid_est[14] 332 1.02
#> incid_est[15] 331 1.02
#> incid_est[16] 330 1.02
#> incid_est[17] 329 1.02
#> incid_est[18] 328 1.02
#> incid_est[19] 327 1.02
#> incid_est[20] 326 1.02
#> incid_est[21] 325 1.02
#> incid_est[22] 324 1.02
#> incid_est[23] 324 1.02
#> incid_est[24] 323 1.02
#> incid_est[25] 322 1.02
#> incid_est[26] 321 1.02
#> incid_est[27] 321 1.02
#> incid_est[28] 320 1.02
#> incid_est[29] 320 1.02
#> incid_est[30] 319 1.02
#> incid_est[31] 318 1.02
#> incid_est[32] 318 1.02
#> incid_est[33] 317 1.02
#> incid_est[34] 317 1.02
#> incid_est[35] 316 1.02
#> incid_est[36] 316 1.02
#> incid_est[37] 316 1.02
#> incid_est[38] 315 1.02
#> incid_est[39] 315 1.02
#> incid_est[40] 315 1.02
#> incid_est[41] 314 1.02
#> incid_est[42] 314 1.02
#> incid_est[43] 314 1.02
#> incid_est[44] 314 1.02
#> incid_est[45] 313 1.02
#> incid_est[46] 313 1.02
#> incid_est[47] 313 1.02
#> incid_est[48] 313 1.02
#> incid_est[49] 313 1.02
#> incid_est[50] 313 1.02
#> incid_est[51] 313 1.02
#> incid_est[52] 313 1.02
#> incid_est[53] 313 1.02
#> incid_est[54] 313 1.02
#> incid_est[55] 313 1.02
#> incid_est[56] 313 1.02
#> incid_est[57] 313 1.02
#> incid_est[58] 313 1.02
#> incid_est[59] 313 1.02
#> incid_est[60] 314 1.02
#> incid_est[61] 314 1.02
#> incid_est[62] 314 1.02
#> incid_est[63] 314 1.02
#> incid_est[64] 315 1.02
#> incid_est[65] 315 1.02
#> incid_est[66] 315 1.02
#> incid_est[67] 316 1.02
#> incid_est[68] 316 1.01
#> incid_est[69] 317 1.01
#> incid_est[70] 317 1.01
#> incid_est[71] 318 1.01
#> incid_est[72] 318 1.01
#> incid_est[73] 319 1.01
#> incid_est[74] 320 1.01
#> incid_est[75] 320 1.01
#> incid_est[76] 321 1.01
#> incid_est[77] 322 1.01
#> incid_est[78] 323 1.01
#> incid_est[79] 324 1.01
#> incid_est[80] 325 1.01
#> incid_est[81] 326 1.01
#> incid_est[82] 328 1.01
#> incid_est[83] 329 1.01
#> incid_est[84] 331 1.01
#> incid_est[85] 333 1.01
#> incid_est[86] 335 1.01
#> incid_est[87] 337 1.01
#> incid_est[88] 340 1.01
#> incid_est[89] 343 1.01
#> incid_est[90] 347 1.01
#> incid_est[91] 352 1.01
#> incid_est[92] 358 1.01
#> incid_est[93] 365 1.01
#> incid_est[94] 374 1.01
#> incid_est[95] 385 1.01
#> incid_est[96] 401 1.01
#> incid_est[97] 423 1.01
#> incid_est[98] 454 1.01
#> incid_est[99] 502 1.01
#> incid_est[100] 584 1.01
#> incid_est[101] 731 1.00
#> incid_est[102] 1044 1.00
#> incid_est[103] 1683 1.00
#> incid_est[104] 3070 1.00
#> incid_est[105] 3562 1.00
#> incid_est[106] 2702 1.00
#> incid_est[107] 1492 1.00
#> incid_est[108] 1003 1.01
#> incid_est[109] 736 1.01
#> incid_est[110] 607 1.01
#> incid_est[111] 536 1.01
#> incid_est[112] 491 1.01
#> incid_est[113] 460 1.01
#> incid_est[114] 439 1.01
#> incid_est[115] 424 1.01
#> incid_est[116] 413 1.01
#> incid_est[117] 405 1.01
#> lp__ 638 1.01
#>
#> Samples were drawn using NUTS(diag_e) at Sun Jul 19 04:58:04 2026.
#> For each parameter, n_eff is a crude measure of effective sample size,
#> and Rhat is the potential scale reduction factor on split chains (at
#> convergence, Rhat=1).