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 2.3e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.23 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
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#> Chain 1:
#> Chain 1: Elapsed Time: 0.494 seconds (Warm-up)
#> Chain 1: 0.64 seconds (Sampling)
#> Chain 1: 1.134 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL 'rti0_bayesian' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 1.8e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.18 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2:
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#> Chain 2:
#> Chain 2: Elapsed Time: 0.526 seconds (Warm-up)
#> Chain 2: 0.605 seconds (Sampling)
#> Chain 2: 1.131 seconds (Total)
#> Chain 2:
#>
#> SAMPLING FOR MODEL 'rti0_bayesian' NOW (CHAIN 3).
#> Chain 3:
#> Chain 3: Gradient evaluation took 2.2e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.22 seconds.
#> Chain 3: Adjust your expectations accordingly!
#> Chain 3:
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#> Chain 3:
#> Chain 3: Elapsed Time: 0.513 seconds (Warm-up)
#> Chain 3: 0.752 seconds (Sampling)
#> Chain 3: 1.265 seconds (Total)
#> Chain 3:
#>
#> SAMPLING FOR MODEL 'rti0_bayesian' NOW (CHAIN 4).
#> Chain 4:
#> Chain 4: Gradient evaluation took 1.7e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.17 seconds.
#> Chain 4: Adjust your expectations accordingly!
#> Chain 4:
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#> Chain 4:
#> Chain 4: Elapsed Time: 0.558 seconds (Warm-up)
#> Chain 4: 0.698 seconds (Sampling)
#> Chain 4: 1.256 seconds (Total)
#> Chain 4:
#> 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 4.89 0.07 1.38 2.08 3.95 4.94 5.82 7.56
#> rt_est 1.06 0.00 0.09 0.90 1.00 1.05 1.12 1.24
#> incid_est[1] 335.97 33.96 985.85 7.98 51.73 139.52 336.33 1928.68
#> incid_est[2] 5.55 0.49 13.57 0.17 1.01 2.57 5.87 30.26
#> incid_est[3] 27.35 2.41 66.85 0.85 4.98 12.68 28.94 149.15
#> incid_est[4] 40.87 3.59 99.58 1.28 7.46 18.98 43.28 222.63
#> incid_est[5] 46.08 4.02 111.24 1.46 8.49 21.52 48.93 250.21
#> incid_est[6] 47.84 4.12 113.68 1.56 8.95 22.56 51.02 258.39
#> incid_est[7] 48.29 4.10 112.40 1.63 9.22 23.06 51.79 258.97
#> incid_est[8] 48.25 4.02 109.72 1.70 9.42 23.37 52.10 256.69
#> incid_est[9] 48.03 3.93 106.56 1.76 9.61 23.61 52.24 253.39
#> incid_est[10] 47.77 3.83 103.30 1.83 9.78 23.84 52.32 249.80
#> incid_est[11] 47.49 3.73 100.08 1.89 9.97 24.06 52.38 246.12
#> incid_est[12] 47.21 3.64 96.96 1.96 10.15 24.26 52.42 242.45
#> incid_est[13] 46.95 3.55 93.95 2.04 10.33 24.49 52.46 238.83
#> incid_est[14] 46.69 3.46 91.06 2.11 10.52 24.72 52.50 235.25
#> incid_est[15] 46.44 3.37 88.28 2.19 10.72 24.93 52.54 231.72
#> incid_est[16] 46.20 3.29 85.61 2.27 10.91 25.16 52.60 228.25
#> incid_est[17] 45.96 3.20 83.04 2.35 11.12 25.41 52.61 224.83
#> incid_est[18] 45.74 3.13 80.58 2.43 11.32 25.65 52.65 221.46
#> incid_est[19] 45.53 3.05 78.21 2.52 11.54 25.89 52.72 217.93
#> incid_est[20] 45.32 2.98 75.93 2.62 11.75 26.14 52.79 214.27
#> incid_est[21] 45.13 2.90 73.74 2.71 11.96 26.39 52.86 211.01
#> incid_est[22] 44.39 2.79 70.31 2.79 12.07 26.37 52.31 204.79
#> incid_est[23] 44.34 2.73 68.61 2.89 12.32 26.69 52.45 202.36
#> incid_est[24] 44.19 2.67 66.75 3.00 12.54 26.94 52.47 199.40
#> incid_est[25] 44.00 2.61 64.85 3.10 12.76 27.14 52.44 196.22
#> incid_est[26] 43.80 2.54 62.98 3.21 12.98 27.34 52.41 193.01
#> incid_est[27] 43.61 2.48 61.18 3.32 13.21 27.57 52.39 189.83
#> incid_est[28] 43.43 2.42 59.45 3.44 13.44 27.80 52.35 186.70
#> incid_est[29] 43.25 2.36 57.77 3.56 13.69 28.01 52.34 183.63
#> incid_est[30] 43.09 2.31 56.17 3.69 13.94 28.26 52.34 180.60
#> incid_est[31] 42.93 2.26 54.62 3.82 14.19 28.49 52.33 177.63
#> incid_est[32] 42.78 2.21 53.12 3.96 14.44 28.72 52.31 174.66
#> incid_est[33] 42.64 2.16 51.69 4.10 14.69 28.96 52.31 171.84
#> incid_est[34] 42.50 2.11 50.30 4.24 14.95 29.21 52.31 169.02
#> incid_est[35] 42.37 2.06 48.96 4.39 15.21 29.46 52.30 166.24
#> incid_est[36] 42.25 2.02 47.66 4.55 15.47 29.70 52.26 163.51
#> incid_est[37] 42.14 1.97 46.41 4.71 15.75 29.94 52.24 160.72
#> incid_est[38] 42.03 1.93 45.21 4.88 16.03 30.17 52.22 158.07
#> incid_est[39] 41.93 1.89 44.04 5.07 16.32 30.43 52.16 155.40
#> incid_est[40] 41.84 1.85 42.91 5.25 16.61 30.68 52.18 152.68
#> incid_est[41] 41.76 1.81 41.81 5.45 16.91 30.96 52.18 150.00
#> incid_est[42] 41.68 1.77 40.75 5.65 17.22 31.22 52.16 147.38
#> incid_est[43] 41.61 1.73 39.73 5.86 17.52 31.49 52.15 144.80
#> incid_est[44] 41.54 1.69 38.73 6.08 17.85 31.77 52.12 142.26
#> incid_est[45] 41.49 1.66 37.77 6.30 18.17 32.02 52.08 139.77
#> incid_est[46] 41.44 1.62 36.83 6.53 18.48 32.28 52.04 137.55
#> incid_est[47] 41.39 1.58 35.92 6.77 18.83 32.56 52.03 135.37
#> incid_est[48] 41.36 1.55 35.04 7.02 19.17 32.83 52.08 133.21
#> incid_est[49] 41.33 1.52 34.18 7.28 19.47 33.10 52.06 131.09
#> incid_est[50] 41.30 1.48 33.34 7.55 19.80 33.39 51.99 129.03
#> incid_est[51] 41.29 1.45 32.52 7.82 20.14 33.67 51.93 127.04
#> incid_est[52] 41.28 1.42 31.73 8.10 20.48 33.93 51.91 125.08
#> incid_est[53] 41.28 1.39 30.95 8.39 20.83 34.20 51.90 123.16
#> incid_est[54] 41.28 1.36 30.19 8.69 21.20 34.45 51.90 121.26
#> incid_est[55] 41.29 1.33 29.45 9.01 21.58 34.72 51.86 119.34
#> incid_est[56] 41.31 1.30 28.73 9.33 21.96 35.00 51.85 117.51
#> incid_est[57] 41.33 1.27 28.03 9.66 22.36 35.27 51.87 115.73
#> incid_est[58] 41.36 1.24 27.33 9.99 22.74 35.54 51.88 113.91
#> incid_est[59] 41.40 1.22 26.66 10.33 23.16 35.82 51.89 111.90
#> incid_est[60] 41.45 1.19 25.99 10.71 23.59 36.07 51.83 109.93
#> incid_est[61] 41.50 1.17 25.34 11.11 23.98 36.36 51.85 108.18
#> incid_est[62] 41.56 1.14 24.70 11.52 24.38 36.62 51.86 106.46
#> incid_est[63] 41.62 1.12 24.07 11.95 24.83 36.89 51.85 104.74
#> incid_est[64] 41.69 1.10 23.45 12.39 25.26 37.16 51.80 102.90
#> incid_est[65] 41.77 1.07 22.84 12.83 25.71 37.47 51.80 101.38
#> incid_est[66] 41.86 1.05 22.24 13.27 26.16 37.79 51.73 99.87
#> incid_est[67] 41.95 1.03 21.65 13.77 26.64 38.08 51.69 98.29
#> incid_est[68] 42.05 1.00 21.07 14.27 27.10 38.41 51.76 96.68
#> incid_est[69] 42.16 0.98 20.49 14.79 27.58 38.72 51.77 95.09
#> incid_est[70] 42.27 0.96 19.92 15.27 28.07 38.99 51.76 93.53
#> incid_est[71] 42.39 0.93 19.36 15.79 28.57 39.25 51.77 92.00
#> incid_est[72] 42.52 0.91 18.81 16.32 29.12 39.52 51.75 90.49
#> incid_est[73] 42.65 0.89 18.25 16.88 29.61 39.81 51.77 89.04
#> incid_est[74] 42.80 0.86 17.71 17.48 30.14 40.12 51.84 87.54
#> incid_est[75] 42.95 0.84 17.17 18.08 30.67 40.47 51.90 86.11
#> incid_est[76] 43.11 0.82 16.63 18.72 31.20 40.79 51.93 84.61
#> incid_est[77] 43.27 0.79 16.09 19.36 31.76 41.10 51.93 82.88
#> incid_est[78] 43.45 0.77 15.56 20.05 32.30 41.43 51.92 81.39
#> incid_est[79] 43.63 0.74 15.03 20.73 32.84 41.74 51.92 79.80
#> incid_est[80] 43.82 0.71 14.50 21.51 33.40 42.08 51.91 78.67
#> incid_est[81] 44.02 0.69 13.98 22.26 33.95 42.41 51.89 77.31
#> incid_est[82] 44.22 0.66 13.46 23.01 34.57 42.75 51.90 76.06
#> incid_est[83] 44.44 0.63 12.93 23.77 35.16 43.10 51.86 74.89
#> incid_est[84] 44.66 0.61 12.41 24.56 35.77 43.43 51.82 73.74
#> incid_est[85] 44.89 0.58 11.89 25.43 36.36 43.77 51.80 72.59
#> incid_est[86] 45.13 0.55 11.37 26.28 36.99 44.17 51.87 71.36
#> incid_est[87] 45.38 0.53 10.85 27.18 37.63 44.49 51.85 70.07
#> incid_est[88] 45.64 0.50 10.33 28.05 38.25 44.84 51.94 69.02
#> incid_est[89] 45.90 0.47 9.81 28.98 38.92 45.19 51.95 68.00
#> incid_est[90] 46.18 0.45 9.29 30.05 39.53 45.50 51.96 66.85
#> incid_est[91] 46.46 0.42 8.77 31.05 40.20 45.86 51.98 65.76
#> incid_est[92] 46.76 0.39 8.26 32.08 40.91 46.25 52.01 64.66
#> incid_est[93] 47.06 0.36 7.74 33.13 41.60 46.65 51.98 63.62
#> incid_est[94] 47.38 0.34 7.23 34.24 42.31 47.01 51.96 62.73
#> incid_est[95] 47.70 0.31 6.72 35.41 43.02 47.36 51.96 61.81
#> incid_est[96] 48.04 0.28 6.22 36.48 43.73 47.75 52.03 61.10
#> incid_est[97] 48.38 0.25 5.73 37.59 44.46 48.16 52.02 60.24
#> incid_est[98] 48.74 0.22 5.26 38.78 45.15 48.55 52.08 59.44
#> incid_est[99] 49.10 0.19 4.81 39.87 45.80 48.95 52.16 58.93
#> incid_est[100] 49.48 0.16 4.39 40.92 46.45 49.41 52.30 58.32
#> incid_est[101] 49.87 0.13 4.01 41.95 47.18 49.75 52.50 57.95
#> incid_est[102] 50.27 0.11 3.70 42.86 47.84 50.17 52.72 57.65
#> incid_est[103] 50.68 0.08 3.48 43.75 48.35 50.64 52.99 57.65
#> incid_est[104] 51.11 0.06 3.37 44.52 48.84 51.04 53.26 58.00
#> incid_est[105] 51.54 0.06 3.39 44.89 49.32 51.52 53.65 58.51
#> incid_est[106] 51.99 0.07 3.55 45.19 49.67 51.91 54.23 59.36
#> incid_est[107] 52.45 0.09 3.82 45.21 49.93 52.30 54.90 60.48
#> incid_est[108] 52.93 0.12 4.21 45.14 50.04 52.81 55.62 61.76
#> incid_est[109] 53.42 0.15 4.68 44.95 50.18 53.26 56.42 63.36
#> incid_est[110] 53.92 0.19 5.22 44.62 50.30 53.66 57.23 65.18
#> incid_est[111] 54.44 0.22 5.82 44.24 50.40 54.09 58.05 67.08
#> incid_est[112] 54.97 0.26 6.47 43.81 50.43 54.54 58.84 69.12
#> incid_est[113] 55.51 0.30 7.15 43.30 50.48 54.95 59.84 71.22
#> incid_est[114] 56.07 0.35 7.88 42.80 50.52 55.41 60.80 73.46
#> incid_est[115] 56.65 0.39 8.64 42.20 50.53 55.89 61.75 75.99
#> incid_est[116] 57.24 0.43 9.43 41.46 50.59 56.35 62.84 78.70
#> incid_est[117] 57.85 0.48 10.25 40.88 50.61 56.91 63.90 81.24
#> lp__ 1507.25 0.03 0.94 1504.78 1506.88 1507.56 1507.94 1508.18
#> n_eff Rhat
#> log_i0 388 1.01
#> rt_est 386 1.01
#> incid_est[1] 843 1.01
#> incid_est[2] 770 1.01
#> incid_est[3] 770 1.01
#> incid_est[4] 769 1.01
#> incid_est[5] 765 1.01
#> incid_est[6] 760 1.01
#> incid_est[7] 753 1.01
#> incid_est[8] 745 1.01
#> incid_est[9] 736 1.01
#> incid_est[10] 728 1.01
#> incid_est[11] 719 1.01
#> incid_est[12] 711 1.01
#> incid_est[13] 702 1.01
#> incid_est[14] 694 1.01
#> incid_est[15] 687 1.01
#> incid_est[16] 679 1.01
#> incid_est[17] 672 1.01
#> incid_est[18] 664 1.01
#> incid_est[19] 658 1.01
#> incid_est[20] 651 1.01
#> incid_est[21] 644 1.01
#> incid_est[22] 636 1.01
#> incid_est[23] 631 1.01
#> incid_est[24] 625 1.01
#> incid_est[25] 619 1.01
#> incid_est[26] 613 1.01
#> incid_est[27] 608 1.01
#> incid_est[28] 602 1.01
#> incid_est[29] 597 1.01
#> incid_est[30] 592 1.01
#> incid_est[31] 586 1.01
#> incid_est[32] 580 1.01
#> incid_est[33] 575 1.01
#> incid_est[34] 569 1.01
#> incid_est[35] 564 1.01
#> incid_est[36] 559 1.01
#> incid_est[37] 554 1.01
#> incid_est[38] 549 1.01
#> incid_est[39] 545 1.01
#> incid_est[40] 541 1.01
#> incid_est[41] 536 1.01
#> incid_est[42] 532 1.01
#> incid_est[43] 528 1.01
#> incid_est[44] 524 1.01
#> incid_est[45] 521 1.01
#> incid_est[46] 517 1.01
#> incid_est[47] 514 1.01
#> incid_est[48] 511 1.01
#> incid_est[49] 508 1.01
#> incid_est[50] 505 1.01
#> incid_est[51] 502 1.01
#> incid_est[52] 499 1.01
#> incid_est[53] 497 1.01
#> incid_est[54] 494 1.01
#> incid_est[55] 492 1.01
#> incid_est[56] 489 1.01
#> incid_est[57] 487 1.01
#> incid_est[58] 485 1.01
#> incid_est[59] 480 1.01
#> incid_est[60] 475 1.01
#> incid_est[61] 470 1.01
#> incid_est[62] 466 1.01
#> incid_est[63] 462 1.01
#> incid_est[64] 458 1.01
#> incid_est[65] 453 1.01
#> incid_est[66] 449 1.01
#> incid_est[67] 445 1.01
#> incid_est[68] 441 1.01
#> incid_est[69] 437 1.01
#> incid_est[70] 434 1.01
#> incid_est[71] 430 1.01
#> incid_est[72] 427 1.01
#> incid_est[73] 424 1.01
#> incid_est[74] 421 1.01
#> incid_est[75] 418 1.01
#> incid_est[76] 416 1.01
#> incid_est[77] 414 1.01
#> incid_est[78] 414 1.01
#> incid_est[79] 414 1.01
#> incid_est[80] 415 1.01
#> incid_est[81] 416 1.01
#> incid_est[82] 416 1.01
#> incid_est[83] 418 1.01
#> incid_est[84] 419 1.01
#> incid_est[85] 421 1.01
#> incid_est[86] 422 1.01
#> incid_est[87] 424 1.01
#> incid_est[88] 426 1.01
#> incid_est[89] 428 1.01
#> incid_est[90] 432 1.01
#> incid_est[91] 437 1.01
#> incid_est[92] 443 1.01
#> incid_est[93] 452 1.01
#> incid_est[94] 464 1.01
#> incid_est[95] 480 1.00
#> incid_est[96] 502 1.00
#> incid_est[97] 535 1.00
#> incid_est[98] 579 1.00
#> incid_est[99] 637 1.00
#> incid_est[100] 733 1.00
#> incid_est[101] 903 1.00
#> incid_est[102] 1234 1.00
#> incid_est[103] 2013 1.00
#> incid_est[104] 3188 1.00
#> incid_est[105] 3415 1.00
#> incid_est[106] 2609 1.00
#> incid_est[107] 1828 1.00
#> incid_est[108] 1301 1.00
#> incid_est[109] 973 1.00
#> incid_est[110] 786 1.00
#> incid_est[111] 671 1.00
#> incid_est[112] 600 1.00
#> incid_est[113] 553 1.01
#> incid_est[114] 520 1.01
#> incid_est[115] 495 1.01
#> incid_est[116] 477 1.01
#> incid_est[117] 462 1.01
#> lp__ 779 1.01
#>
#> Samples were drawn using NUTS(diag_e) at Tue Aug 18 02:45:37 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).