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 4.6e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.46 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
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#> Chain 1:
#> Chain 1: Elapsed Time: 0.881 seconds (Warm-up)
#> Chain 1: 0.693 seconds (Sampling)
#> Chain 1: 1.574 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL 'rti0_bayesian' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 2e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.2 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2:
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#> Chain 2:
#> Chain 2: Elapsed Time: 0.592 seconds (Warm-up)
#> Chain 2: 0.651 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 1.9e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.19 seconds.
#> Chain 3: Adjust your expectations accordingly!
#> Chain 3:
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#> Chain 3:
#> Chain 3: Elapsed Time: 0.575 seconds (Warm-up)
#> Chain 3: 0.748 seconds (Sampling)
#> Chain 3: 1.323 seconds (Total)
#> Chain 3:
#>
#> SAMPLING FOR MODEL 'rti0_bayesian' NOW (CHAIN 4).
#> Chain 4:
#> Chain 4: Gradient evaluation took 1.9e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.19 seconds.
#> Chain 4: Adjust your expectations accordingly!
#> Chain 4:
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#> Chain 4:
#> Chain 4: Elapsed Time: 0.657 seconds (Warm-up)
#> Chain 4: 0.612 seconds (Sampling)
#> Chain 4: 1.269 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 5.09 0.06 1.43 2.57 4.09 5.00 6.06 7.99
#> rt_est 1.05 0.00 0.09 0.87 0.98 1.05 1.11 1.21
#> incid_est[1] 493.73 65.68 1437.75 13.08 59.75 148.39 426.80 2948.41
#> incid_est[2] 7.86 0.92 19.94 0.28 1.16 2.73 7.35 45.29
#> incid_est[3] 38.75 4.51 98.27 1.36 5.70 13.45 36.25 223.22
#> incid_est[4] 57.87 6.72 146.39 2.04 8.54 20.15 54.20 332.99
#> incid_est[5] 65.12 7.51 163.55 2.34 9.72 22.84 61.21 373.58
#> incid_est[6] 67.38 7.68 167.18 2.49 10.25 23.94 63.74 384.61
#> incid_est[7] 67.72 7.60 165.35 2.59 10.56 24.46 64.56 383.94
#> incid_est[8] 67.34 7.42 161.44 2.67 10.78 24.77 64.80 378.84
#> incid_est[9] 66.71 7.21 156.82 2.76 10.97 25.01 64.81 372.15
#> incid_est[10] 66.00 6.99 152.03 2.84 11.17 25.23 64.73 364.96
#> incid_est[11] 65.27 6.78 147.29 2.93 11.36 25.44 64.63 357.97
#> incid_est[12] 64.56 6.57 142.67 3.02 11.55 25.64 64.56 351.10
#> incid_est[13] 63.86 6.36 138.20 3.11 11.75 25.84 64.50 344.45
#> incid_est[14] 63.19 6.17 133.88 3.20 11.95 26.05 64.40 337.88
#> incid_est[15] 62.53 5.97 129.72 3.30 12.16 26.28 64.27 331.42
#> incid_est[16] 61.89 5.79 125.70 3.40 12.37 26.49 64.14 325.08
#> incid_est[17] 61.27 5.61 121.82 3.51 12.58 26.71 64.05 318.86
#> incid_est[18] 60.67 5.44 118.08 3.62 12.80 26.94 63.98 312.76
#> incid_est[19] 60.09 5.27 114.47 3.73 13.04 27.17 63.92 306.76
#> incid_est[20] 59.52 5.11 110.99 3.85 13.26 27.40 63.84 300.74
#> incid_est[21] 58.98 4.96 107.63 3.97 13.47 27.64 63.76 294.85
#> incid_est[22] 57.67 4.72 102.43 4.08 13.59 27.61 62.92 284.57
#> incid_est[23] 57.35 4.59 99.78 4.22 13.85 27.93 63.05 280.00
#> incid_est[24] 56.89 4.46 96.90 4.35 14.08 28.18 62.98 274.71
#> incid_est[25] 56.38 4.32 93.94 4.49 14.31 28.40 62.78 269.11
#> incid_est[26] 55.86 4.19 91.04 4.64 14.54 28.63 62.56 263.51
#> incid_est[27] 55.35 4.05 88.22 4.78 14.77 28.86 62.41 258.00
#> incid_est[28] 54.87 3.93 85.50 4.92 15.00 29.08 62.24 252.60
#> incid_est[29] 54.39 3.80 82.88 5.07 15.25 29.30 62.08 247.32
#> incid_est[30] 53.94 3.69 80.35 5.21 15.49 29.52 61.91 242.15
#> incid_est[31] 53.50 3.57 77.91 5.38 15.74 29.74 61.78 237.09
#> incid_est[32] 53.07 3.46 75.55 5.55 16.01 29.97 61.67 232.14
#> incid_est[33] 52.66 3.35 73.27 5.72 16.28 30.21 61.53 227.29
#> incid_est[34] 52.26 3.25 71.07 5.89 16.55 30.43 61.36 222.54
#> incid_est[35] 51.88 3.15 68.95 6.08 16.80 30.63 61.20 217.89
#> incid_est[36] 51.51 3.05 66.89 6.27 17.08 30.84 61.00 213.34
#> incid_est[37] 51.16 2.96 64.91 6.46 17.35 31.08 60.78 208.88
#> incid_est[38] 50.81 2.87 62.98 6.66 17.63 31.32 60.63 204.52
#> incid_est[39] 50.49 2.78 61.13 6.87 17.89 31.58 60.57 200.35
#> incid_est[40] 50.17 2.70 59.33 7.09 18.17 31.85 60.49 196.27
#> incid_est[41] 49.86 2.61 57.59 7.31 18.48 32.10 60.31 192.27
#> incid_est[42] 49.57 2.53 55.90 7.54 18.78 32.31 60.10 188.35
#> incid_est[43] 49.29 2.46 54.27 7.77 19.09 32.56 59.90 184.51
#> incid_est[44] 49.03 2.38 52.69 8.01 19.40 32.83 59.79 180.75
#> incid_est[45] 48.77 2.31 51.16 8.26 19.71 33.06 59.67 177.08
#> incid_est[46] 48.53 2.24 49.67 8.51 20.01 33.31 59.54 173.47
#> incid_est[47] 48.29 2.17 48.23 8.77 20.31 33.59 59.38 169.88
#> incid_est[48] 48.07 2.11 46.84 9.04 20.61 33.84 59.24 166.32
#> incid_est[49] 47.86 2.04 45.48 9.32 20.95 34.09 59.05 162.84
#> incid_est[50] 47.66 1.98 44.17 9.61 21.28 34.32 58.86 159.64
#> incid_est[51] 47.47 1.92 42.89 9.92 21.60 34.59 58.68 156.51
#> incid_est[52] 47.29 1.86 41.65 10.22 21.94 34.86 58.53 153.32
#> incid_est[53] 47.12 1.80 40.44 10.52 22.29 35.13 58.39 150.31
#> incid_est[54] 46.97 1.75 39.26 10.84 22.62 35.36 58.28 147.19
#> incid_est[55] 46.82 1.69 38.12 11.18 22.97 35.58 58.18 144.23
#> incid_est[56] 46.68 1.64 37.01 11.52 23.33 35.82 58.06 141.52
#> incid_est[57] 46.55 1.59 35.93 11.87 23.70 36.13 57.91 138.85
#> incid_est[58] 46.44 1.54 34.87 12.23 24.09 36.43 57.75 136.09
#> incid_est[59] 46.33 1.49 33.85 12.58 24.47 36.68 57.62 133.26
#> incid_est[60] 46.23 1.44 32.84 12.92 24.87 36.95 57.50 130.49
#> incid_est[61] 46.14 1.40 31.86 13.28 25.27 37.22 57.46 127.78
#> incid_est[62] 46.06 1.35 30.91 13.70 25.68 37.50 57.29 125.14
#> incid_est[63] 45.99 1.31 29.98 14.13 26.09 37.78 57.12 122.58
#> incid_est[64] 45.93 1.27 29.06 14.57 26.52 38.02 56.99 120.03
#> incid_est[65] 45.88 1.22 28.17 15.03 26.95 38.27 56.87 117.50
#> incid_est[66] 45.84 1.18 27.30 15.48 27.40 38.56 56.67 115.06
#> incid_est[67] 45.81 1.14 26.45 15.92 27.84 38.83 56.50 112.67
#> incid_est[68] 45.79 1.10 25.61 16.40 28.28 39.11 56.36 110.40
#> incid_est[69] 45.77 1.07 24.79 16.91 28.72 39.44 56.14 108.24
#> incid_est[70] 45.77 1.03 23.98 17.40 29.16 39.72 55.93 106.12
#> incid_est[71] 45.78 0.99 23.19 17.88 29.64 40.02 55.77 104.05
#> incid_est[72] 45.79 0.96 22.42 18.38 30.11 40.32 55.67 101.96
#> incid_est[73] 45.81 0.92 21.65 18.98 30.59 40.64 55.59 99.59
#> incid_est[74] 45.85 0.89 20.90 19.58 31.10 40.94 55.38 97.49
#> incid_est[75] 45.89 0.85 20.17 20.15 31.61 41.25 55.29 95.63
#> incid_est[76] 45.94 0.82 19.44 20.74 32.13 41.54 55.12 93.66
#> incid_est[77] 46.00 0.79 18.72 21.35 32.65 41.82 54.97 91.86
#> incid_est[78] 46.07 0.75 18.02 22.04 33.23 42.11 54.78 90.14
#> incid_est[79] 46.15 0.72 17.32 22.73 33.72 42.46 54.66 88.28
#> incid_est[80] 46.23 0.69 16.63 23.48 34.28 42.77 54.57 86.43
#> incid_est[81] 46.33 0.66 15.95 24.19 34.85 43.11 54.43 84.59
#> incid_est[82] 46.44 0.63 15.28 24.94 35.40 43.44 54.31 82.84
#> incid_est[83] 46.55 0.60 14.62 25.76 36.00 43.77 54.20 81.10
#> incid_est[84] 46.68 0.57 13.96 26.53 36.64 44.09 54.10 79.54
#> incid_est[85] 46.81 0.54 13.31 27.34 37.27 44.47 53.97 77.80
#> incid_est[86] 46.95 0.51 12.66 28.10 37.89 44.83 53.88 76.46
#> incid_est[87] 47.11 0.48 12.02 28.97 38.46 45.16 53.80 74.97
#> incid_est[88] 47.27 0.46 11.39 29.84 39.09 45.53 53.69 73.57
#> incid_est[89] 47.44 0.43 10.76 30.78 39.72 45.90 53.55 72.12
#> incid_est[90] 47.63 0.40 10.14 31.60 40.34 46.21 53.42 70.70
#> incid_est[91] 47.82 0.37 9.53 32.70 40.92 46.54 53.31 69.29
#> incid_est[92] 48.02 0.34 8.92 33.62 41.55 46.89 53.20 67.91
#> incid_est[93] 48.23 0.32 8.32 34.71 42.21 47.20 53.09 66.56
#> incid_est[94] 48.45 0.29 7.72 35.74 42.89 47.54 53.01 65.33
#> incid_est[95] 48.69 0.26 7.14 36.69 43.61 47.95 53.00 64.15
#> incid_est[96] 48.93 0.23 6.57 37.74 44.29 48.34 52.95 62.95
#> incid_est[97] 49.18 0.21 6.02 38.85 44.94 48.74 52.93 61.98
#> incid_est[98] 49.45 0.18 5.48 39.88 45.61 49.12 52.86 60.91
#> incid_est[99] 49.72 0.16 4.98 40.81 46.25 49.47 52.87 59.98
#> incid_est[100] 50.00 0.13 4.52 41.85 46.84 49.84 52.87 59.27
#> incid_est[101] 50.30 0.11 4.11 42.76 47.50 50.15 52.91 58.66
#> incid_est[102] 50.61 0.08 3.78 43.53 48.04 50.49 53.06 58.44
#> incid_est[103] 50.93 0.07 3.54 44.25 48.55 50.83 53.24 58.13
#> incid_est[104] 51.26 0.06 3.43 44.75 48.98 51.15 53.45 58.18
#> incid_est[105] 51.60 0.06 3.46 45.15 49.27 51.51 53.80 58.58
#> incid_est[106] 51.95 0.07 3.63 45.18 49.44 51.81 54.27 59.37
#> incid_est[107] 52.32 0.10 3.92 45.04 49.58 52.14 54.84 60.28
#> incid_est[108] 52.69 0.12 4.32 44.65 49.71 52.55 55.53 61.39
#> incid_est[109] 53.08 0.15 4.81 44.10 49.77 52.89 56.23 62.84
#> incid_est[110] 53.48 0.18 5.35 43.56 49.79 53.24 56.99 64.45
#> incid_est[111] 53.90 0.20 5.95 42.88 49.86 53.59 57.85 66.04
#> incid_est[112] 54.33 0.23 6.59 42.21 49.87 53.95 58.70 67.87
#> incid_est[113] 54.77 0.26 7.27 41.44 49.77 54.34 59.55 69.67
#> incid_est[114] 55.22 0.29 7.97 40.61 49.72 54.79 60.47 71.57
#> incid_est[115] 55.69 0.32 8.70 39.90 49.68 55.22 61.36 73.66
#> incid_est[116] 56.17 0.36 9.46 39.12 49.54 55.68 62.32 75.84
#> incid_est[117] 56.67 0.39 10.24 38.43 49.36 56.12 63.23 78.04
#> lp__ 1507.18 0.04 1.03 1504.48 1506.79 1507.49 1507.92 1508.18
#> n_eff Rhat
#> log_i0 614 1.01
#> rt_est 621 1.00
#> incid_est[1] 479 1.01
#> incid_est[2] 474 1.01
#> incid_est[3] 474 1.01
#> incid_est[4] 474 1.01
#> incid_est[5] 474 1.01
#> incid_est[6] 474 1.01
#> incid_est[7] 474 1.01
#> incid_est[8] 473 1.01
#> incid_est[9] 473 1.01
#> incid_est[10] 472 1.01
#> incid_est[11] 472 1.01
#> incid_est[12] 472 1.01
#> incid_est[13] 472 1.01
#> incid_est[14] 472 1.01
#> incid_est[15] 471 1.01
#> incid_est[16] 471 1.01
#> incid_est[17] 471 1.01
#> incid_est[18] 471 1.01
#> incid_est[19] 471 1.01
#> incid_est[20] 471 1.01
#> incid_est[21] 472 1.01
#> incid_est[22] 472 1.01
#> incid_est[23] 472 1.01
#> incid_est[24] 472 1.01
#> incid_est[25] 473 1.01
#> incid_est[26] 473 1.01
#> incid_est[27] 474 1.01
#> incid_est[28] 474 1.01
#> incid_est[29] 475 1.01
#> incid_est[30] 475 1.01
#> incid_est[31] 476 1.01
#> incid_est[32] 477 1.01
#> incid_est[33] 477 1.01
#> incid_est[34] 478 1.01
#> incid_est[35] 479 1.01
#> incid_est[36] 480 1.01
#> incid_est[37] 481 1.01
#> incid_est[38] 482 1.01
#> incid_est[39] 483 1.01
#> incid_est[40] 484 1.01
#> incid_est[41] 485 1.01
#> incid_est[42] 487 1.01
#> incid_est[43] 488 1.01
#> incid_est[44] 489 1.01
#> incid_est[45] 491 1.01
#> incid_est[46] 492 1.01
#> incid_est[47] 493 1.01
#> incid_est[48] 495 1.01
#> incid_est[49] 497 1.01
#> incid_est[50] 498 1.01
#> incid_est[51] 500 1.01
#> incid_est[52] 502 1.01
#> incid_est[53] 503 1.01
#> incid_est[54] 505 1.01
#> incid_est[55] 507 1.01
#> incid_est[56] 509 1.01
#> incid_est[57] 511 1.01
#> incid_est[58] 513 1.01
#> incid_est[59] 515 1.01
#> incid_est[60] 517 1.01
#> incid_est[61] 520 1.01
#> incid_est[62] 522 1.01
#> incid_est[63] 524 1.01
#> incid_est[64] 527 1.01
#> incid_est[65] 529 1.01
#> incid_est[66] 532 1.01
#> incid_est[67] 534 1.01
#> incid_est[68] 537 1.01
#> incid_est[69] 540 1.01
#> incid_est[70] 543 1.01
#> incid_est[71] 546 1.01
#> incid_est[72] 549 1.01
#> incid_est[73] 552 1.01
#> incid_est[74] 555 1.01
#> incid_est[75] 559 1.01
#> incid_est[76] 562 1.01
#> incid_est[77] 566 1.01
#> incid_est[78] 570 1.01
#> incid_est[79] 574 1.01
#> incid_est[80] 578 1.01
#> incid_est[81] 583 1.01
#> incid_est[82] 587 1.01
#> incid_est[83] 593 1.01
#> incid_est[84] 598 1.01
#> incid_est[85] 604 1.01
#> incid_est[86] 611 1.00
#> incid_est[87] 618 1.00
#> incid_est[88] 627 1.00
#> incid_est[89] 636 1.00
#> incid_est[90] 647 1.00
#> incid_est[91] 660 1.00
#> incid_est[92] 675 1.00
#> incid_est[93] 694 1.00
#> incid_est[94] 716 1.00
#> incid_est[95] 745 1.00
#> incid_est[96] 783 1.00
#> incid_est[97] 835 1.00
#> incid_est[98] 910 1.00
#> incid_est[99] 1021 1.00
#> incid_est[100] 1200 1.00
#> incid_est[101] 1508 1.00
#> incid_est[102] 2035 1.00
#> incid_est[103] 2852 1.00
#> incid_est[104] 3610 1.00
#> incid_est[105] 3622 1.00
#> incid_est[106] 2407 1.00
#> incid_est[107] 1683 1.00
#> incid_est[108] 1280 1.00
#> incid_est[109] 1057 1.00
#> incid_est[110] 930 1.00
#> incid_est[111] 851 1.00
#> incid_est[112] 799 1.00
#> incid_est[113] 764 1.00
#> incid_est[114] 740 1.00
#> incid_est[115] 723 1.00
#> incid_est[116] 710 1.00
#> incid_est[117] 701 1.00
#> lp__ 752 1.00
#>
#> Samples were drawn using NUTS(diag_e) at Mon May 25 06:12:37 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).