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 7.7e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.77 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
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#> Chain 1:
#> Chain 1: Elapsed Time: 0.581 seconds (Warm-up)
#> Chain 1: 0.617 seconds (Sampling)
#> Chain 1: 1.198 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: 0.568 seconds (Warm-up)
#> Chain 2: 0.579 seconds (Sampling)
#> Chain 2: 1.147 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!
#> Chain 3:
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#> Chain 3:
#> Chain 3: Elapsed Time: 0.691 seconds (Warm-up)
#> Chain 3: 0.613 seconds (Sampling)
#> Chain 3: 1.304 seconds (Total)
#> 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!
#> Chain 4:
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#> Chain 4:
#> Chain 4: Elapsed Time: 0.55 seconds (Warm-up)
#> Chain 4: 0.631 seconds (Sampling)
#> Chain 4: 1.181 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 5.14 0.06 1.40 2.59 4.17 5.07 6.01 8.17
#> rt_est 1.04 0.00 0.09 0.86 0.99 1.04 1.10 1.20
#> incid_est[1] 526.69 85.62 1539.79 13.30 64.77 159.10 407.01 3517.09
#> incid_est[2] 8.32 1.19 21.45 0.28 1.25 2.91 7.02 52.78
#> incid_est[3] 41.01 5.85 105.72 1.38 6.14 14.33 34.62 260.14
#> incid_est[4] 61.24 8.72 157.49 2.07 9.21 21.46 51.76 387.99
#> incid_est[5] 68.88 9.74 175.97 2.37 10.47 24.33 58.49 435.03
#> incid_est[6] 71.24 9.95 179.91 2.52 11.03 25.49 60.94 447.45
#> incid_est[7] 71.53 9.84 178.00 2.63 11.33 26.04 61.73 446.33
#> incid_est[8] 71.06 9.60 173.84 2.72 11.55 26.35 61.95 440.26
#> incid_est[9] 70.32 9.32 168.91 2.80 11.76 26.59 61.99 431.90
#> incid_est[10] 69.50 9.03 163.79 2.89 11.95 26.82 61.94 422.87
#> incid_est[11] 68.67 8.74 158.72 2.98 12.15 27.02 61.86 414.55
#> incid_est[12] 67.85 8.46 153.77 3.08 12.34 27.24 61.80 406.34
#> incid_est[13] 67.05 8.19 148.98 3.17 12.54 27.44 61.79 398.26
#> incid_est[14] 66.27 7.92 144.34 3.27 12.74 27.66 61.78 390.23
#> incid_est[15] 65.52 7.67 139.85 3.38 12.95 27.88 61.73 382.21
#> incid_est[16] 64.79 7.42 135.52 3.49 13.15 28.11 61.63 374.36
#> incid_est[17] 64.08 7.19 131.34 3.60 13.36 28.33 61.61 366.66
#> incid_est[18] 63.39 6.96 127.30 3.72 13.57 28.55 61.54 359.12
#> incid_est[19] 62.73 6.73 123.39 3.83 13.79 28.77 61.47 351.74
#> incid_est[20] 62.08 6.52 119.62 3.95 14.01 28.99 61.39 344.67
#> incid_est[21] 61.46 6.31 115.97 4.08 14.23 29.21 61.32 337.88
#> incid_est[22] 60.03 5.99 110.34 4.19 14.35 29.16 60.51 326.06
#> incid_est[23] 59.64 5.83 107.46 4.32 14.61 29.45 60.55 320.81
#> incid_est[24] 59.12 5.65 104.31 4.45 14.85 29.69 60.51 314.72
#> incid_est[25] 58.54 5.46 101.09 4.58 15.09 29.90 60.45 308.28
#> incid_est[26] 57.96 5.28 97.92 4.72 15.31 30.11 60.32 301.83
#> incid_est[27] 57.39 5.11 94.84 4.87 15.54 30.33 60.18 295.49
#> incid_est[28] 56.83 4.94 91.87 5.02 15.78 30.53 60.04 289.03
#> incid_est[29] 56.30 4.78 89.01 5.18 16.03 30.74 59.90 282.34
#> incid_est[30] 55.79 4.62 86.24 5.35 16.29 30.93 59.76 275.80
#> incid_est[31] 55.29 4.47 83.56 5.51 16.53 31.15 59.63 269.42
#> incid_est[32] 54.81 4.32 80.98 5.68 16.78 31.37 59.47 263.19
#> incid_est[33] 54.35 4.18 78.48 5.84 17.04 31.60 59.32 257.10
#> incid_est[34] 53.90 4.04 76.06 6.02 17.29 31.83 59.24 251.37
#> incid_est[35] 53.47 3.91 73.73 6.21 17.56 32.09 59.14 245.87
#> incid_est[36] 53.06 3.78 71.47 6.41 17.82 32.34 59.01 240.49
#> incid_est[37] 52.66 3.66 69.29 6.61 18.09 32.57 58.88 235.23
#> incid_est[38] 52.27 3.54 67.17 6.81 18.37 32.80 58.78 230.08
#> incid_est[39] 51.90 3.42 65.13 7.03 18.67 33.03 58.68 225.04
#> incid_est[40] 51.54 3.31 63.15 7.25 18.96 33.28 58.59 220.12
#> incid_est[41] 51.20 3.20 61.24 7.48 19.23 33.50 58.48 215.30
#> incid_est[42] 50.87 3.10 59.38 7.71 19.51 33.74 58.32 210.62
#> incid_est[43] 50.56 3.00 57.59 7.95 19.82 33.93 58.18 206.21
#> incid_est[44] 50.26 2.90 55.85 8.20 20.14 34.16 58.08 201.63
#> incid_est[45] 49.97 2.80 54.17 8.46 20.46 34.36 57.94 197.13
#> incid_est[46] 49.69 2.71 52.54 8.72 20.78 34.57 57.81 192.77
#> incid_est[47] 49.43 2.62 50.95 8.98 21.12 34.83 57.68 188.54
#> incid_est[48] 49.17 2.54 49.42 9.25 21.44 35.06 57.49 184.25
#> incid_est[49] 48.93 2.46 47.93 9.52 21.78 35.30 57.33 180.15
#> incid_est[50] 48.71 2.37 46.49 9.80 22.11 35.57 57.23 176.13
#> incid_est[51] 48.49 2.30 45.09 10.09 22.44 35.76 57.12 172.21
#> incid_est[52] 48.28 2.22 43.72 10.40 22.78 36.00 56.97 168.38
#> incid_est[53] 48.09 2.15 42.40 10.72 23.14 36.27 56.86 164.63
#> incid_est[54] 47.91 2.08 41.12 11.06 23.50 36.52 56.75 160.97
#> incid_est[55] 47.74 2.01 39.87 11.41 23.86 36.73 56.67 157.38
#> incid_est[56] 47.58 1.94 38.66 11.78 24.23 36.95 56.58 153.88
#> incid_est[57] 47.43 1.88 37.48 12.15 24.61 37.22 56.47 150.45
#> incid_est[58] 47.29 1.81 36.33 12.54 24.99 37.49 56.36 147.10
#> incid_est[59] 47.16 1.75 35.21 12.93 25.37 37.74 56.27 143.83
#> incid_est[60] 47.04 1.69 34.12 13.32 25.77 37.95 56.15 140.62
#> incid_est[61] 46.93 1.64 33.06 13.72 26.16 38.19 56.00 137.48
#> incid_est[62] 46.83 1.58 32.03 14.13 26.55 38.45 55.87 134.42
#> incid_est[63] 46.75 1.52 31.02 14.55 26.96 38.68 55.79 131.35
#> incid_est[64] 46.67 1.47 30.04 15.04 27.38 38.92 55.70 128.49
#> incid_est[65] 46.60 1.42 29.08 15.51 27.83 39.25 55.62 125.63
#> incid_est[66] 46.54 1.37 28.14 15.98 28.29 39.50 55.57 122.73
#> incid_est[67] 46.49 1.32 27.22 16.47 28.74 39.77 55.53 119.88
#> incid_est[68] 46.45 1.27 26.33 16.97 29.21 40.00 55.34 117.09
#> incid_est[69] 46.42 1.23 25.45 17.47 29.68 40.27 55.22 114.36
#> incid_est[70] 46.40 1.18 24.59 17.98 30.14 40.52 55.16 111.70
#> incid_est[71] 46.39 1.14 23.75 18.52 30.63 40.77 55.05 109.10
#> incid_est[72] 46.39 1.09 22.93 19.10 31.09 41.02 54.95 106.80
#> incid_est[73] 46.39 1.05 22.12 19.70 31.55 41.30 54.80 104.43
#> incid_est[74] 46.41 1.01 21.33 20.31 32.08 41.59 54.62 102.04
#> incid_est[75] 46.44 0.97 20.55 20.93 32.59 41.85 54.52 100.03
#> incid_est[76] 46.47 0.93 19.79 21.56 33.10 42.12 54.51 98.06
#> incid_est[77] 46.52 0.89 19.03 22.16 33.62 42.36 54.40 95.89
#> incid_est[78] 46.57 0.85 18.30 22.80 34.12 42.64 54.30 93.97
#> incid_est[79] 46.63 0.82 17.57 23.45 34.64 42.98 54.21 91.77
#> incid_est[80] 46.71 0.78 16.85 24.11 35.15 43.29 54.08 89.73
#> incid_est[81] 46.79 0.75 16.15 24.80 35.68 43.53 54.00 87.70
#> incid_est[82] 46.88 0.71 15.45 25.50 36.26 43.80 53.87 86.10
#> incid_est[83] 46.98 0.68 14.77 26.25 36.80 44.11 53.79 84.37
#> incid_est[84] 47.09 0.64 14.09 27.10 37.37 44.41 53.78 82.26
#> incid_est[85] 47.20 0.61 13.42 27.90 37.94 44.73 53.72 80.36
#> incid_est[86] 47.33 0.58 12.77 28.76 38.50 45.08 53.64 78.68
#> incid_est[87] 47.47 0.54 12.11 29.66 39.10 45.42 53.54 76.93
#> incid_est[88] 47.61 0.51 11.47 30.61 39.71 45.70 53.48 75.22
#> incid_est[89] 47.77 0.48 10.84 31.44 40.29 46.11 53.34 74.03
#> incid_est[90] 47.93 0.45 10.21 32.29 40.91 46.44 53.24 72.67
#> incid_est[91] 48.11 0.42 9.59 33.20 41.46 46.77 53.24 71.27
#> incid_est[92] 48.29 0.39 8.98 34.10 42.10 47.13 53.20 70.06
#> incid_est[93] 48.49 0.36 8.38 35.02 42.69 47.49 53.20 68.46
#> incid_est[94] 48.69 0.33 7.79 35.96 43.34 47.79 53.17 67.02
#> incid_est[95] 48.90 0.30 7.21 36.83 43.92 48.12 53.12 65.73
#> incid_est[96] 49.12 0.27 6.65 37.87 44.51 48.48 53.06 64.23
#> incid_est[97] 49.36 0.24 6.10 38.76 45.11 48.77 53.07 63.09
#> incid_est[98] 49.60 0.21 5.58 39.84 45.76 49.19 53.10 61.98
#> incid_est[99] 49.85 0.18 5.09 40.80 46.37 49.52 53.02 60.89
#> incid_est[100] 50.12 0.16 4.65 41.69 46.96 49.83 53.10 59.92
#> incid_est[101] 50.39 0.13 4.25 42.60 47.48 50.21 53.17 59.12
#> incid_est[102] 50.67 0.10 3.94 43.28 47.99 50.59 53.26 58.63
#> incid_est[103] 50.97 0.08 3.71 43.88 48.42 50.89 53.33 58.44
#> incid_est[104] 51.27 0.06 3.60 44.43 48.86 51.24 53.68 58.36
#> incid_est[105] 51.59 0.06 3.61 44.77 49.13 51.53 54.01 58.99
#> incid_est[106] 51.92 0.07 3.76 44.85 49.32 51.85 54.45 59.63
#> incid_est[107] 52.25 0.09 4.02 44.57 49.46 52.18 54.93 60.30
#> incid_est[108] 52.60 0.12 4.38 44.34 49.57 52.50 55.53 61.41
#> incid_est[109] 52.97 0.14 4.82 43.76 49.64 52.83 56.25 62.61
#> incid_est[110] 53.34 0.17 5.33 43.37 49.68 53.22 56.94 64.07
#> incid_est[111] 53.72 0.20 5.89 42.63 49.70 53.56 57.61 65.51
#> incid_est[112] 54.12 0.23 6.49 41.85 49.66 53.95 58.35 67.12
#> incid_est[113] 54.53 0.26 7.13 41.19 49.59 54.29 59.10 68.88
#> incid_est[114] 54.95 0.29 7.79 40.54 49.56 54.64 59.93 70.85
#> incid_est[115] 55.38 0.32 8.49 39.92 49.46 54.95 60.82 72.72
#> incid_est[116] 55.83 0.35 9.20 39.27 49.38 55.39 61.68 74.91
#> incid_est[117] 56.29 0.39 9.94 38.59 49.26 55.78 62.61 77.20
#> lp__ 1507.15 0.04 1.11 1504.22 1506.77 1507.51 1507.91 1508.17
#> n_eff Rhat
#> log_i0 526 1.01
#> rt_est 538 1.01
#> incid_est[1] 323 1.02
#> incid_est[2] 326 1.02
#> incid_est[3] 326 1.02
#> incid_est[4] 326 1.02
#> incid_est[5] 327 1.02
#> incid_est[6] 327 1.02
#> incid_est[7] 327 1.02
#> incid_est[8] 328 1.02
#> incid_est[9] 328 1.02
#> incid_est[10] 329 1.02
#> incid_est[11] 330 1.02
#> incid_est[12] 330 1.02
#> incid_est[13] 331 1.02
#> incid_est[14] 332 1.02
#> incid_est[15] 332 1.02
#> incid_est[16] 333 1.02
#> incid_est[17] 334 1.02
#> incid_est[18] 335 1.02
#> incid_est[19] 336 1.02
#> incid_est[20] 337 1.02
#> incid_est[21] 338 1.02
#> incid_est[22] 339 1.02
#> incid_est[23] 340 1.02
#> incid_est[24] 341 1.02
#> incid_est[25] 342 1.02
#> incid_est[26] 343 1.02
#> incid_est[27] 345 1.01
#> incid_est[28] 346 1.01
#> incid_est[29] 347 1.01
#> incid_est[30] 348 1.01
#> incid_est[31] 350 1.01
#> incid_est[32] 351 1.01
#> incid_est[33] 353 1.01
#> incid_est[34] 354 1.01
#> incid_est[35] 356 1.01
#> incid_est[36] 357 1.01
#> incid_est[37] 359 1.01
#> incid_est[38] 360 1.01
#> incid_est[39] 362 1.01
#> incid_est[40] 364 1.01
#> incid_est[41] 366 1.01
#> incid_est[42] 367 1.01
#> incid_est[43] 369 1.01
#> incid_est[44] 371 1.01
#> incid_est[45] 373 1.01
#> incid_est[46] 375 1.01
#> incid_est[47] 377 1.01
#> incid_est[48] 379 1.01
#> incid_est[49] 381 1.01
#> incid_est[50] 383 1.01
#> incid_est[51] 385 1.01
#> incid_est[52] 388 1.01
#> incid_est[53] 390 1.01
#> incid_est[54] 392 1.01
#> incid_est[55] 394 1.01
#> incid_est[56] 397 1.01
#> incid_est[57] 399 1.01
#> incid_est[58] 402 1.01
#> incid_est[59] 404 1.01
#> incid_est[60] 406 1.01
#> incid_est[61] 409 1.01
#> incid_est[62] 411 1.01
#> incid_est[63] 414 1.01
#> incid_est[64] 417 1.01
#> incid_est[65] 419 1.01
#> incid_est[66] 422 1.01
#> incid_est[67] 425 1.01
#> incid_est[68] 427 1.01
#> incid_est[69] 430 1.01
#> incid_est[70] 433 1.01
#> incid_est[71] 436 1.01
#> incid_est[72] 439 1.01
#> incid_est[73] 442 1.01
#> incid_est[74] 445 1.01
#> incid_est[75] 448 1.01
#> incid_est[76] 451 1.01
#> incid_est[77] 455 1.01
#> incid_est[78] 458 1.01
#> incid_est[79] 462 1.01
#> incid_est[80] 465 1.01
#> incid_est[81] 469 1.01
#> incid_est[82] 473 1.01
#> incid_est[83] 477 1.01
#> incid_est[84] 482 1.01
#> incid_est[85] 486 1.01
#> incid_est[86] 491 1.01
#> incid_est[87] 497 1.01
#> incid_est[88] 503 1.01
#> incid_est[89] 510 1.01
#> incid_est[90] 518 1.01
#> incid_est[91] 527 1.01
#> incid_est[92] 537 1.01
#> incid_est[93] 550 1.01
#> incid_est[94] 566 1.01
#> incid_est[95] 586 1.01
#> incid_est[96] 613 1.01
#> incid_est[97] 649 1.00
#> incid_est[98] 701 1.00
#> incid_est[99] 777 1.00
#> incid_est[100] 897 1.00
#> incid_est[101] 1095 1.00
#> incid_est[102] 1441 1.00
#> incid_est[103] 2094 1.00
#> incid_est[104] 3634 1.00
#> incid_est[105] 3719 1.00
#> incid_est[106] 2757 1.00
#> incid_est[107] 1905 1.00
#> incid_est[108] 1434 1.00
#> incid_est[109] 1156 1.00
#> incid_est[110] 987 1.00
#> incid_est[111] 881 1.00
#> incid_est[112] 810 1.00
#> incid_est[113] 761 1.00
#> incid_est[114] 726 1.00
#> incid_est[115] 700 1.00
#> incid_est[116] 680 1.00
#> incid_est[117] 665 1.00
#> lp__ 640 1.00
#>
#> Samples were drawn using NUTS(diag_e) at Sun Feb 23 04:34:19 2025.
#> 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).