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 4.9e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.49 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
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#> Chain 1:
#> Chain 1: Elapsed Time: 0.644 seconds (Warm-up)
#> Chain 1: 0.61 seconds (Sampling)
#> Chain 1: 1.254 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: 0.571 seconds (Warm-up)
#> Chain 2: 0.703 seconds (Sampling)
#> Chain 2: 1.274 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: 0.54 seconds (Warm-up)
#> Chain 3: 0.598 seconds (Sampling)
#> Chain 3: 1.138 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: 0.56 seconds (Warm-up)
#> Chain 4: 0.606 seconds (Sampling)
#> Chain 4: 1.166 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 4.97 0.07 1.46 2.15 3.95 4.92 5.96 7.84
#> rt_est 1.05 0.00 0.09 0.88 0.99 1.05 1.12 1.24
#> incid_est[1] 417.36 48.73 946.14 8.59 52.19 137.53 385.97 2533.88
#> incid_est[2] 6.77 0.72 13.77 0.19 1.02 2.53 6.68 38.97
#> incid_est[3] 33.40 3.55 67.89 0.92 5.04 12.46 32.95 192.12
#> incid_est[4] 49.89 5.29 101.21 1.37 7.55 18.66 49.27 286.64
#> incid_est[5] 56.19 5.93 113.32 1.57 8.60 21.17 55.65 321.74
#> incid_est[6] 58.24 6.09 116.29 1.68 9.07 22.21 57.99 331.52
#> incid_est[7] 58.65 6.06 115.60 1.75 9.34 22.71 58.82 331.32
#> incid_est[8] 58.46 5.96 113.52 1.82 9.55 23.01 59.08 327.33
#> incid_est[9] 58.05 5.84 110.95 1.88 9.73 23.25 59.14 321.99
#> incid_est[10] 57.58 5.71 108.26 1.94 9.90 23.45 59.12 316.21
#> incid_est[11] 57.09 5.57 105.56 2.01 10.08 23.66 59.09 310.56
#> incid_est[12] 56.60 5.44 102.91 2.08 10.27 23.87 59.06 304.75
#> incid_est[13] 56.13 5.32 100.32 2.16 10.45 24.09 59.04 299.18
#> incid_est[14] 55.66 5.19 97.81 2.24 10.64 24.31 59.02 293.83
#> incid_est[15] 55.21 5.07 95.37 2.32 10.83 24.52 59.03 288.66
#> incid_est[16] 54.78 4.95 93.00 2.40 11.02 24.75 59.03 283.58
#> incid_est[17] 54.35 4.83 90.69 2.49 11.21 24.98 58.97 278.59
#> incid_est[18] 53.94 4.72 88.45 2.58 11.42 25.21 58.91 273.69
#> incid_est[19] 53.54 4.61 86.27 2.67 11.63 25.46 58.85 268.88
#> incid_est[20] 53.15 4.50 84.15 2.77 11.85 25.71 58.83 264.22
#> incid_est[21] 52.78 4.40 82.09 2.87 12.07 25.94 58.80 259.71
#> incid_est[22] 51.74 4.23 78.73 2.96 12.19 25.94 58.07 251.48
#> incid_est[23] 51.56 4.14 77.12 3.07 12.43 26.23 58.28 248.06
#> incid_est[24] 51.25 4.05 75.31 3.18 12.66 26.47 58.34 243.99
#> incid_est[25] 50.89 3.95 73.43 3.29 12.88 26.69 58.27 239.65
#> incid_est[26] 50.52 3.86 71.57 3.40 13.11 26.91 58.18 235.28
#> incid_est[27] 50.16 3.76 69.75 3.51 13.34 27.14 58.07 231.11
#> incid_est[28] 49.82 3.67 67.98 3.63 13.57 27.37 57.98 227.09
#> incid_est[29] 49.48 3.58 66.26 3.75 13.82 27.60 57.91 223.15
#> incid_est[30] 49.16 3.49 64.59 3.87 14.06 27.83 57.82 219.23
#> incid_est[31] 48.85 3.41 62.96 4.00 14.31 28.05 57.69 215.18
#> incid_est[32] 48.55 3.32 61.38 4.15 14.57 28.29 57.62 211.21
#> incid_est[33] 48.26 3.24 59.85 4.31 14.83 28.52 57.49 207.30
#> incid_est[34] 47.98 3.16 58.35 4.47 15.09 28.75 57.42 203.33
#> incid_est[35] 47.71 3.09 56.89 4.62 15.36 29.00 57.30 199.24
#> incid_est[36] 47.46 3.01 55.47 4.78 15.66 29.24 57.21 195.59
#> incid_est[37] 47.21 2.94 54.09 4.94 15.95 29.48 57.09 192.01
#> incid_est[38] 46.97 2.86 52.75 5.11 16.24 29.73 56.96 188.50
#> incid_est[39] 46.74 2.79 51.44 5.28 16.52 29.97 56.82 185.04
#> incid_est[40] 46.52 2.72 50.16 5.46 16.79 30.21 56.69 181.66
#> incid_est[41] 46.31 2.66 48.91 5.64 17.06 30.46 56.59 178.03
#> incid_est[42] 46.11 2.59 47.70 5.84 17.35 30.71 56.51 174.30
#> incid_est[43] 45.93 2.53 46.51 6.04 17.67 30.95 56.42 170.66
#> incid_est[44] 45.75 2.46 45.36 6.26 17.97 31.22 56.26 167.09
#> incid_est[45] 45.58 2.40 44.23 6.48 18.30 31.49 56.13 163.97
#> incid_est[46] 45.41 2.34 43.13 6.71 18.61 31.76 56.00 160.93
#> incid_est[47] 45.26 2.28 42.06 6.95 18.95 32.01 55.97 157.95
#> incid_est[48] 45.12 2.22 41.01 7.18 19.26 32.27 55.94 155.03
#> incid_est[49] 44.98 2.17 39.98 7.43 19.59 32.53 55.85 152.15
#> incid_est[50] 44.86 2.11 38.98 7.68 19.95 32.79 55.73 149.33
#> incid_est[51] 44.74 2.06 38.00 7.95 20.28 33.07 55.62 146.22
#> incid_est[52] 44.63 2.00 37.04 8.24 20.63 33.32 55.52 143.31
#> incid_est[53] 44.53 1.95 36.10 8.54 20.98 33.58 55.45 140.68
#> incid_est[54] 44.44 1.90 35.18 8.83 21.34 33.85 55.35 138.10
#> incid_est[55] 44.36 1.85 34.29 9.13 21.70 34.11 55.26 135.56
#> incid_est[56] 44.29 1.80 33.41 9.43 22.09 34.41 55.20 133.12
#> incid_est[57] 44.22 1.75 32.54 9.75 22.47 34.67 55.10 130.72
#> incid_est[58] 44.17 1.71 31.70 10.08 22.86 34.96 54.99 128.23
#> incid_est[59] 44.12 1.66 30.87 10.41 23.27 35.26 54.90 125.83
#> incid_est[60] 44.08 1.61 30.05 10.76 23.68 35.57 54.81 123.45
#> incid_est[61] 44.05 1.57 29.25 11.18 24.10 35.87 54.68 121.14
#> incid_est[62] 44.03 1.53 28.47 11.61 24.52 36.18 54.60 118.75
#> incid_est[63] 44.02 1.48 27.70 12.06 24.93 36.47 54.52 116.41
#> incid_est[64] 44.01 1.44 26.94 12.52 25.37 36.76 54.45 114.11
#> incid_est[65] 44.01 1.40 26.19 13.00 25.80 37.07 54.36 111.88
#> incid_est[66] 44.03 1.36 25.46 13.47 26.24 37.37 54.40 109.74
#> incid_est[67] 44.05 1.32 24.73 13.93 26.70 37.74 54.35 107.65
#> incid_est[68] 44.07 1.28 24.02 14.38 27.17 38.05 54.28 105.56
#> incid_est[69] 44.11 1.24 23.32 14.90 27.66 38.35 54.20 103.55
#> incid_est[70] 44.16 1.20 22.63 15.45 28.15 38.67 54.09 101.62
#> incid_est[71] 44.21 1.16 21.94 15.97 28.62 39.05 53.97 99.71
#> incid_est[72] 44.28 1.12 21.27 16.51 29.14 39.34 53.91 97.84
#> incid_est[73] 44.35 1.08 20.60 17.07 29.60 39.65 53.79 96.00
#> incid_est[74] 44.43 1.05 19.94 17.70 30.14 40.01 53.75 94.19
#> incid_est[75] 44.52 1.01 19.29 18.34 30.68 40.35 53.67 92.41
#> incid_est[76] 44.61 0.98 18.65 18.99 31.21 40.68 53.65 90.63
#> incid_est[77] 44.72 0.94 18.01 19.66 31.73 41.01 53.61 88.85
#> incid_est[78] 44.84 0.90 17.37 20.37 32.27 41.34 53.54 87.21
#> incid_est[79] 44.96 0.87 16.74 21.09 32.80 41.69 53.52 85.62
#> incid_est[80] 45.09 0.83 16.12 21.81 33.35 42.02 53.43 84.04
#> incid_est[81] 45.24 0.80 15.50 22.61 33.94 42.40 53.34 82.50
#> incid_est[82] 45.39 0.77 14.89 23.42 34.54 42.76 53.30 80.90
#> incid_est[83] 45.55 0.73 14.28 24.28 35.18 43.13 53.29 79.45
#> incid_est[84] 45.72 0.70 13.67 25.05 35.82 43.49 53.25 77.92
#> incid_est[85] 45.90 0.67 13.07 25.88 36.45 43.88 53.26 76.49
#> incid_est[86] 46.09 0.63 12.47 26.74 37.05 44.24 53.22 74.98
#> incid_est[87] 46.29 0.60 11.87 27.67 37.64 44.58 53.13 73.52
#> incid_est[88] 46.49 0.57 11.27 28.61 38.31 45.00 53.05 72.15
#> incid_est[89] 46.71 0.53 10.68 29.59 38.99 45.43 53.01 70.76
#> incid_est[90] 46.94 0.50 10.09 30.56 39.65 45.78 52.97 69.50
#> incid_est[91] 47.18 0.47 9.50 31.60 40.29 46.18 52.91 68.38
#> incid_est[92] 47.43 0.44 8.92 32.60 40.97 46.57 52.89 67.29
#> incid_est[93] 47.69 0.40 8.34 33.61 41.69 46.94 52.92 66.08
#> incid_est[94] 47.96 0.37 7.77 34.65 42.37 47.33 52.88 64.93
#> incid_est[95] 48.24 0.34 7.21 35.82 43.07 47.74 52.82 63.77
#> incid_est[96] 48.53 0.31 6.65 37.02 43.78 48.12 52.82 62.87
#> incid_est[97] 48.84 0.27 6.11 38.14 44.47 48.47 52.79 61.85
#> incid_est[98] 49.15 0.24 5.58 39.16 45.19 48.91 52.80 61.08
#> incid_est[99] 49.47 0.21 5.08 40.25 45.87 49.29 52.93 60.19
#> incid_est[100] 49.81 0.18 4.62 41.33 46.53 49.70 52.93 59.41
#> incid_est[101] 50.16 0.14 4.21 42.32 47.14 50.09 53.02 58.66
#> incid_est[102] 50.52 0.11 3.87 43.18 47.80 50.46 53.17 58.13
#> incid_est[103] 50.90 0.08 3.63 44.09 48.35 50.85 53.39 57.94
#> incid_est[104] 51.28 0.06 3.50 44.66 48.86 51.19 53.70 58.00
#> incid_est[105] 51.68 0.06 3.52 45.15 49.21 51.61 54.09 58.64
#> incid_est[106] 52.09 0.07 3.68 45.21 49.48 52.04 54.58 59.57
#> incid_est[107] 52.52 0.09 3.97 45.21 49.71 52.47 55.17 60.67
#> incid_est[108] 52.96 0.13 4.38 45.07 49.91 52.84 55.82 62.01
#> incid_est[109] 53.41 0.16 4.87 44.60 50.04 53.20 56.61 63.46
#> incid_est[110] 53.87 0.20 5.44 43.89 50.12 53.64 57.36 65.17
#> incid_est[111] 54.35 0.23 6.07 43.32 50.17 54.01 58.27 67.05
#> incid_est[112] 54.85 0.27 6.74 42.71 50.17 54.46 59.19 69.15
#> incid_est[113] 55.36 0.31 7.45 42.10 50.18 54.90 60.10 71.42
#> incid_est[114] 55.89 0.35 8.20 41.56 50.15 55.29 61.09 73.53
#> incid_est[115] 56.43 0.39 8.98 40.91 50.13 55.78 62.13 75.88
#> incid_est[116] 56.98 0.44 9.80 40.22 50.08 56.26 63.15 78.22
#> incid_est[117] 57.56 0.48 10.64 39.53 50.00 56.79 64.19 80.95
#> lp__ 1507.16 0.04 1.02 1504.52 1506.77 1507.47 1507.88 1508.16
#> n_eff Rhat
#> log_i0 397 1.01
#> rt_est 403 1.01
#> incid_est[1] 377 1.01
#> incid_est[2] 366 1.01
#> incid_est[3] 366 1.01
#> incid_est[4] 366 1.01
#> incid_est[5] 365 1.01
#> incid_est[6] 365 1.01
#> incid_est[7] 364 1.01
#> incid_est[8] 362 1.01
#> incid_est[9] 361 1.01
#> incid_est[10] 360 1.01
#> incid_est[11] 359 1.01
#> incid_est[12] 357 1.01
#> incid_est[13] 356 1.01
#> incid_est[14] 355 1.01
#> incid_est[15] 354 1.01
#> incid_est[16] 353 1.01
#> incid_est[17] 352 1.01
#> incid_est[18] 351 1.01
#> incid_est[19] 350 1.01
#> incid_est[20] 349 1.01
#> incid_est[21] 348 1.01
#> incid_est[22] 347 1.01
#> incid_est[23] 346 1.01
#> incid_est[24] 346 1.01
#> incid_est[25] 345 1.01
#> incid_est[26] 344 1.01
#> incid_est[27] 344 1.01
#> incid_est[28] 343 1.01
#> incid_est[29] 342 1.01
#> incid_est[30] 342 1.01
#> incid_est[31] 341 1.01
#> incid_est[32] 341 1.01
#> incid_est[33] 341 1.01
#> incid_est[34] 340 1.01
#> incid_est[35] 340 1.01
#> incid_est[36] 340 1.01
#> incid_est[37] 339 1.01
#> incid_est[38] 339 1.01
#> incid_est[39] 339 1.01
#> incid_est[40] 339 1.01
#> incid_est[41] 339 1.01
#> incid_est[42] 339 1.01
#> incid_est[43] 339 1.01
#> incid_est[44] 339 1.01
#> incid_est[45] 339 1.01
#> incid_est[46] 339 1.01
#> incid_est[47] 340 1.01
#> incid_est[48] 340 1.01
#> incid_est[49] 340 1.01
#> incid_est[50] 341 1.01
#> incid_est[51] 341 1.01
#> incid_est[52] 341 1.01
#> incid_est[53] 342 1.01
#> incid_est[54] 342 1.01
#> incid_est[55] 343 1.01
#> incid_est[56] 344 1.01
#> incid_est[57] 344 1.01
#> incid_est[58] 345 1.01
#> incid_est[59] 346 1.01
#> incid_est[60] 346 1.01
#> incid_est[61] 347 1.01
#> incid_est[62] 348 1.01
#> incid_est[63] 349 1.01
#> incid_est[64] 350 1.01
#> incid_est[65] 351 1.01
#> incid_est[66] 352 1.01
#> incid_est[67] 353 1.01
#> incid_est[68] 354 1.01
#> incid_est[69] 356 1.01
#> incid_est[70] 357 1.01
#> incid_est[71] 358 1.01
#> incid_est[72] 359 1.01
#> incid_est[73] 361 1.01
#> incid_est[74] 362 1.01
#> incid_est[75] 364 1.01
#> incid_est[76] 366 1.01
#> incid_est[77] 367 1.01
#> incid_est[78] 369 1.01
#> incid_est[79] 371 1.01
#> incid_est[80] 373 1.01
#> incid_est[81] 375 1.01
#> incid_est[82] 377 1.01
#> incid_est[83] 380 1.01
#> incid_est[84] 382 1.01
#> incid_est[85] 385 1.01
#> incid_est[86] 388 1.01
#> incid_est[87] 391 1.01
#> incid_est[88] 395 1.01
#> incid_est[89] 399 1.01
#> incid_est[90] 404 1.01
#> incid_est[91] 410 1.01
#> incid_est[92] 417 1.01
#> incid_est[93] 425 1.01
#> incid_est[94] 436 1.01
#> incid_est[95] 450 1.01
#> incid_est[96] 468 1.01
#> incid_est[97] 493 1.01
#> incid_est[98] 530 1.01
#> incid_est[99] 585 1.01
#> incid_est[100] 678 1.01
#> incid_est[101] 845 1.01
#> incid_est[102] 1189 1.00
#> incid_est[103] 1988 1.00
#> incid_est[104] 3387 1.00
#> incid_est[105] 3774 1.00
#> incid_est[106] 2928 1.00
#> incid_est[107] 1839 1.00
#> incid_est[108] 1225 1.00
#> incid_est[109] 935 1.00
#> incid_est[110] 770 1.00
#> incid_est[111] 675 1.00
#> incid_est[112] 614 1.01
#> incid_est[113] 573 1.01
#> incid_est[114] 544 1.01
#> incid_est[115] 522 1.01
#> incid_est[116] 506 1.01
#> incid_est[117] 493 1.01
#> lp__ 537 1.01
#>
#> Samples were drawn using NUTS(diag_e) at Fri Jan 24 04:29:03 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).