Full simulation experiments of Vihola, Helske and Franks (2020) takes some time, here we only run a single replication to test that the methods work as expected. To generate Table 1 in the paper, the code below should be run say 1000 times, from which IREs could be computed.
library("bssm")##
## Attaching package: 'bssm'## The following object is masked from 'package:base':
##
## gammadata(poisson_series)
s <- sd(log(pmax(0.1, poisson_series)))
model <- bsm_ng(poisson_series, sd_level = uniform(0.115, 0, 2 * s),
sd_slope = uniform(0.004, 0, 2 * s), P1 = diag(0.1, 2), distribution = "poisson")
d <- data.frame(mean = NA, se = NA,
variable = c("sd_level", "sd_slope", "u_1", "u_100"),
mcmc_type = rep(c("approx", "da", "is1", "is2", "pm"),
times = 4*c(2, 6, 6, 6, 6)),
sampling_method = c(rep("psi", 8),
rep(rep(c("bsf", "spdk", "psi"), each = 2 * 4), 4)),
local_approx = rep(c(TRUE, FALSE), each = 4),
time = NA,
acceptance_rate = NA)
iter <- 1e4 # Use less iterations than in the paper for faster experiment
for(i in seq(1, nrow(d), by = 4)) {
cat("Testing method '", d$mcmc_type[i], "' with sampling by '",
d$sampling_method[i], "' and local_approx '", d$local_approx[i], "'\n",
sep = "")
res <- run_mcmc(model, iter = iter,
sampling_method = d$sampling_method[i],
particles = switch(d$sampling_method[i],
bsf = 200,
spdk = 10,
psi = 10),
mcmc_type = d$mcmc_type[i],
local_approx = d$local_approx[i],
end_adaptive_phase = TRUE)
w <- res$counts *
if (res$mcmc_type %in% paste0("is", 1:2)) res$weights else 1
d[((i - 1) + 1):((i - 1) + 4), "mean"] <- c(
diagis::weighted_mean(res$theta, w),
diagis::weighted_mean(res$alpha[1, 1, ], w),
diagis::weighted_mean(res$alpha[100, 1, ], w))
d[((i - 1) + 1):((i - 1) + 4), "se"] <- c(
sqrt(asymptotic_var(res$theta[, 1], w)),
sqrt(asymptotic_var(res$theta[, 2], w)),
sqrt(asymptotic_var(res$alpha[1, 1, ], w)),
sqrt(asymptotic_var(res$alpha[100, 1, ], w)))
d$time[((i - 1) + 1):((i - 1) + 4)] <- res$time["elapsed"]
d$acceptance_rate[((i - 1) + 1):((i - 1) + 4)] <- res$acceptance_rate
}## Testing method 'approx' with sampling by 'psi' and local_approx 'TRUE'
## Testing method 'approx' with sampling by 'psi' and local_approx 'FALSE'
## Testing method 'da' with sampling by 'bsf' and local_approx 'TRUE'
## Testing method 'da' with sampling by 'bsf' and local_approx 'FALSE'
## Testing method 'da' with sampling by 'spdk' and local_approx 'TRUE'
## Testing method 'da' with sampling by 'spdk' and local_approx 'FALSE'
## Testing method 'da' with sampling by 'psi' and local_approx 'TRUE'
## Testing method 'da' with sampling by 'psi' and local_approx 'FALSE'
## Testing method 'is1' with sampling by 'bsf' and local_approx 'TRUE'
## Testing method 'is1' with sampling by 'bsf' and local_approx 'FALSE'
## Testing method 'is1' with sampling by 'spdk' and local_approx 'TRUE'
## Testing method 'is1' with sampling by 'spdk' and local_approx 'FALSE'
## Testing method 'is1' with sampling by 'psi' and local_approx 'TRUE'
## Testing method 'is1' with sampling by 'psi' and local_approx 'FALSE'
## Testing method 'is2' with sampling by 'bsf' and local_approx 'TRUE'
## Testing method 'is2' with sampling by 'bsf' and local_approx 'FALSE'
## Testing method 'is2' with sampling by 'spdk' and local_approx 'TRUE'
## Testing method 'is2' with sampling by 'spdk' and local_approx 'FALSE'
## Testing method 'is2' with sampling by 'psi' and local_approx 'TRUE'
## Testing method 'is2' with sampling by 'psi' and local_approx 'FALSE'
## Testing method 'pm' with sampling by 'bsf' and local_approx 'TRUE'
## Testing method 'pm' with sampling by 'bsf' and local_approx 'FALSE'
## Testing method 'pm' with sampling by 'spdk' and local_approx 'TRUE'
## Testing method 'pm' with sampling by 'spdk' and local_approx 'FALSE'
## Testing method 'pm' with sampling by 'psi' and local_approx 'TRUE'
## Testing method 'pm' with sampling by 'psi' and local_approx 'FALSE'Results:
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, uniond %>%
arrange(local_approx, variable, mcmc_type, sampling_method)## mean se variable mcmc_type sampling_method local_approx
## 1 0.09578772 0.0022141806 sd_level approx psi FALSE
## 2 0.09183384 0.0025847529 sd_level da bsf FALSE
## 3 0.09056407 0.0034324313 sd_level da psi FALSE
## 4 0.09693717 0.0019153340 sd_level da spdk FALSE
## 5 0.09562614 0.0025997452 sd_level is1 bsf FALSE
## 6 0.09303018 0.0027318562 sd_level is1 psi FALSE
## 7 0.09758895 0.0025748789 sd_level is1 spdk FALSE
## 8 0.10105081 0.0025722112 sd_level is2 bsf FALSE
## 9 0.09536685 0.0027073170 sd_level is2 psi FALSE
## 10 0.09590957 0.0023060056 sd_level is2 spdk FALSE
## 11 0.09698759 0.0038890507 sd_level pm bsf FALSE
## 12 0.09430755 0.0024183804 sd_level pm psi FALSE
## 13 0.08704774 0.0035083078 sd_level pm spdk FALSE
## 14 0.01506997 0.0004887884 sd_slope approx psi FALSE
## 15 0.01622993 0.0007867216 sd_slope da bsf FALSE
## 16 0.01736272 0.0007476045 sd_slope da psi FALSE
## 17 0.01542487 0.0004711415 sd_slope da spdk FALSE
## 18 0.01533332 0.0005808372 sd_slope is1 bsf FALSE
## 19 0.01653758 0.0006161702 sd_slope is1 psi FALSE
## 20 0.01555065 0.0006237624 sd_slope is1 spdk FALSE
## 21 0.01450235 0.0007518923 sd_slope is2 bsf FALSE
## 22 0.01555210 0.0005458160 sd_slope is2 psi FALSE
## 23 0.01522803 0.0005224722 sd_slope is2 spdk FALSE
## 24 0.01526484 0.0008580442 sd_slope pm bsf FALSE
## 25 0.01726606 0.0005463481 sd_slope pm psi FALSE
## 26 0.01719711 0.0005954383 sd_slope pm spdk FALSE
## 27 -0.07869788 0.0105559757 u_1 approx psi FALSE
## 28 -0.06847499 0.0092537409 u_1 da bsf FALSE
## 29 -0.07676795 0.0124369314 u_1 da psi FALSE
## 30 -0.08390600 0.0098000700 u_1 da spdk FALSE
## 31 -0.08702685 0.0125916067 u_1 is1 bsf FALSE
## 32 -0.07410507 0.0095352137 u_1 is1 psi FALSE
## 33 -0.08393639 0.0114658112 u_1 is1 spdk FALSE
## 34 -0.08050907 0.0179799047 u_1 is2 bsf FALSE
## 35 -0.07701605 0.0105821573 u_1 is2 psi FALSE
## 36 -0.07846330 0.0121624205 u_1 is2 spdk FALSE
## 37 -0.09249907 0.0106879249 u_1 pm bsf FALSE
## 38 -0.08991847 0.0111100364 u_1 pm psi FALSE
## 39 -0.06743786 0.0106694815 u_1 pm spdk FALSE
## 40 2.63760608 0.0079707360 u_100 approx psi FALSE
## 41 2.63182502 0.0080169407 u_100 da bsf FALSE
## 42 2.62174704 0.0073447869 u_100 da psi FALSE
## 43 2.61369859 0.0072760694 u_100 da spdk FALSE
## 44 2.62253096 0.0086131210 u_100 is1 bsf FALSE
## 45 2.62697081 0.0073913295 u_100 is1 psi FALSE
## 46 2.61395948 0.0065218848 u_100 is1 spdk FALSE
## 47 2.62980275 0.0117036903 u_100 is2 bsf FALSE
## 48 2.62820881 0.0061786231 u_100 is2 psi FALSE
## 49 2.61647003 0.0066978454 u_100 is2 spdk FALSE
## 50 2.62452635 0.0071852884 u_100 pm bsf FALSE
## 51 2.62372637 0.0064406343 u_100 pm psi FALSE
## 52 2.61946902 0.0053898263 u_100 pm spdk FALSE
## 53 0.09332580 0.0026097129 sd_level approx psi TRUE
## 54 0.08850704 0.0034589396 sd_level da bsf TRUE
## 55 0.09495943 0.0026074340 sd_level da psi TRUE
## 56 0.09321799 0.0025949141 sd_level da spdk TRUE
## 57 0.08969266 0.0024885812 sd_level is1 bsf TRUE
## 58 0.09524581 0.0026432277 sd_level is1 psi TRUE
## 59 0.09200344 0.0025662615 sd_level is1 spdk TRUE
## 60 0.09164685 0.0029147370 sd_level is2 bsf TRUE
## 61 0.09085042 0.0026602853 sd_level is2 psi TRUE
## 62 0.09401393 0.0023809428 sd_level is2 spdk TRUE
## 63 0.09946007 0.0029061242 sd_level pm bsf TRUE
## 64 0.09425689 0.0026954951 sd_level pm psi TRUE
## 65 0.09196438 0.0034327278 sd_level pm spdk TRUE
## 66 0.01649875 0.0006084374 sd_slope approx psi TRUE
## 67 0.01629020 0.0007204475 sd_slope da bsf TRUE
## 68 0.01675024 0.0005625769 sd_slope da psi TRUE
## 69 0.01596388 0.0005902601 sd_slope da spdk TRUE
## 70 0.01684928 0.0005048439 sd_slope is1 bsf TRUE
## 71 0.01619417 0.0006082412 sd_slope is1 psi TRUE
## 72 0.01549983 0.0005977432 sd_slope is1 spdk TRUE
## 73 0.01704707 0.0007564945 sd_slope is2 bsf TRUE
## 74 0.01713414 0.0005378904 sd_slope is2 psi TRUE
## 75 0.01581035 0.0006098587 sd_slope is2 spdk TRUE
## 76 0.01493558 0.0007570220 sd_slope pm bsf TRUE
## 77 0.01681022 0.0005775678 sd_slope pm psi TRUE
## 78 0.01669934 0.0006237532 sd_slope pm spdk TRUE
## 79 -0.04763190 0.0098184938 u_1 approx psi TRUE
## 80 -0.06303314 0.0108945672 u_1 da bsf TRUE
## 81 -0.07412832 0.0118281401 u_1 da psi TRUE
## 82 -0.06864390 0.0107736811 u_1 da spdk TRUE
## 83 -0.06413780 0.0102697767 u_1 is1 bsf TRUE
## 84 -0.07305205 0.0087975786 u_1 is1 psi TRUE
## 85 -0.05281387 0.0087550795 u_1 is1 spdk TRUE
## 86 -0.06758727 0.0181045578 u_1 is2 bsf TRUE
## 87 -0.08541492 0.0092005051 u_1 is2 psi TRUE
## 88 -0.06533748 0.0107268023 u_1 is2 spdk TRUE
## 89 -0.07094869 0.0127049274 u_1 pm bsf TRUE
## 90 -0.08475790 0.0099826212 u_1 pm psi TRUE
## 91 -0.07116972 0.0117171069 u_1 pm spdk TRUE
## 92 2.62666325 0.0064783980 u_100 approx psi TRUE
## 93 2.63482193 0.0078166866 u_100 da bsf TRUE
## 94 2.61414177 0.0064441268 u_100 da psi TRUE
## 95 2.61282885 0.0065739149 u_100 da spdk TRUE
## 96 2.61354285 0.0064132143 u_100 is1 bsf TRUE
## 97 2.61608214 0.0071682674 u_100 is1 psi TRUE
## 98 2.62069831 0.0067225577 u_100 is1 spdk TRUE
## 99 2.60570014 0.0103065461 u_100 is2 bsf TRUE
## 100 2.62148516 0.0074049226 u_100 is2 psi TRUE
## 101 2.61732719 0.0067673451 u_100 is2 spdk TRUE
## 102 2.61310072 0.0074142079 u_100 pm bsf TRUE
## 103 2.60707729 0.0068890297 u_100 pm psi TRUE
## 104 2.60921701 0.0070487136 u_100 pm spdk TRUE
## time acceptance_rate
## 1 1.04 0.2336
## 2 16.59 0.2466
## 3 2.31 0.2068
## 4 1.65 0.2202
## 5 143.79 0.2348
## 6 4.13 0.2238
## 7 2.34 0.2262
## 8 8.51 0.2300
## 9 1.63 0.2470
## 10 1.26 0.2396
## 11 65.08 0.2388
## 12 7.94 0.2354
## 13 4.34 0.2410
## 14 1.04 0.2336
## 15 16.59 0.2466
## 16 2.31 0.2068
## 17 1.65 0.2202
## 18 143.79 0.2348
## 19 4.13 0.2238
## 20 2.34 0.2262
## 21 8.51 0.2300
## 22 1.63 0.2470
## 23 1.26 0.2396
## 24 65.08 0.2388
## 25 7.94 0.2354
## 26 4.34 0.2410
## 27 1.04 0.2336
## 28 16.59 0.2466
## 29 2.31 0.2068
## 30 1.65 0.2202
## 31 143.79 0.2348
## 32 4.13 0.2238
## 33 2.34 0.2262
## 34 8.51 0.2300
## 35 1.63 0.2470
## 36 1.26 0.2396
## 37 65.08 0.2388
## 38 7.94 0.2354
## 39 4.34 0.2410
## 40 1.04 0.2336
## 41 16.59 0.2466
## 42 2.31 0.2068
## 43 1.65 0.2202
## 44 143.79 0.2348
## 45 4.13 0.2238
## 46 2.34 0.2262
## 47 8.51 0.2300
## 48 1.63 0.2470
## 49 1.26 0.2396
## 50 65.08 0.2388
## 51 7.94 0.2354
## 52 4.34 0.2410
## 53 3.74 0.2404
## 54 20.38 0.2408
## 55 4.83 0.2250
## 56 4.02 0.2448
## 57 147.64 0.2434
## 58 5.78 0.2432
## 59 4.56 0.2322
## 60 11.19 0.2510
## 61 3.89 0.2384
## 62 3.59 0.2342
## 63 61.67 0.2428
## 64 11.47 0.2358
## 65 6.64 0.2358
## 66 3.74 0.2404
## 67 20.38 0.2408
## 68 4.83 0.2250
## 69 4.02 0.2448
## 70 147.64 0.2434
## 71 5.78 0.2432
## 72 4.56 0.2322
## 73 11.19 0.2510
## 74 3.89 0.2384
## 75 3.59 0.2342
## 76 61.67 0.2428
## 77 11.47 0.2358
## 78 6.64 0.2358
## 79 3.74 0.2404
## 80 20.38 0.2408
## 81 4.83 0.2250
## 82 4.02 0.2448
## 83 147.64 0.2434
## 84 5.78 0.2432
## 85 4.56 0.2322
## 86 11.19 0.2510
## 87 3.89 0.2384
## 88 3.59 0.2342
## 89 61.67 0.2428
## 90 11.47 0.2358
## 91 6.64 0.2358
## 92 3.74 0.2404
## 93 20.38 0.2408
## 94 4.83 0.2250
## 95 4.02 0.2448
## 96 147.64 0.2434
## 97 5.78 0.2432
## 98 4.56 0.2322
## 99 11.19 0.2510
## 100 3.89 0.2384
## 101 3.59 0.2342
## 102 61.67 0.2428
## 103 11.47 0.2358
## 104 6.64 0.2358