This function wraps the functionality of 
estimate_infections() in order
to estimate Rt and cases by date of infection and forecast these infections
into the future. In addition to the functionality of
estimate_infections() it produces additional summary output useful for
reporting results and interpreting them as well as error catching and
reporting, making it particularly useful for production use e.g. running at
set intervals on a dedicated server.
Usage
epinow(
  data,
  generation_time = gt_opts(),
  delays = delay_opts(),
  truncation = trunc_opts(),
  rt = rt_opts(),
  backcalc = backcalc_opts(),
  gp = gp_opts(),
  obs = obs_opts(),
  forecast = forecast_opts(),
  stan = stan_opts(),
  CrIs = c(0.2, 0.5, 0.9),
  return_output = is.null(target_folder),
  output = c("samples", "plots", "latest", "fit", "timing"),
  plot_args = list(),
  target_folder = NULL,
  target_date,
  logs = tempdir(),
  id = "epinow",
  verbose = interactive(),
  filter_leading_zeros = TRUE,
  zero_threshold = Inf,
  horizon
)Arguments
- data
- A - <data.frame>of disease reports (confirm) by date (date).- confirmmust be numeric and- datemust be in date format. Optionally this can also have a logical- accumulatecolumn which indicates whether data should be added to the next data point. This is useful when modelling e.g. weekly incidence data. See also the- fill_missing()function which helps add the- accumulatecolumn with the desired properties when dealing with non-daily data. If any accumulation is done this happens after truncation as specified by the- truncationargument.
- generation_time
- A call to - gt_opts()(or its alias- generation_time_opts()) defining the generation time distribution used. For backwards compatibility a list of summary parameters can also be passed.
- delays
- A call to - delay_opts()defining delay distributions and options. See the documentation of- delay_opts()and the examples below for details.
- truncation
- A call to - trunc_opts()defining the truncation of the observed data. Defaults to- trunc_opts(), i.e. no truncation. See the- estimate_truncation()help file for an approach to estimating this from data where the- distlist element returned by- estimate_truncation()is used as the- truncationargument here, thereby propagating the uncertainty in the estimate.
- rt
- A list of options as generated by - rt_opts()defining Rt estimation. Defaults to- rt_opts(). To generate new infections using the non-mechanistic model instead of the renewal equation model, use- rt = NULL. The non-mechanistic model internally uses the setting- rt = rt_opts(use_rt = FALSE, future = "project", gp_on = "R0").
- backcalc
- A list of options as generated by - backcalc_opts()to define the back calculation. Defaults to- backcalc_opts().
- gp
- A list of options as generated by - gp_opts()to define the Gaussian process. Defaults to- gp_opts(). Set to- NULLto disable the Gaussian process.
- obs
- A list of options as generated by - obs_opts()defining the observation model. Defaults to- obs_opts().
- forecast
- A list of options as generated by - forecast_opts()defining the forecast opitions. Defaults to- forecast_opts(). If NULL then no forecasting will be done.
- stan
- A list of stan options as generated by - stan_opts(). Defaults to- stan_opts(). Can be used to override- data,- init, and- verbosesettings if desired.
- CrIs
- Numeric vector of credible intervals to calculate. 
- return_output
- Logical, defaults to FALSE. Should output be returned, this automatically updates to TRUE if no directory for saving is specified. 
- output
- A character vector of optional output to return. Supported options are samples ("samples"), plots ("plots"), the run time ("timing"), copying the dated folder into a latest folder (if - target_folderis not null, set using "latest"), and the stan fit ("fit"). The default is to return all options.
- plot_args
- A list of optional arguments passed to - plot.epinow().
- target_folder
- Character string specifying where to save results (will create if not present). 
- target_date
- Date, defaults to maximum found in the data if not specified. 
- logs
- Character path indicating the target folder in which to store log information. Defaults to the temporary directory if not specified. Default logging can be disabled if - logsis set to NULL. If specifying a custom logging setup then the code for- setup_default_logging()and the- setup_logging()function are a sensible place to start.
- id
- A character string used to assign logging information on error. Used by - regional_epinow()to assign errors to regions. Alter the default to run with error catching.
- verbose
- Logical, defaults to - TRUEwhen used interactively and otherwise- FALSE. Should verbose debug progress messages be printed. Corresponds to the "DEBUG" level from- futile.logger. See- setup_loggingfor more detailed logging options.
- filter_leading_zeros
- Logical, defaults to TRUE. Should zeros at the start of the time series be filtered out. 
- zero_threshold
- Numeric defaults to Inf. Indicates if detected zero cases are meaningful by using a threshold number of cases based on the 7-day average. If the average is above this threshold then the zero is replaced using - fill.
- horizon
- Deprecated; use - forecastinstead to specify the predictive horizon
Value
A list of output from estimate_infections with additional elements summarising results and reporting errors if they have occurred.
Examples
# \donttest{
# set number of cores to use
old_opts <- options()
options(mc.cores = ifelse(interactive(), 4, 1))
# set an example generation time. In practice this should use an estimate
# from the literature or be estimated from data
generation_time <- Gamma(
  shape = Normal(1.3, 0.3),
  rate = Normal(0.37, 0.09),
  max = 14
)
# set an example incubation period. In practice this should use an estimate
# from the literature or be estimated from data
incubation_period <- LogNormal(
  meanlog = Normal(1.6, 0.06),
  sdlog = Normal(0.4, 0.07),
  max = 14
)
# set an example reporting delay. In practice this should use an estimate
# from the literature or be estimated from data
reporting_delay <- LogNormal(mean = 2, sd = 1, max = 10)
# example case data
reported_cases <- example_confirmed[1:40]
# estimate Rt and nowcast/forecast cases by date of infection
out <- epinow(
  data = reported_cases,
  generation_time = gt_opts(generation_time),
  rt = rt_opts(prior = LogNormal(mean = 2, sd = 0.1)),
  delays = delay_opts(incubation_period + reporting_delay)
)
#> Logging threshold set at INFO for the name logger
#> Writing EpiNow2 logs to the console and:
#> /tmp/RtmpXOk7Bx/regional-epinow/2020-04-01.log.
#> Logging threshold set at INFO for the name logger
#> Writing EpiNow2.epinow logs to the console and:
#> /tmp/RtmpXOk7Bx/epinow/2020-04-01.log.
# summary of the latest estimates
summary(out)
#>                         measure                estimate
#>                          <char>                  <char>
#> 1:       New infections per day     3310 (1955 -- 5493)
#> 2:   Expected change in reports              Decreasing
#> 3:   Effective reproduction no.     0.79 (0.63 -- 0.96)
#> 4:               Rate of growth -0.07 (-0.13 -- -0.011)
#> 5: Doubling/halving time (days)      -9.8 (-61 -- -5.2)
# plot estimates
plot(out)
 # summary of R estimates
summary(out, type = "parameters", params = "R")
#>           date variable  strat                           type    median
#>         <Date>   <char> <char>                         <char>     <num>
#>  1: 2020-02-22        R   <NA>                       estimate 2.0987207
#>  2: 2020-02-23        R   <NA>                       estimate 2.0754808
#>  3: 2020-02-24        R   <NA>                       estimate 2.0487027
#>  4: 2020-02-25        R   <NA>                       estimate 2.0223509
#>  5: 2020-02-26        R   <NA>                       estimate 1.9912721
#>  6: 2020-02-27        R   <NA>                       estimate 1.9594218
#>  7: 2020-02-28        R   <NA>                       estimate 1.9266973
#>  8: 2020-02-29        R   <NA>                       estimate 1.8914099
#>  9: 2020-03-01        R   <NA>                       estimate 1.8532962
#> 10: 2020-03-02        R   <NA>                       estimate 1.8141504
#> 11: 2020-03-03        R   <NA>                       estimate 1.7743298
#> 12: 2020-03-04        R   <NA>                       estimate 1.7335510
#> 13: 2020-03-05        R   <NA>                       estimate 1.6907881
#> 14: 2020-03-06        R   <NA>                       estimate 1.6477187
#> 15: 2020-03-07        R   <NA>                       estimate 1.6029951
#> 16: 2020-03-08        R   <NA>                       estimate 1.5580322
#> 17: 2020-03-09        R   <NA>                       estimate 1.5124562
#> 18: 2020-03-10        R   <NA>                       estimate 1.4682517
#> 19: 2020-03-11        R   <NA>                       estimate 1.4237879
#> 20: 2020-03-12        R   <NA>                       estimate 1.3786538
#> 21: 2020-03-13        R   <NA>                       estimate 1.3345298
#> 22: 2020-03-14        R   <NA>                       estimate 1.2911031
#> 23: 2020-03-15        R   <NA>                       estimate 1.2490166
#> 24: 2020-03-16        R   <NA>                       estimate 1.2075496
#> 25: 2020-03-17        R   <NA>                       estimate 1.1681567
#> 26: 2020-03-18        R   <NA>                       estimate 1.1299403
#> 27: 2020-03-19        R   <NA> estimate based on partial data 1.0922585
#> 28: 2020-03-20        R   <NA> estimate based on partial data 1.0576061
#> 29: 2020-03-21        R   <NA> estimate based on partial data 1.0242178
#> 30: 2020-03-22        R   <NA> estimate based on partial data 0.9936076
#> 31: 2020-03-23        R   <NA> estimate based on partial data 0.9643452
#> 32: 2020-03-24        R   <NA> estimate based on partial data 0.9351807
#> 33: 2020-03-25        R   <NA> estimate based on partial data 0.9105087
#> 34: 2020-03-26        R   <NA> estimate based on partial data 0.8871577
#> 35: 2020-03-27        R   <NA> estimate based on partial data 0.8657751
#> 36: 2020-03-28        R   <NA> estimate based on partial data 0.8471155
#> 37: 2020-03-29        R   <NA> estimate based on partial data 0.8295278
#> 38: 2020-03-30        R   <NA> estimate based on partial data 0.8135621
#> 39: 2020-03-31        R   <NA> estimate based on partial data 0.8009558
#> 40: 2020-04-01        R   <NA> estimate based on partial data 0.7879312
#> 41: 2020-04-02        R   <NA>                       forecast 0.7879312
#> 42: 2020-04-03        R   <NA>                       forecast 0.7879312
#> 43: 2020-04-04        R   <NA>                       forecast 0.7879312
#> 44: 2020-04-05        R   <NA>                       forecast 0.7879312
#> 45: 2020-04-06        R   <NA>                       forecast 0.7879312
#> 46: 2020-04-07        R   <NA>                       forecast 0.7879312
#> 47: 2020-04-08        R   <NA>                       forecast 0.7879312
#>           date variable  strat                           type    median
#>          mean         sd  lower_90  lower_50  lower_20  upper_20  upper_50
#>         <num>      <num>     <num>     <num>     <num>     <num>     <num>
#>  1: 2.1012704 0.07700072 1.9740871 2.0479042 2.0788945 2.1193230 2.1521614
#>  2: 2.0775460 0.06948226 1.9654164 2.0299124 2.0579332 2.0929414 2.1231087
#>  3: 2.0515730 0.06370201 1.9485254 2.0089004 2.0344024 2.0654725 2.0927812
#>  4: 2.0234273 0.05971429 1.9285705 1.9826895 2.0068829 2.0373530 2.0627739
#>  5: 1.9931992 0.05729360 1.9032112 1.9534110 1.9784567 2.0068667 2.0297651
#>  6: 1.9609927 0.05599123 1.8725267 1.9220645 1.9463741 1.9735042 1.9968954
#>  7: 1.9269255 0.05528901 1.8378698 1.8878413 1.9127552 1.9406538 1.9617031
#>  8: 1.8911272 0.05474929 1.8031218 1.8539703 1.8767059 1.9037048 1.9266167
#>  9: 1.8537364 0.05408630 1.7679177 1.8174124 1.8388091 1.8665227 1.8891584
#> 10: 1.8148976 0.05315983 1.7299549 1.7781656 1.8006241 1.8285721 1.8482118
#> 11: 1.7747580 0.05193170 1.6925754 1.7392643 1.7610363 1.7874276 1.8070515
#> 12: 1.7334649 0.05042207 1.6549154 1.6985087 1.7193144 1.7456136 1.7644351
#> 13: 1.6911663 0.04868325 1.6156299 1.6574498 1.6774989 1.7034227 1.7208192
#> 14: 1.6480122 0.04678926 1.5734888 1.6154640 1.6350119 1.6594585 1.6776272
#> 15: 1.6041570 0.04482861 1.5332405 1.5727153 1.5916593 1.6140898 1.6336246
#> 16: 1.5597631 0.04288979 1.4930342 1.5301525 1.5478697 1.5692190 1.5882140
#> 17: 1.5150032 0.04104054 1.4510450 1.4867950 1.5034932 1.5236102 1.5421551
#> 18: 1.4700625 0.03931326 1.4091316 1.4429441 1.4584181 1.4785115 1.4953720
#> 19: 1.4251396 0.03771049 1.3662355 1.3993646 1.4140534 1.4331423 1.4492261
#> 20: 1.3804465 0.03623173 1.3234528 1.3561454 1.3698586 1.3880396 1.4037111
#> 21: 1.3362064 0.03490801 1.2820572 1.3132452 1.3261058 1.3434968 1.3582953
#> 22: 1.2926492 0.03382384 1.2399030 1.2696574 1.2827785 1.2999451 1.3140280
#> 23: 1.2500055 0.03311345 1.1978301 1.2271807 1.2407869 1.2573496 1.2711483
#> 24: 1.2084994 0.03293258 1.1569087 1.1863096 1.1992810 1.2164916 1.2297878
#> 25: 1.1683406 0.03342023 1.1154798 1.1455470 1.1588151 1.1762510 1.1897449
#> 26: 1.1297184 0.03467038 1.0750114 1.1057336 1.1206076 1.1375114 1.1519491
#> 27: 1.0927963 0.03672389 1.0355686 1.0673032 1.0829708 1.1018262 1.1158054
#> 28: 1.0577091 0.03957483 0.9952069 1.0304219 1.0468536 1.0672296 1.0827618
#> 29: 1.0245608 0.04317916 0.9558434 0.9946861 1.0127255 1.0341251 1.0525960
#> 30: 0.9934240 0.04746092 0.9162837 0.9604001 0.9800734 1.0040551 1.0239138
#> 31: 0.9643409 0.05231926 0.8806355 0.9281218 0.9500420 0.9768953 0.9985642
#> 32: 0.9373253 0.05763925 0.8442062 0.8972369 0.9210776 0.9521026 0.9745901
#> 33: 0.9123657 0.06330452 0.8107650 0.8688467 0.8937323 0.9285243 0.9550391
#> 34: 0.8894301 0.06920751 0.7791641 0.8430676 0.8689188 0.9056922 0.9355642
#> 35: 0.8684700 0.07525385 0.7476993 0.8191366 0.8462164 0.8863985 0.9182219
#> 36: 0.8494248 0.08136099 0.7194329 0.7957884 0.8261123 0.8690991 0.9029698
#> 37: 0.8322251 0.08745331 0.6929442 0.7747152 0.8080737 0.8543639 0.8866709
#> 38: 0.8167957 0.09345732 0.6686556 0.7549158 0.7906305 0.8397127 0.8746487
#> 39: 0.8030582 0.09929933 0.6475656 0.7368810 0.7749963 0.8269730 0.8630794
#> 40: 0.7909331 0.10490614 0.6260708 0.7198230 0.7609500 0.8155162 0.8536035
#> 41: 0.7909331 0.10490614 0.6260708 0.7198230 0.7609500 0.8155162 0.8536035
#> 42: 0.7909331 0.10490614 0.6260708 0.7198230 0.7609500 0.8155162 0.8536035
#> 43: 0.7909331 0.10490614 0.6260708 0.7198230 0.7609500 0.8155162 0.8536035
#> 44: 0.7909331 0.10490614 0.6260708 0.7198230 0.7609500 0.8155162 0.8536035
#> 45: 0.7909331 0.10490614 0.6260708 0.7198230 0.7609500 0.8155162 0.8536035
#> 46: 0.7909331 0.10490614 0.6260708 0.7198230 0.7609500 0.8155162 0.8536035
#> 47: 0.7909331 0.10490614 0.6260708 0.7198230 0.7609500 0.8155162 0.8536035
#>          mean         sd  lower_90  lower_50  lower_20  upper_20  upper_50
#>      upper_90
#>         <num>
#>  1: 2.2338878
#>  2: 2.1983366
#>  3: 2.1598563
#>  4: 2.1238080
#>  5: 2.0901096
#>  6: 2.0526979
#>  7: 2.0173847
#>  8: 1.9805676
#>  9: 1.9443761
#> 10: 1.9038163
#> 11: 1.8603001
#> 12: 1.8168031
#> 13: 1.7722062
#> 14: 1.7260806
#> 15: 1.6817339
#> 16: 1.6344296
#> 17: 1.5862501
#> 18: 1.5394304
#> 19: 1.4908763
#> 20: 1.4437181
#> 21: 1.3953830
#> 22: 1.3499199
#> 23: 1.3062198
#> 24: 1.2638973
#> 25: 1.2240363
#> 26: 1.1888992
#> 27: 1.1545999
#> 28: 1.1248947
#> 29: 1.0982726
#> 30: 1.0729177
#> 31: 1.0515221
#> 32: 1.0330873
#> 33: 1.0169763
#> 34: 1.0027002
#> 35: 0.9904370
#> 36: 0.9810909
#> 37: 0.9757736
#> 38: 0.9694022
#> 39: 0.9646681
#> 40: 0.9620268
#> 41: 0.9620268
#> 42: 0.9620268
#> 43: 0.9620268
#> 44: 0.9620268
#> 45: 0.9620268
#> 46: 0.9620268
#> 47: 0.9620268
#>      upper_90
options(old_opts)
# }
# summary of R estimates
summary(out, type = "parameters", params = "R")
#>           date variable  strat                           type    median
#>         <Date>   <char> <char>                         <char>     <num>
#>  1: 2020-02-22        R   <NA>                       estimate 2.0987207
#>  2: 2020-02-23        R   <NA>                       estimate 2.0754808
#>  3: 2020-02-24        R   <NA>                       estimate 2.0487027
#>  4: 2020-02-25        R   <NA>                       estimate 2.0223509
#>  5: 2020-02-26        R   <NA>                       estimate 1.9912721
#>  6: 2020-02-27        R   <NA>                       estimate 1.9594218
#>  7: 2020-02-28        R   <NA>                       estimate 1.9266973
#>  8: 2020-02-29        R   <NA>                       estimate 1.8914099
#>  9: 2020-03-01        R   <NA>                       estimate 1.8532962
#> 10: 2020-03-02        R   <NA>                       estimate 1.8141504
#> 11: 2020-03-03        R   <NA>                       estimate 1.7743298
#> 12: 2020-03-04        R   <NA>                       estimate 1.7335510
#> 13: 2020-03-05        R   <NA>                       estimate 1.6907881
#> 14: 2020-03-06        R   <NA>                       estimate 1.6477187
#> 15: 2020-03-07        R   <NA>                       estimate 1.6029951
#> 16: 2020-03-08        R   <NA>                       estimate 1.5580322
#> 17: 2020-03-09        R   <NA>                       estimate 1.5124562
#> 18: 2020-03-10        R   <NA>                       estimate 1.4682517
#> 19: 2020-03-11        R   <NA>                       estimate 1.4237879
#> 20: 2020-03-12        R   <NA>                       estimate 1.3786538
#> 21: 2020-03-13        R   <NA>                       estimate 1.3345298
#> 22: 2020-03-14        R   <NA>                       estimate 1.2911031
#> 23: 2020-03-15        R   <NA>                       estimate 1.2490166
#> 24: 2020-03-16        R   <NA>                       estimate 1.2075496
#> 25: 2020-03-17        R   <NA>                       estimate 1.1681567
#> 26: 2020-03-18        R   <NA>                       estimate 1.1299403
#> 27: 2020-03-19        R   <NA> estimate based on partial data 1.0922585
#> 28: 2020-03-20        R   <NA> estimate based on partial data 1.0576061
#> 29: 2020-03-21        R   <NA> estimate based on partial data 1.0242178
#> 30: 2020-03-22        R   <NA> estimate based on partial data 0.9936076
#> 31: 2020-03-23        R   <NA> estimate based on partial data 0.9643452
#> 32: 2020-03-24        R   <NA> estimate based on partial data 0.9351807
#> 33: 2020-03-25        R   <NA> estimate based on partial data 0.9105087
#> 34: 2020-03-26        R   <NA> estimate based on partial data 0.8871577
#> 35: 2020-03-27        R   <NA> estimate based on partial data 0.8657751
#> 36: 2020-03-28        R   <NA> estimate based on partial data 0.8471155
#> 37: 2020-03-29        R   <NA> estimate based on partial data 0.8295278
#> 38: 2020-03-30        R   <NA> estimate based on partial data 0.8135621
#> 39: 2020-03-31        R   <NA> estimate based on partial data 0.8009558
#> 40: 2020-04-01        R   <NA> estimate based on partial data 0.7879312
#> 41: 2020-04-02        R   <NA>                       forecast 0.7879312
#> 42: 2020-04-03        R   <NA>                       forecast 0.7879312
#> 43: 2020-04-04        R   <NA>                       forecast 0.7879312
#> 44: 2020-04-05        R   <NA>                       forecast 0.7879312
#> 45: 2020-04-06        R   <NA>                       forecast 0.7879312
#> 46: 2020-04-07        R   <NA>                       forecast 0.7879312
#> 47: 2020-04-08        R   <NA>                       forecast 0.7879312
#>           date variable  strat                           type    median
#>          mean         sd  lower_90  lower_50  lower_20  upper_20  upper_50
#>         <num>      <num>     <num>     <num>     <num>     <num>     <num>
#>  1: 2.1012704 0.07700072 1.9740871 2.0479042 2.0788945 2.1193230 2.1521614
#>  2: 2.0775460 0.06948226 1.9654164 2.0299124 2.0579332 2.0929414 2.1231087
#>  3: 2.0515730 0.06370201 1.9485254 2.0089004 2.0344024 2.0654725 2.0927812
#>  4: 2.0234273 0.05971429 1.9285705 1.9826895 2.0068829 2.0373530 2.0627739
#>  5: 1.9931992 0.05729360 1.9032112 1.9534110 1.9784567 2.0068667 2.0297651
#>  6: 1.9609927 0.05599123 1.8725267 1.9220645 1.9463741 1.9735042 1.9968954
#>  7: 1.9269255 0.05528901 1.8378698 1.8878413 1.9127552 1.9406538 1.9617031
#>  8: 1.8911272 0.05474929 1.8031218 1.8539703 1.8767059 1.9037048 1.9266167
#>  9: 1.8537364 0.05408630 1.7679177 1.8174124 1.8388091 1.8665227 1.8891584
#> 10: 1.8148976 0.05315983 1.7299549 1.7781656 1.8006241 1.8285721 1.8482118
#> 11: 1.7747580 0.05193170 1.6925754 1.7392643 1.7610363 1.7874276 1.8070515
#> 12: 1.7334649 0.05042207 1.6549154 1.6985087 1.7193144 1.7456136 1.7644351
#> 13: 1.6911663 0.04868325 1.6156299 1.6574498 1.6774989 1.7034227 1.7208192
#> 14: 1.6480122 0.04678926 1.5734888 1.6154640 1.6350119 1.6594585 1.6776272
#> 15: 1.6041570 0.04482861 1.5332405 1.5727153 1.5916593 1.6140898 1.6336246
#> 16: 1.5597631 0.04288979 1.4930342 1.5301525 1.5478697 1.5692190 1.5882140
#> 17: 1.5150032 0.04104054 1.4510450 1.4867950 1.5034932 1.5236102 1.5421551
#> 18: 1.4700625 0.03931326 1.4091316 1.4429441 1.4584181 1.4785115 1.4953720
#> 19: 1.4251396 0.03771049 1.3662355 1.3993646 1.4140534 1.4331423 1.4492261
#> 20: 1.3804465 0.03623173 1.3234528 1.3561454 1.3698586 1.3880396 1.4037111
#> 21: 1.3362064 0.03490801 1.2820572 1.3132452 1.3261058 1.3434968 1.3582953
#> 22: 1.2926492 0.03382384 1.2399030 1.2696574 1.2827785 1.2999451 1.3140280
#> 23: 1.2500055 0.03311345 1.1978301 1.2271807 1.2407869 1.2573496 1.2711483
#> 24: 1.2084994 0.03293258 1.1569087 1.1863096 1.1992810 1.2164916 1.2297878
#> 25: 1.1683406 0.03342023 1.1154798 1.1455470 1.1588151 1.1762510 1.1897449
#> 26: 1.1297184 0.03467038 1.0750114 1.1057336 1.1206076 1.1375114 1.1519491
#> 27: 1.0927963 0.03672389 1.0355686 1.0673032 1.0829708 1.1018262 1.1158054
#> 28: 1.0577091 0.03957483 0.9952069 1.0304219 1.0468536 1.0672296 1.0827618
#> 29: 1.0245608 0.04317916 0.9558434 0.9946861 1.0127255 1.0341251 1.0525960
#> 30: 0.9934240 0.04746092 0.9162837 0.9604001 0.9800734 1.0040551 1.0239138
#> 31: 0.9643409 0.05231926 0.8806355 0.9281218 0.9500420 0.9768953 0.9985642
#> 32: 0.9373253 0.05763925 0.8442062 0.8972369 0.9210776 0.9521026 0.9745901
#> 33: 0.9123657 0.06330452 0.8107650 0.8688467 0.8937323 0.9285243 0.9550391
#> 34: 0.8894301 0.06920751 0.7791641 0.8430676 0.8689188 0.9056922 0.9355642
#> 35: 0.8684700 0.07525385 0.7476993 0.8191366 0.8462164 0.8863985 0.9182219
#> 36: 0.8494248 0.08136099 0.7194329 0.7957884 0.8261123 0.8690991 0.9029698
#> 37: 0.8322251 0.08745331 0.6929442 0.7747152 0.8080737 0.8543639 0.8866709
#> 38: 0.8167957 0.09345732 0.6686556 0.7549158 0.7906305 0.8397127 0.8746487
#> 39: 0.8030582 0.09929933 0.6475656 0.7368810 0.7749963 0.8269730 0.8630794
#> 40: 0.7909331 0.10490614 0.6260708 0.7198230 0.7609500 0.8155162 0.8536035
#> 41: 0.7909331 0.10490614 0.6260708 0.7198230 0.7609500 0.8155162 0.8536035
#> 42: 0.7909331 0.10490614 0.6260708 0.7198230 0.7609500 0.8155162 0.8536035
#> 43: 0.7909331 0.10490614 0.6260708 0.7198230 0.7609500 0.8155162 0.8536035
#> 44: 0.7909331 0.10490614 0.6260708 0.7198230 0.7609500 0.8155162 0.8536035
#> 45: 0.7909331 0.10490614 0.6260708 0.7198230 0.7609500 0.8155162 0.8536035
#> 46: 0.7909331 0.10490614 0.6260708 0.7198230 0.7609500 0.8155162 0.8536035
#> 47: 0.7909331 0.10490614 0.6260708 0.7198230 0.7609500 0.8155162 0.8536035
#>          mean         sd  lower_90  lower_50  lower_20  upper_20  upper_50
#>      upper_90
#>         <num>
#>  1: 2.2338878
#>  2: 2.1983366
#>  3: 2.1598563
#>  4: 2.1238080
#>  5: 2.0901096
#>  6: 2.0526979
#>  7: 2.0173847
#>  8: 1.9805676
#>  9: 1.9443761
#> 10: 1.9038163
#> 11: 1.8603001
#> 12: 1.8168031
#> 13: 1.7722062
#> 14: 1.7260806
#> 15: 1.6817339
#> 16: 1.6344296
#> 17: 1.5862501
#> 18: 1.5394304
#> 19: 1.4908763
#> 20: 1.4437181
#> 21: 1.3953830
#> 22: 1.3499199
#> 23: 1.3062198
#> 24: 1.2638973
#> 25: 1.2240363
#> 26: 1.1888992
#> 27: 1.1545999
#> 28: 1.1248947
#> 29: 1.0982726
#> 30: 1.0729177
#> 31: 1.0515221
#> 32: 1.0330873
#> 33: 1.0169763
#> 34: 1.0027002
#> 35: 0.9904370
#> 36: 0.9810909
#> 37: 0.9757736
#> 38: 0.9694022
#> 39: 0.9646681
#> 40: 0.9620268
#> 41: 0.9620268
#> 42: 0.9620268
#> 43: 0.9620268
#> 44: 0.9620268
#> 45: 0.9620268
#> 46: 0.9620268
#> 47: 0.9620268
#>      upper_90
options(old_opts)
# }