Estimates the posterior modes for the mean (mu) and standard deviation (sigma) of the underlying normal distribution, given truncated data with known truncation point(s).
Arguments
- x
Vector of observations from truncated normal.
- a
Left truncation limit.
- b
Right truncation limit.
- mu_start
Initial value for mu.
- sigma_start
Initial value for sigma.
- ci_level
Confidence level of the interval – gives a 100*ci_level% symmetric HPD interval (defaults to 95%).
- ...
Parameters to pass to
rstan::sampling().
Value
A list with two elements:
- stats
A data frame with two rows and the columns
param(mu,sd),mode(posterior mode),mean(posterior mean),median(posterior median),se(standard error),ci_lower(lower CI bound),ci_upper(upper CI bound),rhat.- fit
A
stanfitobject (the result of fitting the model).
References
Zhou X, Giacometti R, Fabozzi FJ, Tucker AH (2014). “Bayesian estimation of truncated data with applications to operational risk measurement.” Quantitative Finance, 14(5), 863--888. doi:10.1080/14697688.2012.752103 .
Stan Development Team (2022). “RStan: the R interface to Stan.” R package version 2.21.5. https://mc-stan.org.
Examples
set.seed(22)
x <- truncnorm::rtruncnorm(100, a = -1, b = 2, mean = 0.5, sd = 0.5)
trunc_est(x, a = -1, b = 2)
#>
#> SAMPLING FOR MODEL 'trunc_est' NOW (CHAIN 1).
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#> Chain 1: Gradient evaluation took 9e-05 seconds
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#> $stats
#> param mode mean median se ci_lower ci_upper
#> 1 mu 0.5173298 0.5181258 0.5191518 0.0008993825 0.4261705 0.6125553
#> 2 sigma 0.4699284 0.4799267 0.4772683 0.0006998036 0.4134367 0.5599469
#> rhat
#> 1 0.9998396
#> 2 0.9999681
#>
#> $fit
#> Inference for Stan model: trunc_est.
#> 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% n_eff Rhat
#> mu 0.52 0.00 0.05 0.43 0.48 0.52 0.55 0.61 2914 1
#> sigma 0.48 0.00 0.04 0.41 0.45 0.48 0.50 0.56 2807 1
#> log_lik -67.62 0.02 0.98 -70.25 -68.04 -67.33 -66.90 -66.63 1636 1
#> log_prior 6.35 0.00 0.19 5.93 6.23 6.37 6.49 6.70 2789 1
#> log_post -61.27 0.03 1.01 -63.99 -61.68 -60.97 -60.52 -60.24 1630 1
#> lp__ 29.89 0.02 1.00 27.22 29.48 30.18 30.62 30.90 1625 1
#>
#> Samples were drawn using NUTS(diag_e) at Wed Aug 23 03:13:47 2023.
#> 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).
#>