Expectation-Maximization (EM) based fitting of beta
mixture densities to numerical samples. Note that the default value for the
optional parameter constrain_gt1 is set to FALSE, and that the default
value for the optional parameter k is set to 2. These values specify
that the EM algorithm will not constrain all beta parameters a and
b to be greater than 1, and that the standard AIC definition algorithm
will be used. Those settings have been chosen because they match with the
default settings in the corresponding SAS function.
Arguments
- sample
Object of type
bssd_binary_map.- ...
extra parameters are passed to
automixfit.
Value
object of type mix.
Examples
# Generate prior
set.seed(2021)
H <- 10
time <- 0.5 + cumsum(rexp(H, 5))
# Use constant hazard model:
hazard <- 0.15
prob <- 1 - exp(- hazard * time)
n <- rpois(H, lambda = 100 * time)
y <- rbinom(H, size = n, prob = prob)
x <- stan_map_summary_data(y = y, n = n, time = time,
a_alpha = 1 / 3, a_beta = 1 / 3,
b_alpha = 5, b_beta = 5)
#>
#> SAMPLING FOR MODEL 'map_prior_summary_data' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 1.8e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.18 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
#> Chain 1:
#> Chain 1: Iteration: 1 / 2000 [ 0%] (Warmup)
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#> Chain 1: Iteration: 2000 / 2000 [100%] (Sampling)
#> Chain 1:
#> Chain 1: Elapsed Time: 0.076 seconds (Warm-up)
#> Chain 1: 0.081 seconds (Sampling)
#> Chain 1: 0.157 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL 'map_prior_summary_data' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 9e-06 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.09 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2:
#> Chain 2:
#> Chain 2: Iteration: 1 / 2000 [ 0%] (Warmup)
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#> Chain 2: Iteration: 2000 / 2000 [100%] (Sampling)
#> Chain 2:
#> Chain 2: Elapsed Time: 0.07 seconds (Warm-up)
#> Chain 2: 0.081 seconds (Sampling)
#> Chain 2: 0.151 seconds (Total)
#> Chain 2:
#>
#> SAMPLING FOR MODEL 'map_prior_summary_data' NOW (CHAIN 3).
#> Chain 3:
#> Chain 3: Gradient evaluation took 1e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.1 seconds.
#> Chain 3: Adjust your expectations accordingly!
#> Chain 3:
#> Chain 3:
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#> Chain 3: Iteration: 2000 / 2000 [100%] (Sampling)
#> Chain 3:
#> Chain 3: Elapsed Time: 0.073 seconds (Warm-up)
#> Chain 3: 0.076 seconds (Sampling)
#> Chain 3: 0.149 seconds (Total)
#> Chain 3:
#>
#> SAMPLING FOR MODEL 'map_prior_summary_data' NOW (CHAIN 4).
#> Chain 4:
#> Chain 4: Gradient evaluation took 9e-06 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.09 seconds.
#> Chain 4: Adjust your expectations accordingly!
#> Chain 4:
#> Chain 4:
#> Chain 4: Iteration: 1 / 2000 [ 0%] (Warmup)
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#> Chain 4: Iteration: 2000 / 2000 [100%] (Sampling)
#> Chain 4:
#> Chain 4: Elapsed Time: 0.069 seconds (Warm-up)
#> Chain 4: 0.063 seconds (Sampling)
#> Chain 4: 0.132 seconds (Total)
#> Chain 4:
# Fit mixture to MCMC samples of MAP prior
mix <- fit_mixture(x)
mix
#> EM for Beta Mixture Model
#> Log-Likelihood = 10413.85
#>
#> Univariate beta mixture
#> Mixture Components:
#> comp1
#> w 1.00000
#> a 57.82155
#> b 332.19616