Compute weighted expectations
The E_loo() function computes weighted expectations (means, variances,
quantiles) using the importance weights obtained from the
PSIS smoothing procedure. The expectations estimated by the
E_loo() function assume that the PSIS approximation is working well.
A small Pareto k estimate is necessary,
but not sufficient, for E_loo() to give reliable estimates. Additional
diagnostic checks for gauging the reliability of the estimates are in
development and will be added in a future release.
E_loo(x, psis_object, ...)
## Default S3 method:
E_loo(
x,
psis_object,
...,
type = c("mean", "variance", "quantile"),
probs = NULL,
log_ratios = NULL
)
## S3 method for class 'matrix'
E_loo(
x,
psis_object,
...,
type = c("mean", "variance", "quantile"),
probs = NULL,
log_ratios = NULL
)x |
A numeric vector or matrix. |
psis_object |
An object returned by |
... |
Arguments passed to individual methods. |
type |
The type of expectation to compute. The options are
|
probs |
For computing quantiles, a vector of probabilities. |
log_ratios |
Optionally, a vector or matrix (the same dimensions as |
A named list with the following components:
valueThe result of the computation.
For the matrix method, value is a vector with ncol(x)
elements, with one exception: when type="quantile" and
multiple values are specified in probs the value component of
the returned object is a length(probs) by ncol(x) matrix.
For the default/vector method the value component is scalar, with
one exception: when type is "quantile" and multiple values
are specified in probs the value component is a vector with
length(probs) elements.
pareto_kFunction-specific diagnostic.
If log_ratios is not specified when calling E_loo(),
pareto_k will be NULL. Otherwise, for the matrix method it
will be a vector of length ncol(x) containing estimates of the shape
parameter k of the generalized Pareto distribution. For the
default/vector method, the estimate is a scalar.
# Use rstanarm package to quickly fit a model and get both a log-likelihood
# matrix and draws from the posterior predictive distribution
library("rstanarm")
# data from help("lm")
ctl <- c(4.17,5.58,5.18,6.11,4.50,4.61,5.17,4.53,5.33,5.14)
trt <- c(4.81,4.17,4.41,3.59,5.87,3.83,6.03,4.89,4.32,4.69)
d <- data.frame(
weight = c(ctl, trt),
group = gl(2, 10, 20, labels = c("Ctl","Trt"))
)
fit <- stan_glm(weight ~ group, data = d, refresh = 0)
yrep <- posterior_predict(fit)
dim(yrep)
log_ratios <- -1 * log_lik(fit)
dim(log_ratios)
r_eff <- relative_eff(exp(-log_ratios), chain_id = rep(1:4, each = 1000))
psis_object <- psis(log_ratios, r_eff = r_eff, cores = 2)
E_loo(yrep, psis_object, type = "mean")
E_loo(yrep, psis_object, type = "var")
E_loo(yrep, psis_object, type = "quantile", probs = 0.5) # median
E_loo(yrep, psis_object, type = "quantile", probs = c(0.1, 0.9))
# To get Pareto k diagnostic with E_loo we also need to provide the negative
# log-likelihood values using the log_ratios argument.
E_loo(yrep, psis_object, type = "mean", log_ratios = log_ratios)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.