Posterior predictive mean, sd and interval from replicated datasets

sd is across replicate means, sd_pooled across all replicated observations; the second is the predictive spread and is always the wider.

Usage

Ppmean(yrep)

Arguments

yrep

Matrix whose row s is one replicated dataset.

Value

List with estimate, sd, sd_pooled, ci_lower, ci_upper, rep_mean, S, n.

Details

Formula: E[ytilde | y] ~= (1/S) sum_s ytilde^s, interval from empirical quantiles of the pooled draws

References

Gelman, Carlin, Stern, Dunson, Vehtari & Rubin (2013), Bayesian Data Analysis, 3rd edition, Section 6.3.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Ppmean(V)
#> $estimate
#> [1] 4.5
#> 
#> $sd
#> [1] 2.44949
#> 
#> $sd_pooled
#> [1] 2.44949
#> 
#> $ci_lower
#> [1] 1
#> 
#> $ci_upper
#> [1] 8
#> 
#> $rep_mean
#> [1] 1 2 3 4 5 6 7 8
#> 
#> $S
#> [1] 8
#> 
#> $n
#> [1] 1
#> 
#> $method
#> [1] "Posterior predictive summary, BDA3 Section 6.3"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"