dbarts: add standard error for interval predictions

[hfrick]

closes #976

library(parsnip)
library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
data(two_class_dat, package = "modeldata")

set.seed(1)
bt_cls_fit <- 
  parsnip::bart() %>% 
  set_mode("classification") %>% 
  set_engine("dbarts") %>% 
  fit(Class ~ ., data = two_class_dat)

set.seed(2)
bind_cols(
  predict(bt_cls_fit, two_class_dat, type = "prob"),
  predict(bt_cls_fit, two_class_dat, type = "pred_int", std_error = TRUE)
) %>%
 select(-contains(c("lower", "upper")))
#> # A tibble: 791 × 3
#>    .pred_Class1 .pred_Class2 .std_error
#>           <dbl>        <dbl>      <dbl>
#>  1       0.351         0.649      0.478
#>  2       0.823         0.177      0.356
#>  3       0.54          0.46       0.498
#>  4       0.552         0.448      0.497
#>  5       0.454         0.546      0.495
#>  6       0.222         0.778      0.420
#>  7       0.6           0.4        0.486
#>  8       0.412         0.588      0.495
#>  9       0.979         0.021      0.133
#> 10       0.0790        0.921      0.276
#> # ℹ 781 more rows

^{Created on 2023-06-05 with reprex v2.0.2}

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