Skip to contents

The sccomp_remove_outliers function takes as input a table of cell counts with columns for cell-group identifier, sample identifier, integer count, and factors (continuous or discrete). The user can define a linear model using an input R formula, where the first factor is the factor of interest. Alternatively, sccomp accepts single-cell data containers (e.g., Seurat, SingleCellExperiment, cell metadata, or group-size) and derives the count data from cell metadata.

Usage

sccomp_remove_outliers(
  .estimate,
  percent_false_positive = 5,
  cores = detectCores(),
  inference_method = attr(.estimate, "inference_method"),
  output_directory = "sccomp_draws_files",
  verbose = TRUE,
  mcmc_seed = sample_seed(),
  max_sampling_iterations = 20000,
  enable_loo = FALSE,
  sig_figs = 9,
  cache_stan_model = sccomp_stan_models_cache_dir,
  cleanup_draw_files = TRUE,
  approximate_posterior_inference = NULL,
  variational_inference = NULL,
  ...
)

Arguments

.estimate

A tibble including a cell_group name column, sample name column, read counts column (optional depending on the input class), and factor columns.

percent_false_positive

A real number between 0 and 100 (not inclusive), used to identify outliers with a specific false positive rate.

cores

Integer, the number of cores to be used for parallel calculations.

inference_method

Character string specifying the inference method to use ('pathfinder', 'hmc', or 'variational').

output_directory

A character string specifying the output directory for Stan draws.

verbose

Logical, whether to print progression details.

mcmc_seed

Integer, used for Markov-chain Monte Carlo reproducibility. By default, a random number is sampled from 1 to 999999.

max_sampling_iterations

Integer, limits the maximum number of iterations in case a large dataset is used, to limit computation time.

enable_loo

Logical, whether to enable model comparison using the R package LOO. This is useful for comparing fits between models, similar to ANOVA.

sig_figs

Number of significant figures to use for Stan model output. Default is 9.

cache_stan_model

A character string specifying the cache directory for compiled Stan models. The sccomp version will be automatically appended to ensure version isolation. Default is sccomp_stan_models_cache_dir which points to ~/.sccomp_models.

cleanup_draw_files

Logical, whether to automatically delete Stan draw CSV files after extracting results. These files can be large (MBs to GBs) and are typically only needed during the analysis session. Default is TRUE to save disk space. Set to FALSE if you need to inspect draw files for debugging.

approximate_posterior_inference

DEPRECATED, use the variational_inference argument.

variational_inference

DEPRECATED Logical, whether to use variational Bayes for posterior inference. It is faster and convenient. Setting this argument to FALSE runs full Bayesian (Hamiltonian Monte Carlo) inference, which is slower but the gold standard.

...

Additional arguments passed to the cmdstanr::sample function.

Value

A tibble (tbl), with the following columns:

  • cell_group - The cell groups being tested.

  • parameter - The parameter being estimated from the design matrix described by the input formula_composition and formula_variability.

  • factor - The covariate factor in the formula, if applicable (e.g., not present for Intercept or contrasts).

  • c_lower - Lower (2.5%) quantile of the posterior distribution for a composition (c) parameter.

  • c_effect - Mean of the posterior distribution for a composition (c) parameter.

  • c_upper - Upper (97.5%) quantile of the posterior distribution for a composition (c) parameter.

  • c_pH0 - Probability of the c_effect being smaller or bigger than the test_composition_above_logit_fold_change argument.

  • c_FDR - False discovery rate of the c_effect being smaller or bigger than the test_composition_above_logit_fold_change argument. False discovery rate for Bayesian models is calculated differently from frequentists models, as detailed in Mangiola et al, PNAS 2023.

  • c_n_eff - Effective sample size, the number of independent draws in the sample. The higher, the better.

  • c_R_k_hat - R statistic, a measure of chain equilibrium, should be within 0.05 of 1.0.

  • v_lower - Lower (2.5%) quantile of the posterior distribution for a variability (v) parameter.

  • v_effect - Mean of the posterior distribution for a variability (v) parameter.

  • v_upper - Upper (97.5%) quantile of the posterior distribution for a variability (v) parameter.

  • v_pH0 - Probability of the v_effect being smaller or bigger than the test_composition_above_logit_fold_change argument.

  • v_FDR - False discovery rate of the v_effect being smaller or bigger than the test_composition_above_logit_fold_change argument. False discovery rate for Bayesian models is calculated differently from frequentists models, as detailed in Mangiola et al, PNAS 2023.

  • v_n_eff - Effective sample size for a variability (v) parameter.

  • v_R_k_hat - R statistic for a variability (v) parameter, a measure of chain equilibrium.

The function also attaches several attributes to the result:

  • count_data - The original count data used in the analysis, stored as an attribute for efficient access.

  • model_input - The model input data used for fitting.

  • formula_composition - The formula used for composition modeling.

  • formula_variability - The formula used for variability modeling.

  • fit - The Stan fit object (if pass_fit = TRUE).

References

S. Mangiola, A.J. Roth-Schulze, M. Trussart, E. Zozaya-Valdés, M. Ma, Z. Gao, A.F. Rubin, T.P. Speed, H. Shim, & A.T. Papenfuss, sccomp: Robust differential composition and variability analysis for single-cell data, Proc. Natl. Acad. Sci. U.S.A. 120 (33) e2203828120, https://doi.org/10.1073/pnas.2203828120 (2023).

Examples


print("cmdstanr is needed to run this example.")
#> [1] "cmdstanr is needed to run this example."
# Note: Before running the example, ensure that the 'cmdstanr' package is installed:
# install.packages("cmdstanr", repos = c("https://stan-dev.r-universe.dev/", getOption("repos")))

# \donttest{
  if (instantiate::stan_cmdstan_exists()) {
    data("counts_obj")
    
    estimate = sccomp_estimate(
      counts_obj,
      ~ type,
      ~1,
      "sample",
      "cell_group",
      "count",
      cores = 1
    ) |>
    sccomp_remove_outliers(cores = 1)
  }
#> sccomp says: count column is an integer. The sum-constrained beta binomial model will be used
#> sccomp says: estimation
#> sccomp says: the composition design matrix has columns: (Intercept), typecancer
#> sccomp says: the variability design matrix has columns: (Intercept)
#> Loading model from cache...
#> Path [1] :Initial log joint density = -481896.467352 
#> Path [1] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              59      -4.788e+05      2.512e-03   2.101e-01    6.694e-01  6.694e-01      3450 -3.697e+03 -3.715e+03                   
#> Path [1] :Best Iter: [57] ELBO (-3696.807202) evaluations: (3450) 
#> Path [2] :Initial log joint density = -484083.970253 
#> Path [2] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              57      -4.788e+05      6.071e-03   2.271e-01    8.427e-01  8.427e-01      3238 -3.704e+03 -3.711e+03                   
#> Path [2] :Best Iter: [56] ELBO (-3703.553334) evaluations: (3238) 
#> Path [3] :Initial log joint density = -481222.846308 
#> Path [3] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              53      -4.788e+05      1.581e-02   2.352e-01    1.000e+00  1.000e+00      2964 -3.708e+03 -3.709e+03                   
#> Path [3] :Best Iter: [43] ELBO (-3708.289445) evaluations: (2964) 
#> Path [4] :Initial log joint density = -481773.234958 
#> Path [4] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              54      -4.788e+05      1.375e-02   2.651e-01    9.089e-01  9.089e-01      3000 -3.709e+03 -3.724e+03                   
#> Path [4] :Best Iter: [53] ELBO (-3709.305253) evaluations: (3000) 
#> Path [5] :Initial log joint density = -482892.999399 
#> Path [5] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              57      -4.788e+05      6.617e-03   2.319e-01    1.000e+00  1.000e+00      3236 -3.706e+03 -3.703e+03                   
#> Path [5] :Best Iter: [57] ELBO (-3702.996901) evaluations: (3236) 
#> Path [6] :Initial log joint density = -483558.228932 
#> Path [6] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              54      -4.788e+05      4.555e-03   2.101e-01    8.697e-01  8.697e-01      3051 -3.706e+03 -3.721e+03                   
#> Path [6] :Best Iter: [52] ELBO (-3706.340078) evaluations: (3051) 
#> Path [7] :Initial log joint density = -481303.869532 
#> Path [7] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              57      -4.788e+05      5.165e-03   1.924e-01    1.000e+00  1.000e+00      3267 -3.706e+03 -3.710e+03                   
#> Path [7] :Best Iter: [55] ELBO (-3705.578834) evaluations: (3267) 
#> Path [8] :Initial log joint density = -481686.263276 
#> Path [8] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              61      -4.788e+05      9.789e-03   2.467e-01    1.000e+00  1.000e+00      3568 -3.701e+03 -3.705e+03                   
#> Path [8] :Best Iter: [60] ELBO (-3701.034949) evaluations: (3568) 
#> Path [9] :Initial log joint density = -482383.940764 
#> Path [9] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              58      -4.788e+05      7.125e-03   2.594e-01    4.480e-01  1.000e+00      3382 -3.698e+03 -3.711e+03                   
#> Path [9] :Best Iter: [57] ELBO (-3698.114163) evaluations: (3382) 
#> Path [10] :Initial log joint density = -481635.627523 
#> Path [10] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              55      -4.788e+05      7.280e-03   2.332e-01    1.000e+00  1.000e+00      3026 -3.708e+03 -3.702e+03                   
#> Path [10] :Best Iter: [55] ELBO (-3702.392418) evaluations: (3026) 
#> Path [11] :Initial log joint density = -481908.651841 
#> Path [11] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              62      -4.788e+05      3.559e-03   2.659e-01    6.441e-01  6.441e-01      3692 -3.699e+03 -3.711e+03                   
#> Path [11] :Best Iter: [60] ELBO (-3698.670819) evaluations: (3692) 
#> Path [12] :Initial log joint density = -481778.442824 
#> Path [12] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              55      -4.788e+05      7.360e-03   2.485e-01    1.000e+00  1.000e+00      3176 -3.705e+03 -3.705e+03                   
#> Path [12] :Best Iter: [55] ELBO (-3704.517522) evaluations: (3176) 
#> Path [13] :Initial log joint density = -481786.031954 
#> Path [13] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              56      -4.788e+05      9.793e-03   2.057e-01    1.000e+00  1.000e+00      3212 -3.702e+03 -3.703e+03                   
#> Path [13] :Best Iter: [55] ELBO (-3702.209203) evaluations: (3212) 
#> Path [14] :Initial log joint density = -481524.166240 
#> Path [14] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              52      -4.788e+05      6.523e-03   2.533e-01    1.000e+00  1.000e+00      2827 -3.709e+03 -3.715e+03                   
#> Path [14] :Best Iter: [48] ELBO (-3708.587090) evaluations: (2827) 
#> Path [15] :Initial log joint density = -484566.555895 
#> Path [15] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              57      -4.788e+05      5.244e-03   2.183e-01    1.000e+00  1.000e+00      3179 -3.701e+03 -3.700e+03                   
#> Path [15] :Best Iter: [57] ELBO (-3700.362695) evaluations: (3179) 
#> Path [16] :Initial log joint density = -481699.345883 
#> Path [16] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              52      -4.788e+05      5.834e-03   2.240e-01    6.887e-01  6.887e-01      2881 -3.708e+03 -3.720e+03                   
#> Path [16] :Best Iter: [51] ELBO (-3707.595965) evaluations: (2881) 
#> Path [17] :Initial log joint density = -481923.630681 
#> Path [17] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              55      -4.788e+05      2.858e-03   2.180e-01    7.100e-01  7.100e-01      3126 -3.709e+03 -3.717e+03                   
#> Path [17] :Best Iter: [48] ELBO (-3709.464405) evaluations: (3126) 
#> Path [18] :Initial log joint density = -481637.811270 
#> Path [18] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              58      -4.788e+05      1.806e-02   2.750e-01    1.000e+00  1.000e+00      3329 -3.701e+03 -3.700e+03                   
#> Path [18] :Best Iter: [58] ELBO (-3699.721646) evaluations: (3329) 
#> Path [19] :Initial log joint density = -481573.644062 
#> Path [19] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              55      -4.788e+05      1.350e-02   4.022e-01    1.000e+00  1.000e+00      3147 -3.712e+03 -3.705e+03                   
#> Path [19] :Best Iter: [55] ELBO (-3705.105296) evaluations: (3147) 
#> Path [20] :Initial log joint density = -481272.771647 
#> Path [20] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              59      -4.788e+05      4.241e-03   1.373e-01    1.000e+00  1.000e+00      3305 -3.699e+03 -3.712e+03                   
#> Path [20] :Best Iter: [55] ELBO (-3699.089999) evaluations: (3305) 
#> Path [21] :Initial log joint density = -481920.990493 
#> Path [21] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              60      -4.788e+05      1.437e-02   2.811e-01    1.000e+00  1.000e+00      3461 -3.701e+03 -3.700e+03                   
#> Path [21] :Best Iter: [60] ELBO (-3700.482597) evaluations: (3461) 
#> Path [22] :Initial log joint density = -481317.850746 
#> Path [22] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              55      -4.788e+05      1.062e-02   2.637e-01    1.000e+00  1.000e+00      3157 -3.703e+03 -3.703e+03                   
#> Path [22] :Best Iter: [55] ELBO (-3702.786997) evaluations: (3157) 
#> Path [23] :Initial log joint density = -481920.785305 
#> Path [23] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              61      -4.788e+05      8.656e-03   2.784e-01    1.000e+00  1.000e+00      3637 -3.701e+03 -3.704e+03                   
#> Path [23] :Best Iter: [55] ELBO (-3701.470379) evaluations: (3637) 
#> Path [24] :Initial log joint density = -481664.566903 
#> Path [24] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              55      -4.788e+05      9.376e-03   2.411e-01    1.000e+00  1.000e+00      3079 -3.709e+03 -3.711e+03                   
#> Path [24] :Best Iter: [49] ELBO (-3709.097389) evaluations: (3079) 
#> Path [25] :Initial log joint density = -481715.228608 
#> Path [25] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              60      -4.788e+05      1.181e-02   2.195e-01    1.000e+00  1.000e+00      3396 -3.701e+03 -3.700e+03                   
#> Path [25] :Best Iter: [60] ELBO (-3700.467419) evaluations: (3396) 
#> Path [26] :Initial log joint density = -481617.243441 
#> Path [26] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              60      -4.788e+05      8.661e-03   1.846e-01    9.041e-01  9.041e-01      3561 -3.699e+03 -3.704e+03                   
#> Path [26] :Best Iter: [58] ELBO (-3698.751167) evaluations: (3561) 
#> Path [27] :Initial log joint density = -481780.040886 
#> Path [27] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              55      -4.788e+05      7.780e-03   3.650e-01    3.670e-01  1.000e+00      3080 -3.708e+03 -3.715e+03                   
#> Path [27] :Best Iter: [49] ELBO (-3708.210777) evaluations: (3080) 
#> Path [28] :Initial log joint density = -481753.412444 
#> Path [28] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              60      -4.788e+05      7.416e-03   2.171e-01    1.000e+00  1.000e+00      3503 -3.697e+03 -3.704e+03                   
#> Path [28] :Best Iter: [57] ELBO (-3697.241979) evaluations: (3503) 
#> Path [29] :Initial log joint density = -485154.555876 
#> Path [29] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              59      -4.788e+05      1.396e-02   3.088e-01    1.000e+00  1.000e+00      3480 -3.696e+03 -3.706e+03                   
#> Path [29] :Best Iter: [58] ELBO (-3695.713075) evaluations: (3480) 
#> Path [30] :Initial log joint density = -481634.754658 
#> Path [30] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              55      -4.788e+05      5.883e-03   2.410e-01    1.000e+00  1.000e+00      3116 -3.707e+03 -3.703e+03                   
#> Path [30] :Best Iter: [55] ELBO (-3703.316866) evaluations: (3116) 
#> Path [31] :Initial log joint density = -481534.485288 
#> Path [31] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              56      -4.788e+05      1.125e-02   3.355e-01    1.000e+00  1.000e+00      3169 -3.700e+03 -3.708e+03                   
#> Path [31] :Best Iter: [55] ELBO (-3699.736811) evaluations: (3169) 
#> Path [32] :Initial log joint density = -485618.790138 
#> Path [32] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              59      -4.788e+05      7.000e-03   2.063e-01    1.000e+00  1.000e+00      3510 -3.702e+03 -3.704e+03                   
#> Path [32] :Best Iter: [56] ELBO (-3701.928421) evaluations: (3510) 
#> Path [33] :Initial log joint density = -481557.121654 
#> Path [33] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              53      -4.788e+05      4.051e-03   2.690e-01    6.804e-01  6.804e-01      2914 -3.707e+03 -3.723e+03                   
#> Path [33] :Best Iter: [49] ELBO (-3706.863762) evaluations: (2914) 
#> Path [34] :Initial log joint density = -485051.908004 
#> Path [34] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              58      -4.788e+05      1.129e-02   3.728e-01    1.000e+00  1.000e+00      3392 -3.702e+03 -3.706e+03                   
#> Path [34] :Best Iter: [56] ELBO (-3701.716844) evaluations: (3392) 
#> Path [35] :Initial log joint density = -481666.395173 
#> Path [35] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              64      -4.788e+05      1.287e-02   1.850e-01    8.774e-01  8.774e-01      3980 -3.699e+03 -3.705e+03                   
#> Path [35] :Best Iter: [61] ELBO (-3699.279073) evaluations: (3980) 
#> Path [36] :Initial log joint density = -481370.012494 
#> Path [36] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              59      -4.788e+05      1.918e-02   2.577e-01    1.000e+00  1.000e+00      3489 -3.701e+03 -3.699e+03                   
#> Path [36] :Best Iter: [59] ELBO (-3698.869380) evaluations: (3489) 
#> Path [37] :Initial log joint density = -481472.497263 
#> Path [37] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              56      -4.788e+05      1.426e-02   2.420e-01    1.000e+00  1.000e+00      3158 -3.698e+03 -3.702e+03                   
#> Path [37] :Best Iter: [55] ELBO (-3697.732840) evaluations: (3158) 
#> Path [38] :Initial log joint density = -481531.521734 
#> Path [38] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              59      -4.788e+05      1.509e-02   3.466e-01    9.593e-01  9.593e-01      3503 -3.703e+03 -3.712e+03                   
#> Path [38] :Best Iter: [58] ELBO (-3702.999987) evaluations: (3503) 
#> Path [39] :Initial log joint density = -481593.608909 
#> Path [39] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              55      -4.788e+05      4.726e-03   1.832e-01    8.477e-01  8.477e-01      3080 -3.707e+03 -3.712e+03                   
#> Path [39] :Best Iter: [54] ELBO (-3706.922273) evaluations: (3080) 
#> Path [40] :Initial log joint density = -481466.586838 
#> Path [40] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              53      -4.788e+05      6.336e-03   2.282e-01    1.000e+00  1.000e+00      2957 -3.707e+03 -3.719e+03                   
#> Path [40] :Best Iter: [44] ELBO (-3706.614827) evaluations: (2957) 
#> Path [41] :Initial log joint density = -481447.711773 
#> Path [41] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              53      -4.788e+05      1.397e-02   2.186e-01    1.000e+00  1.000e+00      2866 -3.710e+03 -3.714e+03                   
#> Path [41] :Best Iter: [37] ELBO (-3709.965464) evaluations: (2866) 
#> Path [42] :Initial log joint density = -481879.509224 
#> Path [42] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              64      -4.788e+05      2.278e-03   1.989e-01    6.965e-01  6.965e-01      3745 -3.699e+03 -3.715e+03                   
#> Path [42] :Best Iter: [61] ELBO (-3698.616332) evaluations: (3745) 
#> Path [43] :Initial log joint density = -481622.394295 
#> Path [43] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              53      -4.788e+05      4.565e-03   1.590e-01    8.394e-01  8.394e-01      2961 -3.708e+03 -3.720e+03                   
#> Path [43] :Best Iter: [40] ELBO (-3708.435375) evaluations: (2961) 
#> Path [44] :Initial log joint density = -481488.688805 
#> Path [44] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              50      -4.788e+05      9.828e-03   2.527e-01    9.648e-01  9.648e-01      2669 -3.710e+03 -3.718e+03                   
#> Path [44] :Best Iter: [49] ELBO (-3709.822214) evaluations: (2669) 
#> Path [45] :Initial log joint density = -483315.963384 
#> Path [45] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              60      -4.788e+05      1.024e-02   2.202e-01    1.000e+00  1.000e+00      3607 -3.699e+03 -3.701e+03                   
#> Path [45] :Best Iter: [57] ELBO (-3699.050640) evaluations: (3607) 
#> Path [46] :Initial log joint density = -481877.485840 
#> Path [46] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              53      -4.788e+05      6.522e-03   2.358e-01    1.000e+00  1.000e+00      2961 -3.708e+03 -3.724e+03                   
#> Path [46] :Best Iter: [50] ELBO (-3707.996840) evaluations: (2961) 
#> Path [47] :Initial log joint density = -481472.383508 
#> Path [47] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              58      -4.788e+05      1.238e-02   1.873e-01    1.000e+00  1.000e+00      3270 -3.700e+03 -3.703e+03                   
#> Path [47] :Best Iter: [56] ELBO (-3699.971115) evaluations: (3270) 
#> Path [48] :Initial log joint density = -481788.198136 
#> Path [48] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              53      -4.788e+05      6.152e-03   2.292e-01    1.000e+00  1.000e+00      2955 -3.707e+03 -3.713e+03                   
#> Path [48] :Best Iter: [46] ELBO (-3706.822298) evaluations: (2955) 
#> Path [49] :Initial log joint density = -481938.438955 
#> Path [49] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              58      -4.788e+05      8.132e-03   3.560e-01    9.130e-01  9.130e-01      3397 -3.702e+03 -3.712e+03                   
#> Path [49] :Best Iter: [56] ELBO (-3701.745714) evaluations: (3397) 
#> Path [50] :Initial log joint density = -481480.323530 
#> Path [50] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>              55      -4.788e+05      1.104e-02   2.309e-01    1.000e+00  1.000e+00      3074 -3.706e+03 -3.705e+03                   
#> Path [50] :Best Iter: [55] ELBO (-3705.063488) evaluations: (3074) 
#> Finished in  13.6 seconds.
#> sccomp says: to do hypothesis testing run `sccomp_test()`,
#>   the `test_composition_above_logit_fold_change` = 0.1 equates to a change of ~10%, and
#>   0.7 equates to ~100% increase, if the baseline is ~0.1 proportion.
#>   Use `sccomp_proportional_fold_change` to convert c_effect (linear) to proportion difference (non-linear).
#> sccomp says: auto-cleanup removed 1 draw files from 'sccomp_draws_files'
#> Loading model from cache...
#> Running standalone generated quantities after 1 MCMC chain, with 1 thread(s) per chain...
#> 
#> Chain 1 finished in 0.0 seconds.
#> sccomp says: outlier identification - step 1/2
#> Loading model from cache...
#> Path [1] :Initial log joint density = -433080.771678 
#> Path [1] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      4.634e-02   1.005e+03    2.491e-02  2.491e-02      8191 -3.324e+03 -6.933e+04                   
#> Path [1] :Best Iter: [55] ELBO (-3323.856544) evaluations: (8191) 
#> Path [2] :Initial log joint density = -431949.217341 
#> Path [2] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      5.040e-02   2.508e+03    2.158e-02  4.729e-02      8128 -3.327e+03 -4.726e+06                   
#> Path [2] :Best Iter: [41] ELBO (-3327.161313) evaluations: (8128) 
#> Path [3] :Initial log joint density = -432019.189686 
#> Path [3] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      1.315e-01   3.097e+03    1.949e-02  1.949e-02      8599 -3.325e+03 -1.630e+05                   
#> Path [3] :Best Iter: [41] ELBO (-3324.716260) evaluations: (8599) 
#> Path [4] :Initial log joint density = -431569.121141 
#> Path [4] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.290e+05      7.140e-02   1.083e+03    7.080e-02  7.080e-02      7966 -3.324e+03 -1.449e+04                   
#> Path [4] :Best Iter: [52] ELBO (-3324.086912) evaluations: (7966) 
#> Path [5] :Initial log joint density = -432222.364311 
#> Path [5] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      3.282e-02   1.672e+03    2.115e-02  2.115e-02      8291 -3.325e+03 -7.465e+03                   
#> Path [5] :Best Iter: [49] ELBO (-3325.021823) evaluations: (8291) 
#> Path [6] :Initial log joint density = -431890.118415 
#> Path [6] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      3.878e-02   2.137e+03    3.086e-02  3.086e-02      8258 -3.323e+03 -2.249e+04                   
#> Path [6] :Best Iter: [40] ELBO (-3323.407594) evaluations: (8258) 
#> Path [7] :Initial log joint density = -431981.248349 
#> Path [7] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      3.610e-02   5.059e+03    1.371e-02  1.371e-02      8143 -3.327e+03 -1.698e+08                   
#> Path [7] :Best Iter: [43] ELBO (-3326.696557) evaluations: (8143) 
#> Path [8] :Initial log joint density = -431626.062948 
#> Path [8] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      6.964e-02   2.193e+03    1.686e-02  1.686e-02      8386 -3.325e+03 -8.135e+05                   
#> Path [8] :Best Iter: [47] ELBO (-3325.194569) evaluations: (8386) 
#> Path [9] :Initial log joint density = -431579.584206 
#> Path [9] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      3.369e-02   3.128e+03    1.744e-02  1.744e-02      8464 -3.325e+03 -1.025e+05                   
#> Path [9] :Best Iter: [43] ELBO (-3325.470401) evaluations: (8464) 
#> Path [10] :Initial log joint density = -432027.299682 
#> Path [10] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.290e+05      3.763e-02   1.935e+03    3.841e-02  3.841e-02      7940 -3.316e+03 -6.983e+03                   
#> Path [10] :Best Iter: [57] ELBO (-3316.080566) evaluations: (7940) 
#> Path [11] :Initial log joint density = -431774.053774 
#> Path [11] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      1.023e-01   5.848e+03    2.987e-02  2.987e-02      8308 -3.324e+03 -2.909e+06                   
#> Path [11] :Best Iter: [51] ELBO (-3323.559964) evaluations: (8308) 
#> Path [12] :Initial log joint density = -431665.278313 
#> Path [12] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      4.440e-02   2.014e+03    3.339e-02  3.339e-02      8217 -3.328e+03 -1.632e+04                   
#> Path [12] :Best Iter: [48] ELBO (-3328.035515) evaluations: (8217) 
#> Path [13] :Initial log joint density = -431943.842758 
#> Path [13] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.290e+05      3.181e-02   9.060e+02    3.207e-02  8.216e-02      7976 -3.321e+03 -5.119e+03                   
#> Path [13] :Best Iter: [56] ELBO (-3320.715768) evaluations: (7976) 
#> Path [14] :Initial log joint density = -432424.081777 
#> Path [14] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.290e+05      8.557e-02   2.483e+03    4.174e-02  4.174e-02      8085 -3.319e+03 -1.025e+04                   
#> Path [14] :Best Iter: [58] ELBO (-3318.912969) evaluations: (8085) 
#> Path [15] :Initial log joint density = -431916.831548 
#> Path [15] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      9.646e-02   2.569e+03    2.652e-02  2.652e-02      8309 -3.322e+03 -9.905e+07                   
#> Path [15] :Best Iter: [45] ELBO (-3321.558289) evaluations: (8309) 
#> Path [16] :Initial log joint density = -431613.967463 
#> Path [16] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.290e+05      7.636e-02   1.520e+03    5.066e-02  5.066e-02      8181 -3.320e+03 -3.889e+04                   
#> Path [16] :Best Iter: [49] ELBO (-3320.409466) evaluations: (8181) 
#> Path [17] :Initial log joint density = -435333.022189 
#> Path [17] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      6.323e-02   1.012e+03    3.920e-02  3.920e-02      8036 -3.325e+03 -1.417e+04                   
#> Path [17] :Best Iter: [53] ELBO (-3325.137235) evaluations: (8036) 
#> Path [18] :Initial log joint density = -433438.412158 
#> Path [18] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      1.074e-01   1.115e+03    2.409e-02  4.762e-02      8153 -3.326e+03 -9.080e+05                   
#> Path [18] :Best Iter: [48] ELBO (-3326.020790) evaluations: (8153) 
#> Path [19] :Initial log joint density = -432165.426871 
#> Path [19] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      5.548e-02   4.195e+03    2.888e-02  2.888e-02      8338 -3.326e+03 -4.106e+04                   
#> Path [19] :Best Iter: [47] ELBO (-3326.170924) evaluations: (8338) 
#> Path [20] :Initial log joint density = -431915.254627 
#> Path [20] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      6.125e-02   5.710e+03    2.569e-02  2.569e-02      8415 -3.330e+03 -3.149e+06                   
#> Path [20] :Best Iter: [44] ELBO (-3330.336218) evaluations: (8415) 
#> Path [21] :Initial log joint density = -431780.911061 
#> Path [21] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      5.007e-02   1.676e+03    4.320e-02  4.320e-02      8417 -3.330e+03 -5.555e+04                   
#> Path [21] :Best Iter: [44] ELBO (-3330.372516) evaluations: (8417) 
#> Path [22] :Initial log joint density = -434054.169591 
#> Path [22] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      1.356e-02   2.239e+03    1.205e-02  1.205e-02      8474 -3.323e+03 -2.516e+04                   
#> Path [22] :Best Iter: [49] ELBO (-3323.462665) evaluations: (8474) 
#> Path [23] :Initial log joint density = -431891.213400 
#> Path [23] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.290e+05      5.913e-02   1.504e+03    2.470e-02  6.374e-02      7817 -3.319e+03 -1.006e+05                   
#> Path [23] :Best Iter: [57] ELBO (-3318.648636) evaluations: (7817) 
#> Path [24] :Initial log joint density = -434794.393636 
#> Path [24] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.290e+05      4.104e-02   8.288e+02    4.014e-02  4.014e-02      8218 -3.319e+03 -1.002e+05                   
#> Path [24] :Best Iter: [57] ELBO (-3319.263082) evaluations: (8218) 
#> Path [25] :Initial log joint density = -431890.154889 
#> Path [25] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      2.400e-02   2.212e+03    1.871e-02  1.871e-02      8142 -3.327e+03 -1.003e+04                   
#> Path [25] :Best Iter: [48] ELBO (-3327.210831) evaluations: (8142) 
#> Path [26] :Initial log joint density = -433019.061482 
#> Path [26] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      3.014e-02   1.223e+03    2.025e-02  2.025e-02      8143 -3.321e+03 -7.395e+04                   
#> Path [26] :Best Iter: [56] ELBO (-3320.576506) evaluations: (8143) 
#> Path [27] :Initial log joint density = -431506.538666 
#> Path [27] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      4.023e-02   3.331e+03    2.239e-02  2.239e-02      8474 -3.326e+03 -1.743e+04                   
#> Path [27] :Best Iter: [43] ELBO (-3325.880243) evaluations: (8474) 
#> Path [28] :Initial log joint density = -432096.857394 
#> Path [28] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      8.816e-02   1.821e+03    5.257e-02  5.257e-02      8138 -3.320e+03 -2.152e+04                   
#> Path [28] :Best Iter: [57] ELBO (-3319.766831) evaluations: (8138) 
#> Path [29] :Initial log joint density = -433644.226219 
#> Path [29] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      6.936e-02   2.237e+03    2.941e-02  6.226e-02      8162 -3.322e+03 -6.358e+04                   
#> Path [29] :Best Iter: [55] ELBO (-3321.902901) evaluations: (8162) 
#> Path [30] :Initial log joint density = -431605.693849 
#> Path [30] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      7.048e-02   9.244e+03    1.223e-02  1.223e-02      8391 -3.329e+03 -4.184e+06                   
#> Path [30] :Best Iter: [41] ELBO (-3329.094064) evaluations: (8391) 
#> Path [31] :Initial log joint density = -432749.961475 
#> Path [31] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      5.335e-02   2.169e+03    3.714e-02  3.714e-02      8323 -3.326e+03 -5.081e+04                   
#> Path [31] :Best Iter: [49] ELBO (-3326.377036) evaluations: (8323) 
#> Path [32] :Initial log joint density = -431672.913398 
#> Path [32] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      5.208e-02   2.805e+03    2.809e-02  2.809e-02      8322 -3.329e+03 -4.868e+06                   
#> Path [32] :Best Iter: [48] ELBO (-3328.683704) evaluations: (8322) 
#> Path [33] :Initial log joint density = -431859.733699 
#> Path [33] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.290e+05      6.967e-02   1.421e+03    3.466e-02  3.466e-02      8395 -3.327e+03 -1.469e+04                   
#> Path [33] :Best Iter: [56] ELBO (-3327.327368) evaluations: (8395) 
#> Path [34] :Initial log joint density = -431935.416593 
#> Path [34] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      5.787e-02   6.087e+03    2.306e-02  2.306e-02      8095 -3.329e+03 -1.447e+06                   
#> Path [34] :Best Iter: [41] ELBO (-3328.766023) evaluations: (8095) 
#> Path [35] :Initial log joint density = -431884.877672 
#> Path [35] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      4.265e-02   1.961e+03    1.472e-02  1.472e-02      7967 -3.322e+03 -1.160e+08                   
#> Path [35] :Best Iter: [56] ELBO (-3321.509849) evaluations: (7967) 
#> Path [36] :Initial log joint density = -432375.807700 
#> Path [36] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.290e+05      2.325e-02   1.443e+03    2.656e-02  2.656e-02      8181 -3.318e+03 -4.224e+03                   
#> Path [36] :Best Iter: [57] ELBO (-3317.720129) evaluations: (8181) 
#> Path [37] :Initial log joint density = -431770.564516 
#> Path [37] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      1.903e-02   2.102e+03    1.419e-02  1.419e-02      8213 -3.326e+03 -1.356e+05                   
#> Path [37] :Best Iter: [44] ELBO (-3326.111522) evaluations: (8213) 
#> Path [38] :Initial log joint density = -432013.691962 
#> Path [38] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      7.016e-02   2.368e+03    1.806e-02  1.806e-02      8308 -3.327e+03 -1.276e+06                   
#> Path [38] :Best Iter: [51] ELBO (-3326.520923) evaluations: (8308) 
#> Path [39] :Initial log joint density = -431970.270966 
#> Path [39] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      2.262e-02   3.019e+03    1.899e-02  1.899e-02      8280 -3.328e+03 -4.563e+04                   
#> Path [39] :Best Iter: [47] ELBO (-3327.564592) evaluations: (8280) 
#> Path [40] :Initial log joint density = -433811.602858 
#> Path [40] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      3.816e-02   1.438e+03    4.514e-02  4.514e-02      8174 -3.318e+03 -1.947e+04                   
#> Path [40] :Best Iter: [55] ELBO (-3317.538379) evaluations: (8174) 
#> Path [41] :Initial log joint density = -432461.655685 
#> Path [41] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.290e+05      4.283e-02   1.481e+03    1.923e-02  1.923e-02      8168 -3.323e+03 -3.223e+04                   
#> Path [41] :Best Iter: [53] ELBO (-3323.165222) evaluations: (8168) 
#> Path [42] :Initial log joint density = -433669.015119 
#> Path [42] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      5.662e-02   1.680e+03    2.845e-02  2.845e-02      8193 -3.323e+03 -1.639e+05                   
#> Path [42] :Best Iter: [56] ELBO (-3322.586945) evaluations: (8193) 
#> Path [43] :Initial log joint density = -432968.922252 
#> Path [43] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      7.415e-02   3.805e+03    2.685e-02  2.685e-02      8390 -3.325e+03 -3.081e+05                   
#> Path [43] :Best Iter: [46] ELBO (-3325.162424) evaluations: (8390) 
#> Path [44] :Initial log joint density = -433412.858946 
#> Path [44] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      5.931e-02   8.397e+02    3.209e-02  3.209e-02      8271 -3.324e+03 -6.685e+05                   
#> Path [44] :Best Iter: [55] ELBO (-3324.317125) evaluations: (8271) 
#> Path [45] :Initial log joint density = -431728.712645 
#> Path [45] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      4.506e-02   6.576e+03    1.349e-02  1.349e-02      8165 -3.325e+03 -5.641e+07                   
#> Path [45] :Best Iter: [44] ELBO (-3325.043214) evaluations: (8165) 
#> Path [46] :Initial log joint density = -431857.823816 
#> Path [46] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      3.763e-02   3.087e+03    2.643e-02  2.643e-02      8247 -3.329e+03 -1.495e+04                   
#> Path [46] :Best Iter: [53] ELBO (-3329.066212) evaluations: (8247) 
#> Path [47] :Initial log joint density = -434361.617286 
#> Path [47] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      9.612e-02   2.562e+03    1.819e-02  4.067e-02      8049 -3.321e+03 -1.070e+07                   
#> Path [47] :Best Iter: [57] ELBO (-3320.709397) evaluations: (8049) 
#> Path [48] :Initial log joint density = -431866.269737 
#> Path [48] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      6.167e-02   3.462e+03    1.943e-02  1.943e-02      8210 -3.326e+03 -2.014e+06                   
#> Path [48] :Best Iter: [42] ELBO (-3325.995014) evaluations: (8210) 
#> Path [49] :Initial log joint density = -436070.697148 
#> Path [49] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.290e+05      3.161e-02   8.890e+02    3.416e-02  3.416e-02      8260 -3.321e+03 -7.345e+03                   
#> Path [49] :Best Iter: [55] ELBO (-3320.816235) evaluations: (8260) 
#> Path [50] :Initial log joint density = -431968.407034 
#> Path [50] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      2.737e-02   2.390e+03    2.203e-02  2.203e-02      8436 -3.326e+03 -5.640e+04                   
#> Path [50] :Best Iter: [47] ELBO (-3326.208287) evaluations: (8436) 
#> Finished in  30.4 seconds.
#> Running standalone generated quantities after 1 MCMC chain, with 1 thread(s) per chain...
#> 
#> Chain 1 finished in 0.0 seconds.
#> sccomp says: outlier-free model fitting - step 2/2
#> sccomp says: the composition design matrix has columns: (Intercept), typecancer
#> sccomp says: the variability design matrix has columns: (Intercept)
#> Loading model from cache...
#> Path [1] :Initial log joint density = -433080.771678 
#> Path [1] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      4.634e-02   1.005e+03    2.491e-02  2.491e-02      8191 -3.324e+03 -6.933e+04                   
#> Path [1] :Best Iter: [55] ELBO (-3323.856544) evaluations: (8191) 
#> Path [2] :Initial log joint density = -431949.217341 
#> Path [2] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      5.040e-02   2.508e+03    2.158e-02  4.729e-02      8128 -3.327e+03 -4.726e+06                   
#> Path [2] :Best Iter: [41] ELBO (-3327.161313) evaluations: (8128) 
#> Path [3] :Initial log joint density = -432019.189686 
#> Path [3] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      1.315e-01   3.097e+03    1.949e-02  1.949e-02      8599 -3.325e+03 -1.630e+05                   
#> Path [3] :Best Iter: [41] ELBO (-3324.716260) evaluations: (8599) 
#> Path [4] :Initial log joint density = -431569.121141 
#> Path [4] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.290e+05      7.140e-02   1.083e+03    7.080e-02  7.080e-02      7966 -3.324e+03 -1.449e+04                   
#> Path [4] :Best Iter: [52] ELBO (-3324.086912) evaluations: (7966) 
#> Path [5] :Initial log joint density = -432222.364311 
#> Path [5] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      3.282e-02   1.672e+03    2.115e-02  2.115e-02      8291 -3.325e+03 -7.465e+03                   
#> Path [5] :Best Iter: [49] ELBO (-3325.021823) evaluations: (8291) 
#> Path [6] :Initial log joint density = -431890.118415 
#> Path [6] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      3.878e-02   2.137e+03    3.086e-02  3.086e-02      8258 -3.323e+03 -2.249e+04                   
#> Path [6] :Best Iter: [40] ELBO (-3323.407594) evaluations: (8258) 
#> Path [7] :Initial log joint density = -431981.248349 
#> Path [7] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      3.610e-02   5.059e+03    1.371e-02  1.371e-02      8143 -3.327e+03 -1.698e+08                   
#> Path [7] :Best Iter: [43] ELBO (-3326.696557) evaluations: (8143) 
#> Path [8] :Initial log joint density = -431626.062948 
#> Path [8] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      6.964e-02   2.193e+03    1.686e-02  1.686e-02      8386 -3.325e+03 -8.135e+05                   
#> Path [8] :Best Iter: [47] ELBO (-3325.194569) evaluations: (8386) 
#> Path [9] :Initial log joint density = -431579.584206 
#> Path [9] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      3.369e-02   3.128e+03    1.744e-02  1.744e-02      8464 -3.325e+03 -1.025e+05                   
#> Path [9] :Best Iter: [43] ELBO (-3325.470401) evaluations: (8464) 
#> Path [10] :Initial log joint density = -432027.299682 
#> Path [10] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.290e+05      3.763e-02   1.935e+03    3.841e-02  3.841e-02      7940 -3.316e+03 -6.983e+03                   
#> Path [10] :Best Iter: [57] ELBO (-3316.080566) evaluations: (7940) 
#> Path [11] :Initial log joint density = -431774.053774 
#> Path [11] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      1.023e-01   5.848e+03    2.987e-02  2.987e-02      8308 -3.324e+03 -2.909e+06                   
#> Path [11] :Best Iter: [51] ELBO (-3323.559964) evaluations: (8308) 
#> Path [12] :Initial log joint density = -431665.278313 
#> Path [12] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      4.440e-02   2.014e+03    3.339e-02  3.339e-02      8217 -3.328e+03 -1.632e+04                   
#> Path [12] :Best Iter: [48] ELBO (-3328.035515) evaluations: (8217) 
#> Path [13] :Initial log joint density = -431943.842758 
#> Path [13] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.290e+05      3.181e-02   9.060e+02    3.207e-02  8.216e-02      7976 -3.321e+03 -5.119e+03                   
#> Path [13] :Best Iter: [56] ELBO (-3320.715768) evaluations: (7976) 
#> Path [14] :Initial log joint density = -432424.081777 
#> Path [14] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.290e+05      8.557e-02   2.483e+03    4.174e-02  4.174e-02      8085 -3.319e+03 -1.025e+04                   
#> Path [14] :Best Iter: [58] ELBO (-3318.912969) evaluations: (8085) 
#> Path [15] :Initial log joint density = -431916.831548 
#> Path [15] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      9.646e-02   2.569e+03    2.652e-02  2.652e-02      8309 -3.322e+03 -9.905e+07                   
#> Path [15] :Best Iter: [45] ELBO (-3321.558289) evaluations: (8309) 
#> Path [16] :Initial log joint density = -431613.967463 
#> Path [16] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.290e+05      7.636e-02   1.520e+03    5.066e-02  5.066e-02      8181 -3.320e+03 -3.889e+04                   
#> Path [16] :Best Iter: [49] ELBO (-3320.409466) evaluations: (8181) 
#> Path [17] :Initial log joint density = -435333.022189 
#> Path [17] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      6.323e-02   1.012e+03    3.920e-02  3.920e-02      8036 -3.325e+03 -1.417e+04                   
#> Path [17] :Best Iter: [53] ELBO (-3325.137235) evaluations: (8036) 
#> Path [18] :Initial log joint density = -433438.412158 
#> Path [18] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      1.074e-01   1.115e+03    2.409e-02  4.762e-02      8153 -3.326e+03 -9.080e+05                   
#> Path [18] :Best Iter: [48] ELBO (-3326.020790) evaluations: (8153) 
#> Path [19] :Initial log joint density = -432165.426871 
#> Path [19] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      5.548e-02   4.195e+03    2.888e-02  2.888e-02      8338 -3.326e+03 -4.106e+04                   
#> Path [19] :Best Iter: [47] ELBO (-3326.170924) evaluations: (8338) 
#> Path [20] :Initial log joint density = -431915.254627 
#> Path [20] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      6.125e-02   5.710e+03    2.569e-02  2.569e-02      8415 -3.330e+03 -3.149e+06                   
#> Path [20] :Best Iter: [44] ELBO (-3330.336218) evaluations: (8415) 
#> Path [21] :Initial log joint density = -431780.911061 
#> Path [21] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      5.007e-02   1.676e+03    4.320e-02  4.320e-02      8417 -3.330e+03 -5.555e+04                   
#> Path [21] :Best Iter: [44] ELBO (-3330.372516) evaluations: (8417) 
#> Path [22] :Initial log joint density = -434054.169591 
#> Path [22] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      1.356e-02   2.239e+03    1.205e-02  1.205e-02      8474 -3.323e+03 -2.516e+04                   
#> Path [22] :Best Iter: [49] ELBO (-3323.462665) evaluations: (8474) 
#> Path [23] :Initial log joint density = -431891.213400 
#> Path [23] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.290e+05      5.913e-02   1.504e+03    2.470e-02  6.374e-02      7817 -3.319e+03 -1.006e+05                   
#> Path [23] :Best Iter: [57] ELBO (-3318.648636) evaluations: (7817) 
#> Path [24] :Initial log joint density = -434794.393636 
#> Path [24] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.290e+05      4.104e-02   8.288e+02    4.014e-02  4.014e-02      8218 -3.319e+03 -1.002e+05                   
#> Path [24] :Best Iter: [57] ELBO (-3319.263082) evaluations: (8218) 
#> Path [25] :Initial log joint density = -431890.154889 
#> Path [25] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      2.400e-02   2.212e+03    1.871e-02  1.871e-02      8142 -3.327e+03 -1.003e+04                   
#> Path [25] :Best Iter: [48] ELBO (-3327.210831) evaluations: (8142) 
#> Path [26] :Initial log joint density = -433019.061482 
#> Path [26] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      3.014e-02   1.223e+03    2.025e-02  2.025e-02      8143 -3.321e+03 -7.395e+04                   
#> Path [26] :Best Iter: [56] ELBO (-3320.576506) evaluations: (8143) 
#> Path [27] :Initial log joint density = -431506.538666 
#> Path [27] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      4.023e-02   3.331e+03    2.239e-02  2.239e-02      8474 -3.326e+03 -1.743e+04                   
#> Path [27] :Best Iter: [43] ELBO (-3325.880243) evaluations: (8474) 
#> Path [28] :Initial log joint density = -432096.857394 
#> Path [28] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      8.816e-02   1.821e+03    5.257e-02  5.257e-02      8138 -3.320e+03 -2.152e+04                   
#> Path [28] :Best Iter: [57] ELBO (-3319.766831) evaluations: (8138) 
#> Path [29] :Initial log joint density = -433644.226219 
#> Path [29] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      6.936e-02   2.237e+03    2.941e-02  6.226e-02      8162 -3.322e+03 -6.358e+04                   
#> Path [29] :Best Iter: [55] ELBO (-3321.902901) evaluations: (8162) 
#> Path [30] :Initial log joint density = -431605.693849 
#> Path [30] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      7.048e-02   9.244e+03    1.223e-02  1.223e-02      8391 -3.329e+03 -4.184e+06                   
#> Path [30] :Best Iter: [41] ELBO (-3329.094064) evaluations: (8391) 
#> Path [31] :Initial log joint density = -432749.961475 
#> Path [31] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      5.335e-02   2.169e+03    3.714e-02  3.714e-02      8323 -3.326e+03 -5.081e+04                   
#> Path [31] :Best Iter: [49] ELBO (-3326.377036) evaluations: (8323) 
#> Path [32] :Initial log joint density = -431672.913398 
#> Path [32] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      5.208e-02   2.805e+03    2.809e-02  2.809e-02      8322 -3.329e+03 -4.868e+06                   
#> Path [32] :Best Iter: [48] ELBO (-3328.683704) evaluations: (8322) 
#> Path [33] :Initial log joint density = -431859.733699 
#> Path [33] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.290e+05      6.967e-02   1.421e+03    3.466e-02  3.466e-02      8395 -3.327e+03 -1.469e+04                   
#> Path [33] :Best Iter: [56] ELBO (-3327.327368) evaluations: (8395) 
#> Path [34] :Initial log joint density = -431935.416593 
#> Path [34] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      5.787e-02   6.087e+03    2.306e-02  2.306e-02      8095 -3.329e+03 -1.447e+06                   
#> Path [34] :Best Iter: [41] ELBO (-3328.766023) evaluations: (8095) 
#> Path [35] :Initial log joint density = -431884.877672 
#> Path [35] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      4.265e-02   1.961e+03    1.472e-02  1.472e-02      7967 -3.322e+03 -1.160e+08                   
#> Path [35] :Best Iter: [56] ELBO (-3321.509849) evaluations: (7967) 
#> Path [36] :Initial log joint density = -432375.807700 
#> Path [36] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.290e+05      2.325e-02   1.443e+03    2.656e-02  2.656e-02      8181 -3.318e+03 -4.224e+03                   
#> Path [36] :Best Iter: [57] ELBO (-3317.720129) evaluations: (8181) 
#> Path [37] :Initial log joint density = -431770.564516 
#> Path [37] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      1.903e-02   2.102e+03    1.419e-02  1.419e-02      8213 -3.326e+03 -1.356e+05                   
#> Path [37] :Best Iter: [44] ELBO (-3326.111522) evaluations: (8213) 
#> Path [38] :Initial log joint density = -432013.691962 
#> Path [38] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      7.016e-02   2.368e+03    1.806e-02  1.806e-02      8308 -3.327e+03 -1.276e+06                   
#> Path [38] :Best Iter: [51] ELBO (-3326.520923) evaluations: (8308) 
#> Path [39] :Initial log joint density = -431970.270966 
#> Path [39] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      2.262e-02   3.019e+03    1.899e-02  1.899e-02      8280 -3.328e+03 -4.563e+04                   
#> Path [39] :Best Iter: [47] ELBO (-3327.564592) evaluations: (8280) 
#> Path [40] :Initial log joint density = -433811.602858 
#> Path [40] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      3.816e-02   1.438e+03    4.514e-02  4.514e-02      8174 -3.318e+03 -1.947e+04                   
#> Path [40] :Best Iter: [55] ELBO (-3317.538379) evaluations: (8174) 
#> Path [41] :Initial log joint density = -432461.655685 
#> Path [41] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.290e+05      4.283e-02   1.481e+03    1.923e-02  1.923e-02      8168 -3.323e+03 -3.223e+04                   
#> Path [41] :Best Iter: [53] ELBO (-3323.165222) evaluations: (8168) 
#> Path [42] :Initial log joint density = -433669.015119 
#> Path [42] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      5.662e-02   1.680e+03    2.845e-02  2.845e-02      8193 -3.323e+03 -1.639e+05                   
#> Path [42] :Best Iter: [56] ELBO (-3322.586945) evaluations: (8193) 
#> Path [43] :Initial log joint density = -432968.922252 
#> Path [43] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      7.415e-02   3.805e+03    2.685e-02  2.685e-02      8390 -3.325e+03 -3.081e+05                   
#> Path [43] :Best Iter: [46] ELBO (-3325.162424) evaluations: (8390) 
#> Path [44] :Initial log joint density = -433412.858946 
#> Path [44] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      5.931e-02   8.397e+02    3.209e-02  3.209e-02      8271 -3.324e+03 -6.685e+05                   
#> Path [44] :Best Iter: [55] ELBO (-3324.317125) evaluations: (8271) 
#> Path [45] :Initial log joint density = -431728.712645 
#> Path [45] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      4.506e-02   6.576e+03    1.349e-02  1.349e-02      8165 -3.325e+03 -5.641e+07                   
#> Path [45] :Best Iter: [44] ELBO (-3325.043214) evaluations: (8165) 
#> Path [46] :Initial log joint density = -431857.823816 
#> Path [46] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      3.763e-02   3.087e+03    2.643e-02  2.643e-02      8247 -3.329e+03 -1.495e+04                   
#> Path [46] :Best Iter: [53] ELBO (-3329.066212) evaluations: (8247) 
#> Path [47] :Initial log joint density = -434361.617286 
#> Path [47] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      9.612e-02   2.562e+03    1.819e-02  4.067e-02      8049 -3.321e+03 -1.070e+07                   
#> Path [47] :Best Iter: [57] ELBO (-3320.709397) evaluations: (8049) 
#> Path [48] :Initial log joint density = -431866.269737 
#> Path [48] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      6.167e-02   3.462e+03    1.943e-02  1.943e-02      8210 -3.326e+03 -2.014e+06                   
#> Path [48] :Best Iter: [42] ELBO (-3325.995014) evaluations: (8210) 
#> Path [49] :Initial log joint density = -436070.697148 
#> Path [49] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.290e+05      3.161e-02   8.890e+02    3.416e-02  3.416e-02      8260 -3.321e+03 -7.345e+03                   
#> Path [49] :Best Iter: [55] ELBO (-3320.816235) evaluations: (8260) 
#> Path [50] :Initial log joint density = -431968.407034 
#> Path [50] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>             100      -4.289e+05      2.737e-02   2.390e+03    2.203e-02  2.203e-02      8436 -3.326e+03 -5.640e+04                   
#> Path [50] :Best Iter: [47] ELBO (-3326.208287) evaluations: (8436) 
#> Finished in  27.3 seconds.
#> sccomp says: auto-cleanup removed 2 draw files from 'sccomp_draws_files'
# }