# An introduction to BASiCStan

### A Stan implementation of BASiCS

# Outline

This package implements alternative inference methods for BASiCS. The original package uses adaptive Metropolis within Gibbs sampling, while BASiCStan uses Stan to enable the use of maximum a posteriori estimation, variational inference, and Hamiltonian Monte Carlo. These each have advantages for different use cases.

# Use

To use `BASiCStan`, we can first use `BASICS_MockSCE()` to generate an toy example dataset. We will also set a seed for reproducibility.

    suppressPackageStartupMessages(library("BASiCStan"))
    set.seed(42)
    sce <- BASiCS_MockSCE()

The interface for running MCMC using BASiCS and using alternative inference methods using Stan is very similar. It is worth noting that the joint prior between mean and over-dispersion parameters, corresponding to `Regression = TRUE`, is the only supported mode in `BASiCStan()`.

    amwg_fit <- BASiCS_MCMC(
        sce,
        N = 200,
        Thin = 10,
        Burn = 100,
        Regression = TRUE
    )
    #> altExp 'spike-ins' is assumed to contain spike-in genes.
    #> see help(altExp) for details.
    #> Running with spikes BASiCS sampler (regression case) ...
    #> -------------------------------------------------------------
    #> MCMC running time
    #> -------------------------------------------------------------
    #> user: 0.71
    #> system: 0.02
    #> elapsed: 0.72
    #> -------------------------------------------------------------
    #> Output
    #> -------------------------------------------------------------
    #> -------------------------------------------------------------
    #> BASiCS version 2.16.0 :
    #> vertical integration (spikes case)
    #> -------------------------------------------------------------
    stan_fit <- BASiCStan(sce, Method = "sampling", iter = 10)
    #> Warning: There were 5 divergent transitions after warmup. See
    #> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
    #> to find out why this is a problem and how to eliminate them.
    #> Warning: Examine the pairs() plot to diagnose sampling problems

The output of `BASiCStan()` is an object of class `BASiCS_Chain`, similar to the output of `BASiCS_MCMC()`. Therefore, you could use these as you would an object generated using Metropolis within Gibbs sampling. For example, we can plot the relationship between mean and over-dispersion estimated using the joint regression prior:

    BASiCS_ShowFit(amwg_fit)

    BASiCS_ShowFit(stan_fit)

# Stan MCMC diagnostics

Using Stan has advantages outside of the variety of inference engines available. By returning a Stan object that we can later convert to a `BASiCS_Chain` object, we can leverage an even broader set of functionality. For example, Stan has the ability to easily generate MCMC diagnostics using simple functions. For example, `summary()` outputs a number of useful per-chain and across-chain diagnostics:

    stan_obj <- BASiCStan(sce, ReturnBASiCS = FALSE, Method = "sampling", iter = 10)
    #>
    #> SAMPLING FOR MODEL 'basics_regression' NOW (CHAIN 1).
    #> Chain 1:
    #> Chain 1: Gradient evaluation took 0.007635 seconds
    #> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 76.35 seconds.
    #> Chain 1: Adjust your expectations accordingly!
    #> Chain 1:
    #> Chain 1:
    #> Chain 1: WARNING: No variance estimation is
    #> Chain 1:          performed for num_warmup < 20
    #> Chain 1:
    #> Chain 1: Iteration: 1 / 10 [ 10%]  (Warmup)
    #> Chain 1: Iteration: 2 / 10 [ 20%]  (Warmup)
    #> Chain 1: Iteration: 3 / 10 [ 30%]  (Warmup)
    #> Chain 1: Iteration: 4 / 10 [ 40%]  (Warmup)
    #> Chain 1: Iteration: 5 / 10 [ 50%]  (Warmup)
    #> Chain 1: Iteration: 6 / 10 [ 60%]  (Sampling)
    #> Chain 1: Iteration: 7 / 10 [ 70%]  (Sampling)
    #> Chain 1: Iteration: 8 / 10 [ 80%]  (Sampling)
    #> Chain 1: Iteration: 9 / 10 [ 90%]  (Sampling)
    #> Chain 1: Iteration: 10 / 10 [100%]  (Sampling)
    #> Chain 1:
    #> Chain 1:  Elapsed Time: 0.104 seconds (Warm-up)
    #> Chain 1:                0.054 seconds (Sampling)
    #> Chain 1:                0.158 seconds (Total)
    #> Chain 1:
    #> Warning: There were 5 divergent transitions after warmup. See
    #> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
    #> to find out why this is a problem and how to eliminate them.
    #> Warning: Examine the pairs() plot to diagnose sampling problems
    head(summary(stan_obj)$summary)
    #>               mean se_mean sd     2.5%      25%      50%      75%    97.5%
    #> log_mu[1] 3.098420     NaN  0 3.098420 3.098420 3.098420 3.098420 3.098420
    #> log_mu[2] 1.058488     NaN  0 1.058488 1.058488 1.058488 1.058488 1.058488
    #> log_mu[3] 2.107672     NaN  0 2.107672 2.107672 2.107672 2.107672 2.107672
    #> log_mu[4] 2.245089     NaN  0 2.245089 2.245089 2.245089 2.245089 2.245089
    #> log_mu[5] 2.002693     NaN  0 2.002693 2.002693 2.002693 2.002693 2.002693
    #> log_mu[6] 1.457520     NaN  0 1.457520 1.457520 1.457520 1.457520 1.457520
    #>           n_eff Rhat
    #> log_mu[1]   NaN  NaN
    #> log_mu[2]   NaN  NaN
    #> log_mu[3]   NaN  NaN
    #> log_mu[4]   NaN  NaN
    #> log_mu[5]   NaN  NaN
    #> log_mu[6]   NaN  NaN

We can then convert this object to a `BASiCS_Chain` and carry on a workflow as before:

    Stan2BASiCS(stan_obj)
    #> An object of class BASiCS_Chain
    #>  5 MCMC samples.
    #>  Dataset contains 100 biological genes and 100 cells (2 batches).
    #>  Object stored using BASiCS version:  2.16.0
    #>  Parameters:  mu delta s nu theta epsilon phi beta

# Session info

    sessionInfo()
    #> R version 4.4.0 beta (2024-04-15 r86425 ucrt)
    #> Platform: x86_64-w64-mingw32/x64
    #> Running under: Windows Server 2022 x64 (build 20348)
    #>
    #> Matrix products: default
    #>
    #>
    #> locale:
    #> [1] LC_COLLATE=C
    #> [2] LC_CTYPE=English_United States.utf8
    #> [3] LC_MONETARY=English_United States.utf8
    #> [4] LC_NUMERIC=C
    #> [5] LC_TIME=English_United States.utf8
    #>
    #> time zone: America/New_York
    #> tzcode source: internal
    #>
    #> attached base packages:
    #> [1] stats4    stats     graphics  grDevices utils     datasets  methods
    #> [8] base
    #>
    #> other attached packages:
    #>  [1] BASiCStan_1.6.0             rstan_2.32.6
    #>  [3] StanHeaders_2.32.7          BASiCS_2.16.0
    #>  [5] SingleCellExperiment_1.26.0 SummarizedExperiment_1.34.0
    #>  [7] Biobase_2.64.0              GenomicRanges_1.56.0
    #>  [9] GenomeInfoDb_1.40.0         IRanges_2.38.0
    #> [11] S4Vectors_0.42.0            BiocGenerics_0.50.0
    #> [13] MatrixGenerics_1.16.0       matrixStats_1.3.0
    #>
    #> loaded via a namespace (and not attached):
    #>   [1] gridExtra_2.3             inline_0.3.19
    #>   [3] rlang_1.1.3               magrittr_2.0.3
    #>   [5] compiler_4.4.0            loo_2.7.0
    #>   [7] DelayedMatrixStats_1.26.0 vctrs_0.6.5
    #>   [9] pkgconfig_2.0.3           crayon_1.5.2
    #>  [11] fastmap_1.1.1             backports_1.4.1
    #>  [13] XVector_0.44.0            labeling_0.4.3
    #>  [15] scuttle_1.14.0            utf8_1.2.4
    #>  [17] promises_1.3.0            rmarkdown_2.26
    #>  [19] UCSC.utils_1.0.0          xfun_0.43
    #>  [21] bluster_1.14.0            zlibbioc_1.50.0
    #>  [23] cachem_1.0.8              beachmat_2.20.0
    #>  [25] jsonlite_1.8.8            highr_0.10
    #>  [27] later_1.3.2               DelayedArray_0.30.0
    #>  [29] BiocParallel_1.38.0       irlba_2.3.5.1
    #>  [31] parallel_4.4.0            cluster_2.1.6
    #>  [33] R6_2.5.1                  bslib_0.7.0
    #>  [35] limma_3.60.0              jquerylib_0.1.4
    #>  [37] Rcpp_1.0.12               assertthat_0.2.1
    #>  [39] knitr_1.46                splines_4.4.0
    #>  [41] httpuv_1.6.15             Matrix_1.7-0
    #>  [43] igraph_2.0.3              tidyselect_1.2.1
    #>  [45] abind_1.4-5               yaml_2.3.8
    #>  [47] viridis_0.6.5             codetools_0.2-20
    #>  [49] miniUI_0.1.1.1            curl_5.2.1
    #>  [51] pkgbuild_1.4.4            lattice_0.22-6
    #>  [53] tibble_3.2.1              withr_3.0.0
    #>  [55] shiny_1.8.1.1             posterior_1.5.0
    #>  [57] coda_0.19-4.1             evaluate_0.23
    #>  [59] RcppParallel_5.1.7        pillar_1.9.0
    #>  [61] tensorA_0.36.2.1          checkmate_2.3.1
    #>  [63] distributional_0.4.0      generics_0.1.3
    #>  [65] ggplot2_3.5.1             rstantools_2.4.0
    #>  [67] sparseMatrixStats_1.16.0  munsell_0.5.1
    #>  [69] scales_1.3.0              xtable_1.8-4
    #>  [71] glue_1.7.0                metapod_1.12.0
    #>  [73] tools_4.4.0               hexbin_1.28.3
    #>  [75] BiocNeighbors_1.22.0      ScaledMatrix_1.12.0
    #>  [77] locfit_1.5-9.9            scran_1.32.0
    #>  [79] cowplot_1.1.3             grid_4.4.0
    #>  [81] QuickJSR_1.1.3            edgeR_4.2.0
    #>  [83] colorspace_2.1-0          GenomeInfoDbData_1.2.12
    #>  [85] BiocSingular_1.20.0       cli_3.6.2
    #>  [87] rsvd_1.0.5                fansi_1.0.6
    #>  [89] viridisLite_0.4.2         S4Arrays_1.4.0
    #>  [91] dplyr_1.1.4               V8_4.4.2
    #>  [93] glmGamPoi_1.16.0          gtable_0.3.5
    #>  [95] sass_0.4.9                digest_0.6.35
    #>  [97] SparseArray_1.4.0         dqrng_0.3.2
    #>  [99] farver_2.1.1              htmltools_0.5.8.1
    #> [101] lifecycle_1.0.4           httr_1.4.7
    #> [103] statmod_1.5.0             mime_0.12
    #> [105] ggExtra_0.10.1            MASS_7.3-60.2