---
title: "Introduction to bootRanges"
author: "Wancen Mu"
date: "`r format(Sys.Date(), '%m/%d/%Y')`"
bibliography: library.bib
output:
  rmarkdown::html_document:
    highlight: tango
    toc: true
    toc_float: true	
vignette: |
  %\VignetteIndexEntry{1. Introduction to bootRanges}
  %\VignetteEncoding{UTF-8}
  %\VignetteEngine{knitr::rmarkdown}
editor_options: 
  markdown: 
    wrap: 72
---

# Introduction 

```{r setup, include=FALSE}
knitr::opts_chunk$set(fig.width=5, fig.height=5, message=FALSE, warning=FALSE)
```

In this vignette, we demonstrate the block bootstrap functionality
implemented in *nullranges*. See the main nullranges vignette for an
overview of the idea of bootstrapping, or the diagram below.

*nullranges* contains an implementation of a block bootstrap for
genomic data, as proposed by @bickel_2010,
such that features (ranges) are sampled from the genome in
blocks. The original block bootstrapping algorithm for genomic data is
implemented in a python software called Genome Structure Correlation,
[GSC](https://github.com/ParkerLab/encodegsc).

Our description of the *bootRanges* methods is described in @bootRanges.

# Quick start

Minimal code for running `bootRanges()` is shown below. Genome
segmentation `seg` and excluded regions `exclude` are optional.

```{r eval=FALSE}
eh <- ExperimentHub()
ah <- AnnotationHub()
# some default resources:
seg <- eh[["EH7307"]] # pre-built genome segmentation for hg38
exclude <- ah[["AH107305"]] # Kundaje excluded regions for hg38, see below

set.seed(5) # set seed for reproducibility
blockLength <- 5e5 # size of blocks to bootstrap
R <- 10 # number of iterations of the bootstrap

# input `ranges` require seqlengths, if missing see `GenomeInfoDb::Seqinfo`
seqlengths(ranges)
# next, we remove non-standard chromosomes ...
ranges <- keepStandardChromosomes(ranges, pruning.mode="coarse")
# ... and mitochondrial genome, as these are too short
seqlevels(ranges, pruning.mode="coarse") <- setdiff(seqlevels(ranges), "MT")

# generate bootstraps
boots <- bootRanges(ranges, blockLength=blockLength, R=R,
                    seg=seg, exclude=exclude)
# `boots` can then be used with plyranges commands, e.g. join_overlap_*
```

The `boots` object will contain a column, `iter` which marks the
different bootstrap samples that were generated. This allows for tidy
analysis with *plyranges*, e.g. counting the number of overlapping
ranges, per bootstrap iteration. For more examples of combining
`bootRanges` with *plyranges* operations, see the
[tidy ranges tutorial](https://tidyomics.github.io/tidy-ranges-tutorial/).

# Method overview

Several algorithms are implemented in `bootRanges()`, including a
segmented and unsegmented version, where in the former, blocks are
sampled with respect to a particular genome segmentation.
Overall, we recommend the segmented block bootstrap given the
heterogeneity of structure across the entire genome. If the purpose is
block bootstrapping ranges within a smaller set of sequences, such as
motifs within transcript sequence, then the unsegmented algorithm
would be sufficient.

In a segmented block bootstrap, the blocks are sampled and placed
within regions of a genome *segmentation*. That is, for a genome
segmented into states $1,2, \dots, S$, only blocks from state *s* will
be used to sample the ranges of state *s* in each bootstrap
sample. The process can be visualized in diagram panel (A) below,
where a block with length $L_b$ is randomly sampled with replacement
from state "red" and the features (ranges) that overlap this block are
then copied to the first tile (which is in the "red" state). The
sampling is allowed across chromosome (as shown here), as long as the
two blocks are in the same state.

Note that *nullranges* provides both functions for generating a genome
segmentation from e.g. gene density, described below, as well as a
default segmentation for hg38 that can be used directly.

An example workflow of `bootRanges()` used in combination with
*plyranges* [@Lee2019] is diagrammed in panel (B) below, and can be
summarized as:

1.  Compute statistics of interest between *GRanges* of feature $x$
    and *GRanges* of feature $y$ to assess association in the original
    data. This could be an enrichment (amount of overlap) or other
    possible statistics making use of covariates associated with each
    range
2.  Generate bootstrap samples of $y$: `bootRanges()` with optional
    arguments `seg` (segmentation) and `exclude` (excluded regions as
    compiled by @excluderanges) to create a *BootRanges* object ($y'$)
3.  Compute the bootstrap distribution of test statistics between
    *GRanges* of feature $x$ and $y'$ using *plyranges* (compute
    overlaps of all features in $x$ with all features in $y'$,
    grouping by the bootstrap sample)
4.  Conpute a bootstrap p-value or $z$ test to test the null
    hypothesis that there is no association between $x$ and $y$
    (e.g. that the bootstrap data often has as high an enrichment
    as the observed data)

```{r, echo=FALSE}
knitr::include_graphics("images/bootRanges.jpeg")
```

In this vignette, we give an example of segmenting the hg38 genome by
Ensembl gene density, performing bootstrap sampling of peaks ranges,
and evaluating overlaps for observed peaks and bootstrap peaks. We
also provide other examples of statistics that can be computed with
the `bootRanges` framework, including a single cell multi-omics
example and a special case of bootstrapping features in one region of
the genome.

**Proportional blocks:**
A finally consideration is whether the blocks used to generate the
bootstrap samples should scale
proportionally to the segment state length, with the default setting
of `proportionLength=TRUE`. When blocks scale proportionally,
`blockLength` provides the maximal length of a block, while the actual
block length used for a segmentation state is proportional to the
fraction of genomic basepairs covered by that state. It is
theoretically motivated to have the blocks scale with the overall
extent of the segment state. However, in practice, if the genome
segmentation states are very heterogeneous in size (e.g. orders of
magnitude differences), then the blocks constructed via the
proportional length method for the smaller segmentation states can be
too short to effectively capture inter-range distances. We therefore
recommend proportional length blocks unless some segmentation states
have a much smaller extent than others, in which case fixed length
blocks can be used. This option is visualized on toy data at the end
of this vignette.

# Segmented block bootstrap

## Case study I: DHS

### Import excluded regions

To avoid placing bootstrap features into regions
of the genome that don’t typically have features, we import
excluded regions including ENCODE-produced excludable
regions[@encode_exclude], telomeres from UCSC, centromeres. These, and
other excludable sets, are assembled in the
[excluderanges](https://dozmorovlab.github.io/excluderanges/) package
[@excluderanges].

```{r excluderanges}
suppressPackageStartupMessages(library(AnnotationHub))
ah <- AnnotationHub()
# hg38.Kundaje.GRCh38_unified_Excludable
exclude_1 <- ah[["AH107305"]]
# hg38.UCSC.centromere
exclude_2 <- ah[["AH107354"]]
# hg38.UCSC.telomere
exclude_3 <- ah[["AH107355"]]
# hg38.UCSC.short_arm
exclude_4 <- ah[["AH107356"]]
# combine them
suppressWarnings({
  exclude <- trim(c(exclude_1, exclude_2, exclude_3, exclude_4))
})
exclude <- sort(GenomicRanges::reduce(exclude))
```

### Segmentations choices

For most genomic datasets we examine, the density of ranges of interest
(e.g. ChIP- or ATAC-seq peaks) is often correlated to other
large-scale patterns of other genomic features, such as density of
genes. 
@bickel_2010 therefore proposed the idea of bootstrapping with respect to
a **segmented genome** given known, large-scale genomic structures such as
isochores ("larger than 300kb").

A genomic segmentation can be considered if
it defines large (e.g. on the order of ∼1 Mb), relatively
homogeneous segments with respect to feature density, and 
the variance of the distribution of the test statistics become stable
as block length increases (see @bootRanges Fig 2A). 

There are two options for choosing a segmentation, either:

- Use an exiting segmentation (e.g. ChromHMM, etc.) downloaded from
  AnnotationHub or external to Bioconductor (BED files imported with
  *rtracklayer*)
- Perform a *de novo* segmentation of the genome using feature density,
  e.g. gene density

**Pre-built segmentations**

Given that these genome segmentation evaluations take time and involve consideration of
multiple criteria, we have provided our recommended segmentation for
hg38. *nullranges* has generated pre-built segmentations for easy use,
which were generated using code outlined below in the *Segmentation by
gene density* section.

Pre-built segmentations using either *CBS* or *HMM* methods with
$L_s=2e6$ considering excludable regions can be downloaded directly
from *ExperimentHub*. We find that the segmentation and block length
(500kb) shown in the case study below could be used for most analyses
of hg38.

```{r, message=FALSE, warning=FALSE}
suppressPackageStartupMessages(library(ExperimentHub))
eh <- ExperimentHub()
seg_cbs <- eh[["EH7307"]] # prefer CBS for hg38
seg_hmm <- eh[["EH7308"]]
seg <- seg_cbs
```

**Segmentation by gene density**

This section describes how we generated the pre-built segmentations,
such that users with a different genome can generate a segmentation
for their own purposes. First we obtain the Ensembl genes
[@ensembl2021] for segmenting by gene density. We obtain these using
the *ensembldb* package [@ensembldb].

```{r}
suppressPackageStartupMessages(library(ensembldb))
suppressPackageStartupMessages(library(EnsDb.Hsapiens.v86))
edb <- EnsDb.Hsapiens.v86
filt <- AnnotationFilterList(GeneIdFilter("ENSG", "startsWith"))
g <- genes(edb, filter = filt)
```

We perform some processing to align the sequences (chromosomes) of `g`
with our excluded regions and our features of interest (DNase
hypersensitive sites, or DHS, defined below).

```{r}
library(GenomeInfoDb)
g <- keepStandardChromosomes(g, pruning.mode = "coarse")
# MT is too small for bootstrapping, so must be removed
seqlevels(g, pruning.mode="coarse") <- setdiff(seqlevels(g), "MT")
# normally we would assign a new style, but for recent host issues
# that produced vignette build problems, we use `paste0`
## seqlevelsStyle(g) <- "UCSC" 
seqlevels(g) <- paste0("chr", seqlevels(g))
genome(g) <- "hg38"
g <- sortSeqlevels(g)
g <- sort(g)
table(seqnames(g))
```

**CBS segmentation**

We first demonstrate the use of a CBS segmentation as implemented in
*DNAcopy* [@dnacopy].

We load the *nullranges* and *plyranges* packages, and *patchwork* in
order to produce grids of plots.

```{r}
library(nullranges)
suppressPackageStartupMessages(library(plyranges))
library(patchwork)
```

We subset the excluded ranges to those which are 500 bp or larger. The
motivation for this step is to avoid segmenting the genome into many
small pieces due to an abundance of short excluded regions. Note that we
re-save the excluded ranges to `exclude`.

Here, and below, we need to specify `plyranges::filter` as it conflicts
with `filter` exported by *ensembldb*.

```{r seg-cbs, fig.width=5, fig.height=4}
set.seed(5)
exclude <- exclude %>%
  plyranges::filter(width(exclude) >= 500)
L_s <- 1e6
seg_cbs <- segmentDensity(g, n = 3, L_s = L_s,
                          exclude = exclude, type = "cbs")
plots <- lapply(c("ranges","barplot","boxplot"), function(t) {
  plotSegment(seg_cbs, exclude, type = t)
})
plots[[1]]
plots[[2]] + plots[[3]]
```

Note here, the default *ranges* plot shows the whole genome.  Some of
the state transitions within small regions cannot be visualized.  One
can look into specific regions to observe segmentation states, by
specifying the `region` argument.

```{r, fig.width=4, fig.height=3}
region <- GRanges("chr16", IRanges(3e7,4e7))
plotSegment(seg_cbs, exclude, type="ranges", region=region)
```

**Alternatively: HMM segmentation**

Here we use an alternative segmentation implemented in the *RcppHMM*
CRAN package, using the `initGHMM`, `learnEM`, and `viterbi` functions.

```{r seg-hmm, fig.width=5, fig.height=4}
seg_hmm <- segmentDensity(g, n = 3, L_s = L_s,
                          exclude = exclude, type = "hmm")
plots <- lapply(c("ranges","barplot","boxplot"), function(t) {
  plotSegment(seg_hmm, exclude, type = t)
})
plots[[1]]
plots[[2]] + plots[[3]]
```

### Running bootRanges

We use a set of DNase hypersensitivity sites (DHS) from the ENCODE
project [@encode] in A549 cell line (ENCSR614GWM). Here, for speed, we
work with a pre-processed data object from ExperimentHub, created using
the following steps:

* Download ENCODE DNase hypersensitive peaks in A549 from
  *AnnotationHub*
* Subset to standard chromosomes and remove mitochondrial DNA
* Use a chain file from UCSC to lift ranges from hg19 to hg38
* Sort the DHS features to be bootstrapped

These steps are included in *nullrangesData* in the
`inst/scripts/make-dhs-data.R` script. 

For speed of the vignette, we restrict to a smaller number of DHS,
filtering by the signal value. We also remove unrelated metadata
columns that we don't need for the bootstrap analysis.
Because we are interested in signal value for DHS peaks later, we only
keep this column. Consider, when creating bootstrapped data, that you will be
creating an object *many times larger* than your original data
(i.e. multipled by `R` the number of bootstrap iterations), so
**filtering** down to key ranges and **selecting** only the relevant
metadata can help make the analysis much more efficient.

```{r}
suppressPackageStartupMessages(library(nullrangesData))
dhs <- DHSA549Hg38()
dhs <- dhs %>% plyranges::filter(signalValue > 100) %>%
  mutate(id = seq_along(.)) %>%
  plyranges::select(id, signalValue)
length(dhs)
table(seqnames(dhs))
```

Now we apply a segmented block bootstrap with blocks of size 500kb, to
the peaks. Here we show generation of 50 iterations of a block bootstrap
followed by a typical overlap analysis using *plyranges* [@Lee2019].

Note that we have already removed non-standard chromosomes and
mitochondrial chromosome, as these are typically shorter than our
desired `blockLength` (see e.g. code in Quick Start above).

```{r}
set.seed(5) # for reproducibility
R <- 50
blockLength <- 5e5
boots <- bootRanges(dhs, blockLength, R = R, seg = seg, exclude=exclude)
boots
```

What is returned here? The `bootRanges` function returns a
*BootRanges* object, which is a simple sub-class of *GRanges*. The
iteration (`iter`) and (optionally) the block length (`blockLength`)
are recorded as metadata columns, accessible via `mcols`. We return
the bootstrapped ranges as *GRanges* rather than *GRangesList*, as the
former is more compatible with downstream overlap joins with
*plyranges*, where the iteration column can be used with `group_by` to
provide per bootstrap summary statistics, as shown below.

Note that we use the `exclude` object from the previous step, which does
not contain small ranges. If one wanted to also avoid generation of
bootstrapped features that overlap small excluded ranges, then omit this
filtering step (use the original, complete `exclude` feature set).

### Assessing quality of bootstrap samples

We can examine properties of permuted y over iterations, and compare
to the original y. To do so, we first add the original features as
iter=0. Then compute summaries: 

```{r}
suppressPackageStartupMessages(library(tidyr))
combined <- dhs %>% 
  mutate(iter=0) %>%
  bind_ranges(boots) %>% 
  plyranges::select(iter)
stats <- combined %>% 
  group_by(iter) %>%
  summarize(n = n()) %>%
  as_tibble()
head(stats)
```

We can also look at distributions of various aspects, e.g. here the
inter-feature distance of features, across a few of the bootstraps and
the original feature set y. 

```{r, warning=FALSE}
suppressPackageStartupMessages(library(ggridges))
suppressPackageStartupMessages(library(purrr))
suppressPackageStartupMessages(library(ggplot2))
interdist <- function(dat) {
    x <- dat[-1,]
    y <- dat[-nrow(dat),]
    ifelse(x$seqnames == y$seqnames,
           x$start + floor((x$width - 1)/2) -
           y$start - floor((y$width - 1)/2), NA)
}
# just looking at first 3 iterations...
combined %>% plyranges::filter(iter %in% 0:3) %>%
  mutate(iter = droplevels(iter)) %>%
  plyranges::select(iter) %>%
  as_tibble() %>% 
  nest(data = !iter) %>%
  mutate(interdist = map(data, interdist)) %>% 
  dplyr::select(iter, interdist) %>% 
  unnest(interdist) %>% 
  mutate(type = ifelse(iter == 0, "original", "boot"),
         interdist = pmax(interdist, 0)) %>%
  filter(!is.na(interdist)) %>%
  ggplot(aes(log10(interdist + 1), iter, fill=type)) +
  geom_density_ridges(alpha = 0.75) +
  geom_text(data = head(stats, 4),
            aes(x=1.5, y=iter, label=paste0("n=",n), fill=NULL),
            vjust=1.5)
```

### Bootstrapping and plyranges

We will now show how to combine bootstrapping with *plyranges* to
perform statistical enrichment analysis.
The general idea will be to combine the long vector of bootstrapped
ranges, indexed by `iter`, with another set of ranges to compute
enrichment. We will explore this idea across a number of case studies
below. In pseudocode, the general outline will be:

```{r eval=FALSE}
# pseudocode for the general paradigm:
boots <- bootRanges(y) # make bootstrapped y
x %>% join_overlap_inner(boots) %>% # overlaps of x with bootstrapped y
  group_by(x_id, iter) %>% # collate by x ID and the bootstrap iteration
  summarize(some_statistic = ...) %>% # compute some summary on metadata
  as_tibble() %>% # pass to tibble
  complete(
    x_id, iter, # for any missing combinations of x ID and iter...
    fill=list(some_statistic = 0) # ...fill in missing values
  )
```

### Statistic I: the total number of overlaps

Suppose we have a set of features `x` and we are interested in
evaluating the enrichment of this set with the
DHS. We can calculate for example the sum observed number of
overlaps for features in `x`  with DHS in whole genome (or something
more complicated, e.g. the maximum log fold change or signal value for
DHS peaks within a `maxgap` window of `x`). 

```{r}
x <- GRanges("chr2", IRanges(1 + 50:99 * 1e6, width=1e6), x_id=1:50)
```

```{r}
x <- x %>% mutate(n_overlaps = count_overlaps(., dhs))
sum( x$n_overlaps )
```

We can repeat this with the bootstrapped features using a `group_by`
command, a `summarize`, followed by a second `group_by` and `summarize`.
If it is your first time working with *plyranges*, it may help you to
step through these commands one by one, breaking the pipe at
intermediate points, to understand what the intermediate 
output is, and how it combines to provide the final statistics.

Note that we need to use `tidyr::complete` in order to fill in
combinations of `x` and `iter` where the overlap was 0.

```{r}
boot_stats <- x %>% join_overlap_inner(boots) %>%
  group_by(x_id, iter) %>%
  summarize(n_overlaps = n()) %>%
  as_tibble() %>%
  complete(x_id, iter, fill=list(n_overlaps = 0)) %>%
  group_by(iter) %>%
  summarize(sumOverlaps = sum(n_overlaps))
```

The above code, first grouping by `x_id` and `iter`, then subsequently
by `iter` is general and allows for more complex analysis than just mean
overlap (e.g. how many times an `x` range has 1 or more overlap, what is
the mean or max signal value for peaks overlapping ranges in `x`, etc.).

If one is interested in assessing *feature-wise*
statistics instead of *genome-wise* statistics, 
eg.,the mean observed number of overlaps per feature or mean base pair 
overlap in `x`, one can also group by both (`block`,`iter`). 10,000 total 
blocks may therefore be sufficient to derive a bootstrap distribution, 
avoiding the need to generate many bootstrap genomes of data.

Finally we can plot a histogram. In this case, as the `x` features were
arbitrary, our observed value falls within the distribution of sum
number of overlap bootstrapped peaks with $x$.

```{r boot-histI}
suppressPackageStartupMessages(library(ggplot2))
ggplot(boot_stats, aes(sumOverlaps)) +
  geom_histogram(binwidth=5)+
  geom_vline(xintercept = sum(x$n_overlaps), linetype = "dashed")
```

### Statistic II: the sum of signal value for nearby peaks

```{r}
x_obs <- x %>% join_overlap_inner(dhs,maxgap=1e3)
sum(x_obs$signalValue )
boot_stats <- x %>% join_overlap_inner(boots,maxgap=1e3)  %>%
  group_by(x_id, iter) %>%
  summarize(Signal = sum(signalValue)) %>%
  as_tibble() %>% 
  complete(x_id, iter, fill=list(Signal = 0)) %>%
  group_by(iter) %>%
  summarize(sumSignal = sum(Signal))
```

Still in this case, our observed value falls within the distribution
of bootstrapped statistics. 

```{r boot-histII}
ggplot(boot_stats, aes(sumSignal)) +
  geom_histogram()+
  geom_vline(xintercept = sum(x_obs$signalValue), linetype = "dashed")
```

## Case study II: Single cell multi-omics

This case study provides an example of a more complex statistic of
interest. 
Instead of computing simple overlap, or some function of a single
metadata column, e.g. `signal` above, a statistic can be computed on a
count matrix from a *SummerizedExperiment* or *SingleCellExperiment*.
Here we provide unevaluated code for such an example.

We use a trick to perform computation on a count matrix within plyranges:
we extract count matrix data from a *SingleCellExperiment*
(e.g. pseudobulk summaries of cell type specific expression or
accessibility) and save it in a GRanges's metadata column as a
`NumericList()` format. This allows us to perform the block bootstrap
and quickly compute statistics using *plyranges*. The case study we
consider here is to assess the correlation of gene expression and
promoter peak accessibility from a dataset of Chromium Single Cell
Multiome ATAC + Gene Expression.

We first load the 10X
[Multiome](https://raw.githack.com/bioFAM/MOFA2_tutorials/master/R_tutorials/10x_scRNA_scATAC.html)
data, as compiled by the MOFA2 tutorial.
The first two pre-processed steps are included in *nullrangesData* in the
`inst/scripts/make-multiome-data.R` script. Here, we aggregate 14
cell types across cluster-sample groups.

```{r eval=FALSE}
## split sparse count matrix into NumericList
# sc_rna <- rna_Granges[-which(rna.sd==0)] %>%
#   mutate(counts1 = NumericList(asplit(rna.scaled, 1))) %>% sort()
# sc_promoter <- promoter_Granges[-which(promoter.sd==0)] %>%
#   mutate(counts2 = NumericList(asplit(promoter.scaled, 1))) %>% sort()
suppressPackageStartupMessages(library(nullrangesData))
data("sc_rna")
sc_rna
sc_rna$counts1
nct <- length(sc_rna$counts1[[1]])
print(paste("There are", nct, "cell types"))
data("sc_promoter")
## bootstrap promoters
library(BSgenome.Hsapiens.UCSC.hg38)
genome <- BSgenome.Hsapiens.UCSC.hg38
seqlengths(sc_promoter) <- seqlengths(genome)[1:22] # pull chrom lens from USCS
bootranges <- bootRanges(sc_promoter, blockLength = 5e5, R=50)
```

There are two options for downstream pipelines for computing
statistics after generating a *BootRanges* object. 
One is to use *plyranges* in downstream analysis as
in the previous sections, while another is to create a
*tidySummarizedExperiment* object used to compute the statistics of
interest.

**Plyranges**

We can compute the mean correlation of the all pairs of genes and
promoter peaks over all bootstrap iterations and compare to the observed
statistic. The histogram will show that our observed value falls far
from the distribution of bootstrapped statistics, as we expected for
this dataset.

```{r eval=FALSE}
cor_gr <- sc_rna %>% join_overlap_inner(sc_promoter, maxgap=1000) %>%
  mutate(rho = 1/(nct-1) * sum(counts1 * counts2)) %>%
  summarise(meanCor = mean(rho))
## mean correlation distribution
cor_boot <- sc_rna %>%
  join_overlap_inner(bootranges, maxgap=1000) %>%
  # vectorized code are 10 times faster than cor(counts1, counts2) for plyranges pipeline
  mutate(rho = 1/(nct-1) * sum(counts1 * counts2)) %>%
  select(rho, iter) %>%
  group_by(iter) %>%
  summarise(meanCor = mean(rho)) %>%
  as.data.frame()
ggplot(cor_boot, aes(meanCor)) +
  geom_histogram(binwidth=0.01)+
  geom_vline(xintercept = cor_gr$meanCor,linetype = "dashed")+
  theme_classic()
```

If one is interested in assessing the significance of gene-promoter pairs
per gene, one can also use `plyranges::select` (*gene*, *peak*, *rho*)
and `plyranges::group_by` *gene*.

**tidySummarizedExperiment**

In order to use *tidySummarizedExperiment* to compute the same
operation, we first must create an RangedSE for each modality, and
then we can find the overlaps..

```{r eval=FALSE}
library(tidySummarizedExperiment)
library(purrr)

# make an SE where each row is an overlap
makeOverlapSE <- function(se_rna, se_promoter) {
  idx <- rowRanges(se_rna) %>% join_overlap_inner(rowRanges(se_promoter),maxgap = 1000)
  assay_x <- assay(se_rna, "rna")[ idx$gene, ]
  assay_y <- assay(se_promoter, "promoter")[ idx$peak, ]
  # this is needed to build the SE
  rownames(assay_x) <- rownames(assay_y) <- seq_along( idx$gene )
  names(idx) <- seq_along( idx$gene )
  SummarizedExperiment(
    assays=list(x=assay_x, y=assay_y),
    rowRanges=idx
  )
}

# create SE for observed data
se_rna <- SummarizedExperiment(
  assays=list(rna=do.call(rbind,sc_rna$counts1)),
  rowRanges=sc_rna)
se_promoter <- SummarizedExperiment(
  assays=list(promoter=do.call(rbind,sc_promoter$counts2)),
  rowRanges=sc_promoter)

se <- makeOverlapSE(se_rna, se_promoter)
se <- se %>%
  as_tibble() %>%
  nest(data = -.feature) %>%
  mutate(rho = map(data,
    function(data) data %>% summarize(rho = cor(x, y))
  )) %>%
  unnest(rho) %>%
  select(-data)

print(paste("mean correlation is", mean(se$rho)))
```

Repeating for the bootstrapping case

```{r eval=FALSE}
# create SE for bootranges data
se_promoter_boots <- SummarizedExperiment(
  assays=list(promoter=do.call(rbind,bootranges$counts2)),
  rowRanges=bootranges)
se_boots <- makeOverlapSE(se_rna, se_promoter_boots)

se_boots <- se_boots %>%
  as_tibble() %>%
  nest(data = -c(.feature,iter)) %>%
  # vectorized code similar to cor(counts1, counts2) for tidySE pipeline
  mutate(rho = map(data,
                   function(data) data %>% summarize(rho = cor(x, y))
  )) %>%
  unnest(rho) %>%
  select(-data)

cor_boot <- se_boots %>% group_by(iter) %>% 
  summarise(meanCor = mean(rho)) 
ggplot(cor_boot, aes(meanCor)) +
  geom_histogram(binwidth=0.01)+
  geom_vline(xintercept = mean(se$rho),linetype = "dashed")+
  theme_classic()
```

For more examples of combining `bootRanges` from *nullranges* with
*plyranges* piped operations, see the relevant chapter in the
[tidy-ranges-tutorial](https://tidyomics.github.io/tidy-ranges-tutorial/bootstrap-overlap.html)
book.

## Case study III: Block bootstrap one region

Generally, it makes sense to block bootstrap the entire genome at
once. This is motivated by the "tidy analysis" paradigm where loops
are avoided by stacking data into a longer format. This makes
computation more efficient in our case (as a single overlap call can
be made with all regions of interest at once, across multiple
bootstrap iterations), and it also can simplify code and avoid
repetition. 

However, in some cases, there is a single region of interest, and it
is desired to generate bootstrap data within this one region. For
this, we have a convenience function that enables bootstrap
computation.

Suppose we have data in the following region of chromosome 1:

```{r}
suppressPackageStartupMessages(library(nullrangesData))
dhs <- DHSA549Hg38()
region <- GRanges("chr1", IRanges(10e6 + 1, width=1e6))
x <- GRanges("chr1", IRanges(10e6 + 0:9 * 1e5 + 1, width=1e4))
y <- dhs %>% filter_by_overlaps(region) %>% select(NULL)
x %>% mutate(num_overlaps = count_overlaps(., y))
```

We can easily bootstrap data just in this region using the following
code:

```{r}
seg <- oneRegionSegment(region, seqlength=248956422)
y <- keepSeqlevels(y, "chr1")
set.seed(1)
boot <- bootRanges(y, blockLength=1e5, R=1, seg=seg,
                   proportionLength=FALSE)
boot
x %>% mutate(num_overlaps = count_overlaps(., boot))
```

Here it is important to use `proportionLength=FALSE` so that the
blocks will be of the size specified and not smaller (they would
otherwise be scaled down proportional to the fraction of `region`
compared to the chromosome).

# Visualizing bootstrap types

Below we present a toy example for visualizing the segmented block
bootstrap. First, we define a helper function for plotting *GRanges*
using *plotgardener* [@Kramer2022]. A key aspect here is that we color
the original and bootstrapped ranges by the genomic state (the state of
the segmentation that the original ranges fall in).

```{r}
suppressPackageStartupMessages(library(plotgardener))
my_palette <- function(n) {
  head(c("red","green3","red3","dodgerblue",
         "blue2","green4","darkred"), n)
}
plotGRanges <- function(gr) {
  pageCreate(width = 5, height = 5, xgrid = 0,
                ygrid = 0, showGuides = TRUE)
  for (i in seq_along(seqlevels(gr))) {
    chrom <- seqlevels(gr)[i]
    chromend <- seqlengths(gr)[[chrom]]
    suppressMessages({
      p <- pgParams(chromstart = 0, chromend = chromend,
                    x = 0.5, width = 4*chromend/500, height = 2,
                    at = seq(0, chromend, 50),
                    fill = colorby("state_col", palette=my_palette))
      prngs <- plotRanges(data = gr, params = p,
                          chrom = chrom,
                          y = 2 * i,
                          just = c("left", "bottom"))
      annoGenomeLabel(plot = prngs, params = p, y = 0.1 + 2 * i)
    })
  }
}
```

Create a toy genome segmentation:

```{r}
library(GenomicRanges)
seq_nms <- rep(c("chr1","chr2"), c(4,3))
seg <- GRanges(
  seqnames = seq_nms,
  IRanges(start = c(1, 101, 201, 401, 1, 201, 301),
          width = c(100, 100, 200, 100, 200, 100, 100)),
  seqlengths=c(chr1=500,chr2=400),
  state = c(1,2,1,3,3,2,1),
  state_col = factor(1:7)
)
```

We can visualize with our helper function:

```{r toysegments, fig.width=5, fig.height=4, eval=FALSE}
plotGRanges(seg)
```

Now create small ranges distributed uniformly across the toy genome:

```{r toyrangesI, fig.width=5, fig.height=4, eval=FALSE}
set.seed(1)
n <- 200
gr <- GRanges(
  seqnames=sort(sample(c("chr1","chr2"), n, TRUE)),
  IRanges(start=round(runif(n, 1, 500-10+1)), width=10)
)
suppressWarnings({
  seqlengths(gr) <- seqlengths(seg)
})
gr <- gr[!(seqnames(gr) == "chr2" & end(gr) > 400)]
gr <- sort(gr)
idx <- findOverlaps(gr, seg, type="within", select="first")
gr <- gr[!is.na(idx)]
idx <- idx[!is.na(idx)]
gr$state <- seg$state[idx]
gr$state_col <- factor(seg$state_col[idx])
plotGRanges(gr)
```

**Scaling vs. not scaling by segment length**

We can visualize block bootstrapped ranges when the blocks do not scale
to segment state length:

```{r toy-no-prop, fig.width=5, fig.height=4, eval=FALSE}
set.seed(1)
gr_prime <- bootRanges(gr, blockLength = 25, seg = seg,
                       proportionLength = FALSE)
plotGRanges(gr_prime)
```

This time the blocks scale to the segment state length. Note that in
this case `blockLength` is the *maximal* block length possible, but the
actual block lengths per segment will be smaller (proportional to the
fraction of basepairs covered by that state in the genome segmentation).

```{r toy-prop, fig.width=5, fig.height=4, eval=FALSE}
set.seed(1)
gr_prime <- bootRanges(gr, blockLength = 50, seg = seg,
                       proportionLength = TRUE)
plotGRanges(gr_prime)
```

Note that some ranges from adjacent states are allowed to be placed
within different states in the bootstrap sample. This is because, during
the random sampling of blocks of original data, a block is allowed to
extend beyond the segmentation region of the state being sampled, and
features from adjacent states are not excluded from the sampled block.

# Session information

```{r}
sessionInfo()
```

# References
