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index.Rmd
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index.Rmd
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---
title: "Introduction to BASS"
author: "Zheng Li"
date: "2022-02-06"
site: workflowr::wflow_site
output:
workflowr::wflow_html:
toc: true
editor_options:
chunk_output_type: console
---
# Welcome to the BASS website!
This website maintains code for reproducing simulation and real data
application results described in the upcoming paper.For the software,
please to refer to [BASS](https://github.com/zhengli09/BASS).
# Introduction to BASS
BASS is a method for multi-scale and multi-sample analysis in spatial
transcriptomics. BASS performs multi-scale transcriptomic analyses in the form
of joint cell type clustering and spatial domain detection, with the two
analytic tasks carried out simultaneously within a Bayesian hierarchical
modeling framework. For both analyses, BASS properly accounts for the spatial
correlation structure and seamlessly integrates gene expression information
with spatial localization information to improve their performance. In addition,
BASS is capable of multi-sample analysis that jointly models multiple tissue
sections/samples, facilitating the integration of spatial transcriptomic data
across tissue samples.
## BASS workflow
![](BASS_workflow.png)
## BASS Model overview
BASS relies on a Bayesian hierarchical modeling framework that describes the
relationship among gene expression features, cell type labels, spatial domain
labels, cell type compositions, and neighborhood graphs in a hierarchical
fashion:
$$
\boldsymbol{x}_i^{(l)} | c_i^{(l)} = c \sim MVN(\boldsymbol{\mu}_c, \boldsymbol{\Sigma})
$$
$$
c_i^{(l)} | z_i^{(l)} = r \sim Cat(\boldsymbol{\pi}_r)
$$
$$
\boldsymbol{z}^{(l)} \sim Potts(V^{(l)}, \beta)
$$
Above, the first equation models the expression feature of the $i$th cell on
section $l$, $\boldsymbol{x}_i^{(l)}$, as depending on its cell type label
$c_i^{(l)}$ with a multivariate normal distribution parameterized by a cell
type-specific mean parameter $\boldsymbol{\mu}_c$ and a variance-covariance
matrix $\boldsymbol{\Sigma}$. The second equation models the probability of the
$i$th cell belonging to the cell type $c$ as depending on the underlying spatial
domain with a categorical distribution parameterized by the $r$ domain-specific
cell type composition vector $\boldsymbol{\pi}_r$. The third equation models the
spatial domain label of all cells on the section $l$, $\boldsymbol{z}^{(l)}$, as
a function of the neighoborhood graph $V^{(l)}$ through a homogeneous Potts model
characterized by an interaction parameter $\beta$.