Recently, single-cell Assay for Transposase Accessible Chromatin (scATAC-seq) has emerged as a promising technique to study chromatin accessibility and gene regulation at single-cell resolution. As with virtually all modern 'omics data appropriately performing statistical analysis on scATAC-seq data is a key challenge. One major hurdle is that chromatin accessibility is widely considered to be binary, hence binarization of the count matrix is a common first step in many scATAC-seq pipelines, followed by Latent Semantic Indexing (LSI) for dimensionality reduction and subsequent downstream tasks. However, recent studies show that the scATAC-seq counts are quantitative instead of qualitative, which violates the assumption of most tools. A deep understanding of statistical properties of scATAC-seq counts is also lacking. Here we show that using the newly proposed counting strategy by Miao and Kim (2022), Paired-Insertion-Counting (PIC), chromatin accessibility counts display characteristics similar to single-cell RNA sequencing (scRNA-seq). Our results also highlight the key differences in modelling scATAC-seq counts when compared to scRNA-seq and that existing normalisation methods should be used with caution when statistical models that assume homoscedasticity are involved in downstream analysis. Lastly, we propose a hierarchical model that provides a principled approach to infer the underlying chromatin accessibility states in scATAC-seq data and identify biologically heterogeneous features.