  Flow cytometry (FCM) is the standard multi-parameter assay for measuring
single cell phenotype and functionality. It is commonly used for quantifying
the relative frequencies of cell subsets in blood and disaggregated tissues. A
typical analysis of FCM data involves cell classification---that is, the
identification of cell subgroups in the sample---and comparisons of the cell
subgroups across samples or conditions. While modern experiments often
necessitate the collection and processing of samples in multiple batches,
analysis of FCM data across batches is challenging because differences across
samples may occur due to either true biological variation or technical reasons
such as antibody lot effects or instrument optics across batches. Thus a
critical step in comparative analyses of multi-sample FCM data---yet missing in
existing automated methods for analyzing such data---is cross-sample
calibration, whose goal is to align corresponding cell subsets across multiple
samples in the presence of technical variations, so that biological variations
can be meaningfully compared. We introduce a Bayesian nonparametric
hierarchical modeling approach for accomplishing both calibration and cell
classification simultaneously in a unified probabilistic manner. Three
important features of our method make it particularly effective for analyzing
multi-sample FCM data: a nonparametric mixture avoids prespecifying the number
of cell clusters; a hierarchical skew normal kernel that allows flexibility in
the shapes of the cell subsets and cross-sample variation in their locations;
and finally the "coarsening" strategy makes inference robust to departures from
the model such as heavy-tailness not captured by the skew normal kernels. We
demonstrate the merits of our approach in simulated examples and carry out a
case study in the analysis of two multi-sample FCM data sets.
