This work provides a class of non‐Gaussian spatial Matérn fields which are useful for analysing geostatistical data. The models are constructed as solutions to stochastic partial differential equations driven by generalized hyperbolic noise and are incorporated in a standard geostatistical setting with irregularly spaced observations, measurement errors and covariates. A maximum likelihood estimation technique based on the Monte Carlo expectation‐maximization algorithm is presented, and a Monte Carlo method for spatial prediction is derived. Finally, an application to precipitation data is presented, and the performance of the non‐Gaussian models is compared with standard Gaussian and transformed Gaussian models through cross‐validation.

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BackgroundFlow cytometry is a widespread single-cell measurement technology with a multitude of clinical and research applications. Interpretation of flow cytometry data is hard; the instrumentation is delicate and can not render absolute measurements, hence samples can only be interpreted in relation to each other while at the same time comparisons are confounded by inter-sample variation. Despite this, most automated flow cytometry data analysis methods either treat samples individually or ignore the variation by for example pooling the data. A key requirement for models that include multiple samples is the ability to visualize and assess inferred variation, since what could be technical variation in one setting would be different phenotypes in another.ResultsWe introduce BayesFlow, a pipeline for latent modeling of flow cytometry cell populations built upon a Bayesian hierarchical model. The model systematizes variation in location as well as shape. Expert knowledge can be incorporated through informative priors and the results can be supervised through compact and comprehensive visualizations.BayesFlow is applied to two synthetic and two real flow cytometry data sets. For the first real data set, taken from the FlowCAP I challenge, BayesFlow does not only give a gating which would place it among the top performers in FlowCAP I for this dataset, it also gives a more consistent treatment of different samples than either manual gating or other automated gating methods. The second real data set contains replicated flow cytometry measurements of samples from healthy individuals. BayesFlow gives here cell populations with clear expression patterns and small technical intra-donor variation as compared to biological inter-donor variation.ConclusionsModeling latent relations between samples through BayesFlow enables a systematic analysis of inter-sample variation. As opposed to other joint gating methods, effort is put at ensuring that the obtained partition of the data corresponds to actual cell populations, and the result is therefore directly biologically interpretable. BayesFlow is freely available at GitHub.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-015-0862-z) contains supplementary material, which is available to authorized users.