Statistical Modelling 23 (2) (2023), 151172
Outlier accommodation with semiparametric density
processes: A study of Antarctic snow density
modelling
Daniel M. Sheanshang,
Department of Statistics,
Brigham Young University,
Provo, UT,
USA.
e-mail: daniel.sheanshang@gmail.com
Philip A. White,
Department of Statistics,
Brigham Young University,
Provo, UT,
USA.
Durban G. Keeler,
Department of Geography,
University of Utah,
Salt Lake City, UT,
USA.
Abstract:
In many settings, data acquisition generates outliers that can obscure inference. Therefore,
practitioners often either identify and remove outliers or accommodate outliers using robust models.
However, identifying and removing outliers is often an ad hoc process that affects inference, and
robust methods are often too simple for some applications. In our motivating application, scientists
drill snow cores and measure snow density to infer densification rates that aid in estimating snow water
accumulation rates and glacier mass balances. Advanced measurement techniques can measure density
at high resolution over depth but are sensitive to core imperfections, making them prone to outliers.
Outlier accommodation is challenging in this setting because the distribution of outliers evolves over
depth and the data demonstrate natural heteroscedasticity. To address these challenges, we present a
two-component mixture model using a physically motivated snow density model and an outlier model,
both of which evolve over depth. The physical component of the mixture model has a mean function
with normally distributed depth-dependent heteroscedastic errors. The outlier component is specified
using a semiparametric prior density process constructed through a normalized process convolution
of log-normal random variables. We demonstrate that this model outperforms alternatives and can be
used for various inferential tasks.
Keywords:
Bayesian statistics, density estimation, heteroscedasticity, outliers, process convolution,
snow density
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