Annals of Applied Statistics

Functional time series models for ultrafine particle distributions

Heidi J. Fischer, Qunfang Zhang, Yifang Zhu, and Robert E. Weiss

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We propose Bayesian functional mixed effect time series models to explain the impact of engine idling on ultrafine particle (UFP) counts inside school buses. UFPs are toxic to humans and school engines emit particles primarily in the UFP size range. As school buses idle at bus stops, UFPs penetrate into cabins through cracks, doors, and windows. Counts increase over time at a size dependent rate once the engine turns on. How UFP counts inside buses vary by particle size over time and under different idling conditions is not yet well understood. We model UFP counts at a given time using a mixed effect model with a cubic B-spline basis as a function of size. The log residual variance over size is modeled using a quadratic B-spline basis to account for heterogeneity in error across size bin, and errors are autoregressive over time. Model predictions are communicated graphically. These methods provide information needed to quantify UFP counts by size and possibly minimize UFP exposure in the future.

Article information

Ann. Appl. Stat., Volume 11, Number 1 (2017), 297-319.

Received: December 2014
Revised: November 2016
First available in Project Euclid: 8 April 2017

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Bayesian statistics hierarchical models varying coefficient models heteroskedasticity


Fischer, Heidi J.; Zhang, Qunfang; Zhu, Yifang; Weiss, Robert E. Functional time series models for ultrafine particle distributions. Ann. Appl. Stat. 11 (2017), no. 1, 297--319. doi:10.1214/16-AOAS1004.

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