Bayesian Analysis Applied on Particulate Matter Measurement Data

• Activity Number: 459 - Methods and Computing for Spatial and Spatio-Temporal Data
• Type: Contributed
• Date/Time: Thursday, August 6, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Shailendra Banerjee* and Gregory M. Zarus
• Companies: Centers for Disease Control and ATSDR
• Keywords: Particulate Matter; Contingency Table; Multinomial Distribution; Uniform Distribution; Bayes Factor

Abstract

Bayesian methodology is applied on particulate matter measurement data collected by Agency for Toxic Substances and Disease Registry (ATSDR/CDC). ATSDR sought to determine efficacy of instruments to measure air concentrations of PM < = 10 microns. In this study, the performance of the low-cost particulate sensor Nova A was compared against standard monitor DustTrak. Both instruments were tested with PM generated by atomizing salt aqueous solution. A contingency table was created with Nova A and DustTrak measurements. Assuming that the cell frequencies follow a multinomial distribution, we obtained posterior distribution under two conditions: (1) when the data are dependent and (2) when the data are independent. Under the dependent model, the cell probabilities are assumed to have a uniform prior, and under the independent model, the marginal probabilities pi+ and p+j follow independent uniform distributions. Based on these two models, we obtained a very high value of Bayes factor in favor of independent model proving that the measurements by standard DustTrak and low-cost sensor NOVA A are not compatible with each other. Bayesian two-sample test will also be done.