Model selection in radon data fusion

Pyne

2021

J Stat Theory Pract

Self Cite

Synthetic data, when properly used, can enhance patterns in real data and thus provide insights into different problems. Here, the estimation of tail probabilities of rare events from a moderately large number of observations is considered. The problem is approached by a large number of augmentations or fusions of the real data with computer-generated synthetic samples. The tail probability of interest is approximated by subsequences created by a novel iterative process. The estimates are found to be quite precise.

Section: Discussionmentioning

confidence: 99%

Section: Getting Upper Bounds For P By Data Fusionmentioning

confidence: 99%

Estimation of Tail Probabilities by Repeated Augmented Reality

Pyne

2021

J Stat Theory Pract

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“…06 . A different approach to residential radon exceedances using fused county data is studied in Zhang et al (2020a,b) [11,12], employing a density ratio model with variable tilt functions.…”

Section: Illustration In Terms Of Radon Datamentioning

confidence: 99%

On the Probabilities of Environmental Extremes

Stauffer

Zhang

et al. 2021

ijsmr

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Environmental researchers, as well as epidemiologists, often encounter the problem of determining the probability of exceeding a high threshold of a variable of interest based on observations that are much smaller than the threshold. Moreover, the data available for that task may only be of moderate size. This generic problem is addressed by repeatedly fusing the real data numerous times with synthetic computer-generated samples. The threshold probability of interest is approximated by certain subsequences created by an iterative algorithm that gives precise estimates. The method is illustrated using environmental data including monitoring data of nitrogen dioxide levels in the air.

“…The selection of the tilts h k 's can be based on [16][17][18]. A flowchart in Figure 1 is provided to illustrate the steps in the data fusion analysis.…”

Section: Density Ratio Modelmentioning

confidence: 99%

Multivariate Tail Probabilities: Predicting Regional Pertussis Cases in Washington State

Zhang

Pyne

2021

Entropy

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In disease modeling, a key statistical problem is the estimation of lower and upper tail probabilities of health events from given data sets of small size and limited range. Assuming such constraints, we describe a computational framework for the systematic fusion of observations from multiple sources to compute tail probabilities that could not be obtained otherwise due to a lack of lower or upper tail data. The estimation of multivariate lower and upper tail probabilities from a given small reference data set that lacks complete information about such tail data is addressed in terms of pertussis case count data. Fusion of data from multiple sources in conjunction with the density ratio model is used to give probability estimates that are non-obtainable from the empirical distribution. Based on a density ratio model with variable tilts, we first present a univariate fit and, subsequently, improve it with a multivariate extension. In the multivariate analysis, we selected the best model in terms of the Akaike Information Criterion (AIC). Regional prediction, in Washington state, of the number of pertussis cases is approached by providing joint probabilities using fused data from several relatively small samples following the selected density ratio model. The model is validated by a graphical goodness-of-fit plot comparing the estimated reference distribution obtained from the fused data with that of the empirical distribution obtained from the reference sample only.