Estimation of Tail Probabilities by Repeated Augmented Reality

Kedem, Benjamin; Pyne, Saumyadipta

doi:10.1007/s42519-020-00152-1

Cited by 3 publications

(6 citation statements)

References 13 publications

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“…In the Weibul(1.1,1) case the down-up shift alternated between 0.0001051111 and 0.0001201111 and we report the average. Similar results can be found in Kedem et al (2019) and Kedem and Pyne (2021) [5,6].…”

Section: Results Summarysupporting

confidence: 88%

“…As we shall see, synthetic data can enhance patterns in real data, a statistical idea highlighted by augmented reality (AR) explored in Kedem, De Oliveira, and Sverchkov (2017, Ch. 5), Kedem et al (2019), and in Kedem and Pyne (2021) [4][5][6].…”

Section: Repeated Fusionmentioning

confidence: 99%

“…The problem is to estimate a small tail probability p = P(X > T ) for a given threshold T from a reference sample X 0 = (X 1 ,..., X n 0 ) , where max( X 0 ) < T . This section follows for the most part Kedem et al (2019) and Kedem and Pyne (2021) [5,6].…”

Section: Upper Bounds For P By Data Fusionmentioning

confidence: 99%

“…However, in the present application the requirement of a known h is weakened considerably by the mild assumption (3) below, which may hold even for misspecified h , as numerous examples with many different tail types show. Accordingly, based on numerous experiments, some of which discussed in Kedem et al (2019) and Kedem and Pyne (2021) [5,6], for non-negative data we shall assume the "gamma tilt" h(x) = (x, log x) . Further justification for choosing the gamma tilt is provided by the rather precise p -estimates in the first eight entries in Table 10 below.…”

Section: ) (X Gmentioning

confidence: 99%

“…when B ( j i ) lies to the left of the true p . Suppose now we solve (6) with B ( j i ) along some p -increments, and find B ( j 2 ) nearest the smallest p which satisfies (6).…”

Section: "Down-up" Subsequencesmentioning

confidence: 99%

See 4 more Smart Citations

On the Probabilities of Environmental Extremes

Kedem

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.

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Section: Results Summarysupporting

confidence: 88%

Section: Repeated Fusionmentioning

confidence: 99%

Section: Upper Bounds For P By Data Fusionmentioning

confidence: 99%

Section: ) (X Gmentioning

confidence: 99%

“…when B ( j i ) lies to the left of the true p . Suppose now we solve (6) with B ( j i ) along some p -increments, and find B ( j 2 ) nearest the smallest p which satisfies (6).…”

Section: "Down-up" Subsequencesmentioning

confidence: 99%

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On the Probabilities of Environmental Extremes

Kedem

Stauffer

Zhang

et al. 2021

ijsmr

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On Rao’s Weighted Distributions for Modeling the Dynamics of Wildfires and Air Pollution

Guha,

Petersen,

Ray

et al. 2023

Indian Statistical Institute Series

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Multivariate Tail Probabilities: Predicting Regional Pertussis Cases in Washington State

Zhang

Pyne

Kedem

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.

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Estimation of Tail Probabilities by Repeated Augmented Reality

Cited by 3 publications

References 13 publications

On the Probabilities of Environmental Extremes

On the Probabilities of Environmental Extremes

On Rao’s Weighted Distributions for Modeling the Dynamics of Wildfires and Air Pollution

Multivariate Tail Probabilities: Predicting Regional Pertussis Cases in Washington State

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