Explaining the Saddlepoint Approximation

Casella, George; Goutis, C.E.

doi:10.2307/2686100

Cited by 43 publications

(1 citation statement)

References 13 publications

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“…More specifically, it can be used to obtain the asymptotic approximations to the computation of integrals. A basic description of the SAP method is illustrated in [29,30], and it is presented below with minor modifications for convenience. A function gðxÞ that is written in p-dimension integral form can be approximated by…”

Section: Saddlepoint Approximation Representationmentioning

confidence: 99%

Parameter Estimation of Gamma‐Gamma Fading with Generalized Pointing Errors in FSO Systems

Miao

Cai

2021

Wireless Communications and Mobile Computing

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In this paper, the challenges of parameter estimation for the Gamma-Gamma turbulence channels with generalized pointing errors are addressed. The Kolmogorov-Smirnov goodness-of-fit statistical test results indicate that the approximate probability density function obtained by the saddlepoint approximation (SAP) method provides a better approximation for a larger value w z , and this means that the proposed method is more efficient for the FSO links over long distances when the transmit divergence angle at the transmitter side is fixed. Also, an additional parameter k needs to be estimated in addition to the shaping parameters α and β under the SAP method. An estimation scheme for the shaping parameters is proposed based on the SAP method. The performance of the proposed estimation is investigated by using the mean square error (MSE) and normalized mean square error (NMSE). The results indicate the proposed estimator exhibits satisfactory performance in both noiseless and noisy environments. The effects of the receiver aperture on the estimation performance are also discussed.

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Section: Saddlepoint Approximation Representationmentioning

confidence: 99%

Parameter Estimation of Gamma‐Gamma Fading with Generalized Pointing Errors in FSO Systems

Miao

Cai

2021

Wireless Communications and Mobile Computing

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Modeling joint abundance of multiple species using Dirichlet process mixtures

Johnson

Sinclair

2017

Environmetrics

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We present a method for modeling the distributions of multiple species simultaneously using Dirichlet process random effects to cluster species into guilds. Guilds are ecological groups of species that behave or react similarly to some environmental conditions. By modeling latent guild structure, we capture the cross‐correlations in abundance or occurrence of species over surveys. In addition, ecological information about the community structure is obtained as a by‐product of the model. By clustering species into similar functional groups, prediction uncertainty of community structure at additional sites is reduced over treating each species separately. The proposed model also presents an improvement over previously proposed joint species distribution models by reducing the number of parameters necessary to capture interspecies correlations and eliminating the need to have a priori information on the number of groups or a distance metric over species traits. The method is illustrated with a small simulation demonstration, as well as an analysis of a mesopelagic fish survey from the eastern Bering Sea near Alaska. The simulation data analysis shows that guild membership can be extracted as the differences between groups become larger and if guild differences are small, the model naturally collapses all the species into a small number of guilds, which increases predictive efficiency by reducing the number of parameters to that which is supported by the data.

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Application of the simple saddlepoint approximation to estimate probability distributions in wildlife research

2011

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The simple saddlepoint approximation (SSA) uses the mean, variance, and skewness (a measure of the asymmetry of the distribution) of a data set to algebraically approximate the probability density function of a selected variable. We compared habitat‐suitability bounds estimated with SSAs and continuous selection functions. Habitat‐suitability bounds for bobwhite nesting based on the SSA method were biologically comparable to the results of the method based on continuous selection functions. The SSA approach allows habitat‐suitability bounds to be estimated using algebra and can be calculated in computer spreadsheets. © 2011 The Wildlife Society.

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Explaining the Saddlepoint Approximation

Cited by 43 publications

References 13 publications

Parameter Estimation of Gamma‐Gamma Fading with Generalized Pointing Errors in FSO Systems

Parameter Estimation of Gamma‐Gamma Fading with Generalized Pointing Errors in FSO Systems

Modeling joint abundance of multiple species using Dirichlet process mixtures

Application of the simple saddlepoint approximation to estimate probability distributions in wildlife research

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