Anwendung elektrochemischer Analysenmethoden

Henze, Günter; Neeb, Rolf

doi:10.1007/978-3-642-70173-3_4

Cited by 3 publications

(3 citation statements)

References 413 publications

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“…In fact, we work with a transformed version (µ, τ 2 , ψ) of (µ, σ, α), such that σ 2 = τ 2 + ψ 2 and α = ψ/τ , with τ > 0 and ψ ∈ R. This re-parameterization facilitates implementation of the computational method for posterior inference as an efficient Gibbs sampler algorithm. Key in this direction is also a stochastic representation of the skewed normal distribution in (13) as a mixture of normal distributions (Henze 1986). The specific result is given in Appendix §A, which includes also the technical details of the MCMC posterior simulation method.…”

Section: Inferring the Neutron Star Mass Distributionmentioning

confidence: 99%

The Neutron Star Mass Distribution

Kızıltan

Kottas

Yoreo

et al. 2013

ApJ

383

351

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In recent years, the number of pulsars with secure mass measurements has increased to a level that allows us to probe the underlying neutron star (NS) mass distribution in detail. We critically review the radio pulsar mass measurements. For the first time, we are able to analyze a sizable population of NSs with a flexible modeling approach that can effectively accommodate a skewed underlying distribution and asymmetric measurement errors. We find that NSs that have evolved through different evolutionary paths reflect distinctive signatures through dissimilar distribution peak and mass cutoff values. NSs in double neutron star and neutron star-white dwarf systems show consistent respective peaks at 1.33 M ⊙ and 1.55 M ⊙ suggesting significant mass accretion (∆m ≈ 0.22 M ⊙ ) has occurred during the spin-up phase. The width of the mass distribution implied by double NS systems is indicative of a tight initial mass function while the inferred mass range is significantly wider for NSs that have gone through recycling. We find a mass cutoff at ∼ 2.1 M ⊙ for NSs with white dwarf companions which establishes a firm lower bound for the maximum NS mass. This rules out the majority of strange quark and soft equation of state models as viable configurations for NS matter. The lack of truncation close to the maximum mass cutoff along with the skewed nature of the inferred mass distribution both enforce the suggestion that the 2.1 M ⊙ limit is set by evolutionary constraints rather than nuclear physics or general relativity, and the existence of rare super-massive NSs is possible.

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Section: Inferring the Neutron Star Mass Distributionmentioning

confidence: 99%

The Neutron Star Mass Distribution

Kızıltan

Kottas

Yoreo

et al. 2013

ApJ

383

351

View full text Add to dashboard Cite

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“…when λ is a shape parameter (Azzalini, 1985;Henze, 1986). Shape parameter λ = 0 gives normal distribution N (0, σ 2 0 ) with a mean 0 and variance σ 2 0 and increasing |λ| increases skewness.…”

Section: Datasets For Regression Taskmentioning

confidence: 99%

What Loss Functions Do Humans Optimize When They Perform Regression and Classification

Ryu,

Srinivasan

2023

Preprint

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Understanding how humans perceive patterns in visually presented data is useful for understanding data-based decision making and, possibly, visually mediated sensorimotor control under disturbances and noise. Here, we conducted human subject experiments to examine how humans perform the simplest machine learning or statistical estimation tasks: linear regression and binary classification in data presented visually as 2D scatter plots. We used simple inverse optimization to infer the loss function humans optimize when they perform these tasks. In classical machine learning, common loss functions for regression are mean squared error or summed absolute error, and logistic loss or hinge loss for classification. For the regression task, minimizing the sum of error raised to the power of 1.7 on average best described human subjects performing regression on sparse data consisting of relatively fewer data points. Loss functions with lower exponents, which would reject outliers more effectively, were better descriptors for regression tasks performed on less sparse data. For the classification task, minimizing a logistic loss function was on average a better descriptor of human choices than an exponential loss function applied to only misclassified data. People changed their strategies as data density increased, such that loss functions with lower exponents described empirical data better. These results represent overall trends across subjects and trials but there was large inter- and intra- subject variability in human choices. Future work may examine other loss function families and other tasks. Such understanding of human loss functions may inform designing computer algorithms that interact with humans better and imitate humans more effectively.

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“…The family of skew-normal distribution which provide an alternative robust approach for modelling asymmetric data which are analytically tractable, accommodate practical values of asymmetry have been introduced by Azzalini (1985Azzalini ( , 1986; Azzalini & Valle (1996); Henze (1986); Azzalini & Capitanio (1999); Branco & Dey (2001) and Sahu et al (2003). And skew-Laplace distribution was presented by (Arslan, 2010;Kotz et al, 2001;Kozubowski et al, 2013) and Okhli et al (2017).…”

Section: Introductionmentioning

confidence: 99%

Flexible Bayesian hierarchical spatial modeling in disease mapping.

Ayalew

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The Gaussian Intrinsic Conditional Autoregressive (ICAR) spatial model, which usually has two components, namely an ICAR for spatial smoothing and standard random effects for non-spatial heterogeneity, is used to estimate spatial distributions of disease risks. The normality assumption in this model may not always be correct and misspecification of the distribution of random effects could result in biased estimation of the spatial distribution of disease risk, which could lead to misleading conclusions and policy recommendations. Limited research studies have been done where the estimation of the spatial distributions of diseases under the ICAR-normal model were compared to those obtained from fitting ICAR-nonnormal model. The results from these studies indicated that the ICAR-nonnormal models performed better than the ICAR-normal in terms of accuracy, efficiency and predictive capacity. However, these efforts have not fully addressed the effect on the estimation of spatial distributions under flexible specification of ICAR models in disease mapping. The overall aim of this PhD thesis was to develop approaches that relax the normality assumption that is often used in modeling and fitting of ICAR models in the estimation of spatial patterns of diseases. In particular, the thesis considered the skewnormal and skew-Laplace distributions under the univariate, and skew-normal for the multivariate specifications to estimate the spatial distributions of either univariable or multivariable areal data. The thesis also considered non-parametric specification of the multivariate spatial effects in the ICAR model, which is a novel extension of an earlier work. The estimation of the models was done using Bayesian statistical approaches. The performances of our suggested alternatives to the ICAR-normal model were evaluated by simulating studies as well as with practical application to the estimation of district-level distribution of HIV prevalence and treatment coverage using health survey data in South Africa. Results from the simulation studies and analysis of real data demonstrated that our approaches performed better in the prediction of spatial distributions for univariable and multivariable areal data in disease mapping approaches. This PhD has shown the limitations of relying on the ICAR-normal model for the estimations of spatial distributions for all spatial analyses, even when the data could be asymmetric and non-normal. In such scenarios, skewed-ICAR and nonparametric ICAR approaches could provide better and unbiased estimation of the spatial pattern of diseases.

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Anwendung elektrochemischer Analysenmethoden

Cited by 3 publications

References 413 publications

The Neutron Star Mass Distribution

The Neutron Star Mass Distribution

What Loss Functions Do Humans Optimize When They Perform Regression and Classification

Flexible Bayesian hierarchical spatial modeling in disease mapping.

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