Hellinger Distance and Non-informative Priors

Shemyakin, Arkady

doi:10.1214/14-ba881

Cited by 18 publications

(15 citation statements)

References 34 publications

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“…This interval is effectively the same as the 95% highest posterior density intervals based on the fiducial and default‐prior (cf. Shemyakin, ) Bayesian posteriors plotted in Figure (b), which are indistinguishable. The two‐sided 95% fiducial interval, (98.49,105.92), reported in Hannig et al (), agrees with the IM plausibility interval obtained by using the “default” random set Eq.…”

Section: Inferential Models For a Class Of Non‐regular Modelsmentioning

confidence: 87%

“…This corresponds to a ( θ ) = θ and b ( θ ) = θ 2 − θ . Bayesian approaches based on default priors are available for this problem, for example, Berger et al (, Example 9) and Shemyakin (, Example 3). Unlike for the regular scalar‐parameter cases where Jeffreys prior is the agreed‐upon default prior, for this non‐regular problem, there are several priors that claim to be “reference” and no general non‐asymptotic guarantees are available on the coverage probability of the corresponding credible intervals.…”

Section: Inferential Models For a Class Of Non‐regular Modelsmentioning

confidence: 99%

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Exact prior‐free probabilistic inference in a class of non‐regular models

Martin

Lin

2016

Stat

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The use of standard statistical methods, such as maximum likelihood, is often justified based on their asymptotic properties. For suitably regular models, this theory is standard but, when the model is non-regular, e.g., the support depends on the parameter, these asymptotic properties may be difficult to assess. Recently, an inferential model (IM) framework has been developed that provides valid prior-free probabilistic inference without the need for asymptotic justification. In this paper, we construct an IM for a class of highly non-regular models with parameter-dependent support. This construction requires conditioning, which is facilitated through the solution of a particular differential equation. We prove that the plausibility intervals derived from this IM are exact confidence intervals, and we demonstrate their efficiency in a simulation study.

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Section: Inferential Models For a Class Of Non‐regular Modelsmentioning

confidence: 87%

Section: Inferential Models For a Class Of Non‐regular Modelsmentioning

confidence: 99%

Exact prior‐free probabilistic inference in a class of non‐regular models

Martin

Lin

2016

Stat

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“…The major advantages of the Hellinger distance are threefold: 1) it defines a true metric for probability distributions, as compared to, for example, the Kullback-Leibler divergence; 2) it is computationally simple, as compared to the Wasserstein distance; 3) and it is a special case of the f -divergence, which enjoys many geometric properties and has been used in many statistical applications. For example, Liese (2012) showed that f -divergence can be viewed as the integrated Bayes risk in hypothesis testing where the integral is with respect to a distribution on the prior; Nguyen et al (2009) linked f -divergence to the achievable accuracy in binary classification problems; Jager and Wellner ( 2007) used a subclass of f -divergences for goodness of fit testing; Rao (1995) demonstrated the advantages of the Hellinger metric for graphical representations of contingency table data; Srivastava and Klassen (2016) adopted the Hellinger distance to measure distances between functional and shape data; Shemyakin (2014) showed the connection of the Hellinger distance to Hellinger information, which is useful in nonregular statistical models when Fisher information is not available; and finally, Servidea and Meng (2006) derived an identity between the Hellinger derivative and the Fisher information that is useful for studying the interplay between statistical physics and statistical computation.…”

Section: Algorithm 1 Generating Process For T-ldamentioning

confidence: 99%

A Geometry-Driven Longitudal Topic Model

Wang¹,

Hougen²,

Oselio³

et al. 2021

Harvard Data Science Review

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A simple and scalable framework for longitudinal analysis of Twitter data is developed that combines latent topic models with computational geometric methods. Dimensionality reduction tools from computational geometry are applied to learn the intrinsic manifold on which the latent, temporal topics reside. Then shortest path distances on the manifold are used to link together these topics. The proposed framework permits visualization of the low-dimensional embedding, which provides clear interpretation of the complex, high-dimensional trajectories that may exist among latent topics. Practical application of the proposed framework is demonstrated through its ability to capture and effectively visualize natural progression of latent COVID-19-related topics learned from Twitter data. Interpretability of the trajectories is achieved by comparing to real-world events. In addition, the framework permits study of spatial variation in Twitter behavior for learned topics. The analysis demonstrates that the proposed framework is able to capture granular-level impact of COVID-19 on public discussions. We end by arguing that Twitter data, when analyzed within the proposed framework, can serve as a valuable supplementary data stream for COVID-related studies.

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“…A prior that maximizes the Kullback–Leibler information is by default a reference prior (for the general discussion of choosing a reference prior, we refer to Jeffreys (1946), Berger, Bernardo, and Sun (2009), and Shemyakin (2014)). The above approach to the construction of the reference prior is due to Bernardo (1979) (an excellent summary is given in Lehmann and Casella 1998 and the recent developments in Berger, Bernardo, and Sun 2009, 2012).…”

Section: Bayesian Solutionmentioning

confidence: 99%

A Note on the Minimax Solution for the Two-Stage Group Testing Problem

Malinovsky¹,

Albert

2015

The American Statistician

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Group testing is an active area of current research and has important applications in medicine, biotechnology, genetics, and product testing. There have been recent advances in design and estimation, but the simple Dorfman procedure introduced by R. Dorfman in 1943 is widely used in practice. In many practical situations, the exact value of the probability p of being affected is unknown. We present both minimax and Bayesian solutions for the group size problem when p is unknown. For unbounded p, we show that the minimax solution for group size is 8, while using a Bayesian strategy with Jeffreys’ prior results in a group size of 13. We also present solutions when p is bounded from above. For the practitioner, we propose strong justification for using a group size of between 8 and 13 when a constraint on p is not incorporated and provide useable code for computing the minimax group size under a constrained p.

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Hellinger Distance and Non-informative Priors

Cited by 18 publications

References 34 publications

Exact prior‐free probabilistic inference in a class of non‐regular models

Exact prior‐free probabilistic inference in a class of non‐regular models

A Geometry-Driven Longitudal Topic Model

A Note on the Minimax Solution for the Two-Stage Group Testing Problem

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