Bayes factor consistency

Chib, Siddhartha; Kuffner, Todd A.

doi:10.48550/arxiv.1607.00292

Cited by 12 publications

(18 citation statements)

References 124 publications

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“…they are consistent Model Selection Criteria, under the assumption of model-correctness, in the context of nested models, for specific classes of models (see e.g. Chib and Kuffner (2016); Nishii (1988); Sin and White (1996), and Yonekura et al (2018) for the case of discrete-time nested HMMs). One can plausibly conjecture such criteria will also perform well for the type of continuous-time HMMs we consider here.…”

Section: Sequential Model Selection -Real Datamentioning

confidence: 94%

Online Smoothing for Diffusion Processes Observed with Noise

Yonekura,

Beskos

2020

Preprint

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We introduce a methodology for online estimation of smoothing expectations for a class of additive functionals, in the context of a rich family of diffusion processes (that may include jumps) -observed at discrete-time instances. We overcome the unavailability of the transition density of the underlying SDE by working on the augmented pathspace. The new method can be applied, for instance, to carry out online parameter inference for the designated class of models. Algorithms defined on the infinite-dimensional pathspace have been developed the last years mainly in the context of MCMC techniques. There, the main benefit is the achievement of mesh-free mixing times for the practical time-discretised algorithm used on a PC. Our own methodology sets up the framework for infinite-dimensional online filtering -an important positive practical consequence is the construct of estimates with variance that does not increase with decreasing mesh-size. Besides regularity conditions, our method is, in principle, applicable under the weak assumption -relatively to restrictive conditions often required in the MCMC or filtering literature of methods defined on pathspace -that the SDE covariance matrix is invertible.

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Section: Sequential Model Selection -Real Datamentioning

confidence: 94%

Online Smoothing for Diffusion Processes Observed with Noise

Yonekura,

Beskos

2020

Preprint

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“…Thirdly, the FAP ignores the potential underlying population of orbital elements, such that it cannot distinguish planets with very rare characteristics, for which a high likelihood is required for detection, and common ones. The Bayes factor is asymptotically consistent (Chib & Kuffner 2016), but in finite sample comparing models only two by two might be problematic if only sequential comparisons are made (1 planet versus 0, 2 planets vs 1 planet and so on). As noted in Brewer & Donovan (2015), the Bayes factor does not marginalise over possible models.…”

Section: Motivationmentioning

confidence: 99%

Improving exoplanet detection capabilities with the false inclusion probability. Comparison with other detection criteria in the context of radial velocities

Hara,

Unger,

Delisle

et al. 2021

Preprint

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Context. It is common practice to claim the detection of a signal if, for a certain statistical significance metric, the signal significance exceeds a certain threshold fixed in advance. In the context of exoplanet searches in radial velocity data, the most common statistical significance metrics are the Bayes factor and the false alarm probability (FAP). Both criteria have proved useful, but do not directly address whether an exoplanet detection should be claimed. Furthermore, it is unclear which detection threshold should be taken and how robust the detections are to model misspecification. Aims. The present work aims at defining a detection criterion which conveys as precisely as possible the information needed to claim an exoplanet detection, as well as efficient numerical methods to compute it. We compare this new criterion to existing ones in terms of sensitivity, and robustness to a change in the model. Methods. We define a detection criterion based on the joint posterior distribution of the number of planets and of their orbital elements called the false inclusion probability (FIP). In the context of exoplanet detections, it provides the probability of presence of a planet with a period in a certain interval. Posterior distributions are computed with the nested sampling package polychord. We show that for FIP and Bayes factor calculations, defining priors on linear parameters as Gaussian mixture models allows to significantly speed up computations. The performances of the FAP, Bayes factor and FIP are studied with simulations as well as analytical arguments. We compare the methods assuming the model is correct, then evaluate their sensitivity to the prior and likelihood choices. Results. Among other properties, the FIP offers ways to test the reliability of the significance levels, it is particularly efficient to account for aliasing and allows to exclude the presence of planets with a certain confidence. We find that, in our simulations, the FIP outperforms existing detection metrics. We show that planet detections are sensitive to priors on period and semi-amplitude and that letting free the noise parameters offers better performances than fixing a noise model based on a fit to ancillary indicators.The exoplanet detection process usually consists in assessing sequentially whether an additional planet should be included in the model. Planet detections are typically claimed based on one of two approaches. The first one is the computation of a periodogram, that is a systematic scan for periodicity on a grid of frequencies. This is followed by the computation of a false alarm probability (FAP) to assess the significance of a detection. There are several definitions of the periodogram, corresponding to different assumptions on the data (e.g.

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“…To begin with, note that both models M 1 and M 2 have the Kullback-Leibler property. Several papers discuss this case, for example Corollary 3.1 in Ghosal et al (2008), Section 5 in Chib and Kuffner (2016) and Corollary 3 in Chatterjee et al (2020) in the general setting of dependent data. For more specific applications, refer also to Tokdar and Martin (2019) where the focus is on testing Gaussianity of the data under a Dirichlet process mixture alternative, Mcvinish et al (2009) for goodness of fit tests using mixtures of triangular distribution and Bhattacharya and Dunson (2012) for data distributed over non-euclidean manifolds.…”

Section: A Proofsmentioning

confidence: 99%

“…To the best of our knowledge, this kind of bounds have been derived only for the very special kind of mixtures in Mcvinish et al (2009). Similarly, the approach by Chib and Kuffner (2016) would require a knowledge of such lower bounds too (see for instance their Assumption 3). Corollary 3 in Chatterjee et al (2020) does not apply in our case as well, because one of their main assumptions presumes that both models specify a population distribution (i.e.…”

Section: A Proofsmentioning

confidence: 99%

The semi-hierarchical Dirichlet Process and its application to clustering homogeneous distributions

Beraha¹,

Guglielmi²,

Quintana³

2020

Preprint

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Assessing homogeneity of distributions is an old problem that has received considerable attention, especially in the nonparametric Bayesian literature. To this effect, we propose the semi-hierarchical Dirichlet process, a novel hierarchical prior that extends the hierarchical Dirichlet process of Teh et al. (2006) and that avoids the degeneracy issues of nested processes recently described by Camerlenghi et al. (2019a). We go beyond the simple yes/no answer to the homogeneity question and embed the proposed prior in a random partition model; this procedure allows us to give a more comprehensive response to the above question and in fact find groups of populations that are internally homogeneous when I ≥ 2 such populations are considered. We study theoretical properties of the semi-hierarchical Dirichlet process and of the Bayes factor for the homogeneity test when I = 2. Extensive simulation studies and applications to educational data are also discussed.

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Bayes factor consistency

Cited by 12 publications

References 124 publications

Online Smoothing for Diffusion Processes Observed with Noise

Online Smoothing for Diffusion Processes Observed with Noise

Improving exoplanet detection capabilities with the false inclusion probability. Comparison with other detection criteria in the context of radial velocities

The semi-hierarchical Dirichlet Process and its application to clustering homogeneous distributions

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