A Generalization of the Savage–Dickey Density Ratio for Testing Equality and Order Constrained Hypotheses

Mulder, Joris; Wagenmakers, Eric‐Jan; Marsman, Maarten

doi:10.1080/00031305.2020.1799861

Cited by 10 publications

(12 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where we have used a 0 k ¼ a k þ x k . Note that this result has also been established for a specific case, albeit for a more general set of hypotheses, in Mulder et al (2020). What the above analysis of the Bayes factor for the mixed hypotheses H m shows is that we are, in general, able to factor the hypotheses and associated likelihoods.…”

Section: Bayes Factors For Mixed Constraintssupporting

confidence: 63%

Evaluating multinomial order restrictions with bridge sampling.

Sarafoglou¹,

Haaf²,

Ly³

et al. 2023

Psychological Methods

Self Cite

View full text Add to dashboard Cite

Hypotheses concerning the distribution of multinomial proportions typically entail exact equality constraints that can be evaluated using standard tests.Whenever researchers formulate inequality constrained hypotheses, however, they must rely on sampling-based methods that are relatively inefficient and computationally expensive. To address this problem we developed a bridge sampling routine that allows an efficient evaluation of multinomial inequality constraints. An empirical application showcases that bridge sampling outperforms current Bayesian methods, especially when relatively little posterior mass falls in the restricted parameter space. The method is extended to mixtures between equality and inequality constrained hypotheses.

show abstract

Section: Bayes Factors For Mixed Constraintssupporting

confidence: 63%

Evaluating multinomial order restrictions with bridge sampling.

Sarafoglou¹,

Haaf²,

Ly³

et al. 2023

Psychological Methods

Self Cite

View full text Add to dashboard Cite

show abstract

“…Verdinelli and Wasserman (1995). Its limitation is that it only holds for a specific form of the pior for the nuisance parameters under Model 1 which is completely determined by the prior under model 2 (Mulder et al, 2020).…”

Section: Model Comparisonmentioning

confidence: 99%

Parameter estimation with gravitational waves

Christensen

Meyer

2022

Rev. Mod. Phys.

View full text Add to dashboard Cite

The new era of gravitational wave astronomy truly began on September 14, 2015 with the detection of GW150914, the sensational first direct observation of gravitational waves from the inspiral and merger of two black holes by the two Advanced LIGO detectors. In the subsequent first three observing runs of the LIGO/Virgo network, gravitational waves from ∼ 50 compact binary mergers have been announced, with more results to come. The events have mostly been produced by binary black holes, but two binary neutron star mergers have so far been observed, as well as the mergers of two neutron star -black hole systems. Furthermore, gravitational waves emitted by core-collapse supernovae, pulsars and the stochastic gravitational wave background are within the LIGO/Virgo/KAGRA sensitivity band and are likely to be observed in future observation runs. Beyond signal detection, a major challenge has been the development of statistical and computational methodology for estimating the physical waveform parameters and quantifying their uncertainties in order to accurately characterise the emitting system. These methods depend on the sources of the gravitational waves and the gravitational waveform model that is used. This article reviews the main waveform models and parameter estimation methods used to extract physical parameters from gravitational wave signals detected to date by LIGO and Virgo and from those expected to be observed in the future, which will include KAGRA, and how these methods interface with various aspects of LIGO/Virgo/KAGRA science. Also presented are the statistical methods used by LIGO and Virgo to estimate detector noise, test general relativity, and draw conclusions about the rates of compact binary mergers in the universe. Furthermore, a summary of major publicly available gravitational wave parameter estimation software packages is given. BinaryBlack Hole Population Results from GWTC-2 42 B. Binary Neutron Stars 43 C. Neutron Star -Black Hole Binaries 43 IX. Other Signal Searches for LIGO and Virgo 44 A. Stochastic Gravitational Wave Background 44 B. Continuous Wave Signals 47 C.

show abstract

“…Finally, the consistency between the Savage-Dickey and the 'Removal of effect' comparison is also noteworthy. Although care should be involved when using the Savage-Dickey ratio, since it may not yield the correct Bayes factor under some circumstances (Heck, 2019;Mulder et al, 2020;Schad, Nicenboim, et al, 2021), these results suggest that the ratio of prior and posterior densities (at zero) is an appropriate way to gauge the Bayes factor for the effect of interest, even in the case of correlated fixed effects (e.g., in the M 1 'Maximal model').…”

Section: Resultsmentioning

confidence: 99%

When fixed and random effects mismatch: Another case of inflation of evidence in non-maximal models

Veríssimo¹

2021

Preprint

View full text Add to dashboard Cite

Mixed-effects models containing both fixed and random effects have become widely used in the cognitive sciences, as they are particularly appropriate for the analysis of clustered data. However, testing hypotheses in the presence of random effects is not completely straightforward, and a set of best practices for statistical inference in mixed-effects models is still lacking. Van Doorn et al. (2021) investigated how Bayesian hypothesis testing in mixed-effects models is impacted by particular model specifications. Here, we extend their work to the more complex case of models with three-level factorial predictors and, more generally, with multiple correlated predictors. We show how non-maximal models with correlated predictors contain 'mismatches' between fixed and random effects, in which the same predictor can refer to different effects in the fixed and random parts of a model. We then demonstrate though a series of Bayesian model comparisons that such mismatches can lead to inaccurate estimations of random variance, and in turn to biases in the assessment of evidence for the effect of interest. We present specific recommendations for how researchers can resolve mismatches or avoid them altogether: by fitting maximal models, eliminating correlations between predictors, or by residualising the random effects. Our results reinforce the observation that model comparisons with mixed-effects models can be surprisingly intricate and highlight that researchers should carefully and explicitly consider which hypotheses are being tested by each model comparison. Data and code are publicly available in an OSF repository at https://osf.io/njaup.

show abstract

A Generalization of the Savage–Dickey Density Ratio for Testing Equality and Order Constrained Hypotheses

Cited by 10 publications

References 28 publications

Evaluating multinomial order restrictions with bridge sampling.

Evaluating multinomial order restrictions with bridge sampling.

Parameter estimation with gravitational waves

When fixed and random effects mismatch: Another case of inflation of evidence in non-maximal models

Contact Info

Product

Resources

About