Dataset Information

On the Null Distribution of Bayes Factors in Linear Regression.

ABSTRACT: We show that under the null, the 2 log(Bayes factor) is asymptotically distributed as a weighted sum of chi-squared random variables with a shifted mean. This claim holds for Bayesian multi-linear regression with a family of conjugate priors, namely, the normal-inverse-gamma prior, the g-prior, and the normal prior. Our results have three immediate impacts. First, we can compute analytically a p-value associated with a Bayes factor without the need of permutation. We provide a software package that can evaluate the p-value associated with Bayes factor efficiently and accurately. Second, the null distribution is illuminating to some intrinsic properties of Bayes factor, namely, how Bayes factor quantitatively depends on prior and the genesis of Bartlett's paradox. Third, enlightened by the null distribution of Bayes factor, we formulate a novel scaled Bayes factor that depends less on the prior and is immune to Bartlett's paradox. When two tests have an identical p-value, the test with a larger power tends to have a larger scaled Bayes factor, a desirable property that is missing for the (unscaled) Bayes factor.

SUBMITTER: Zhou Q

PROVIDER: S-EPMC6205752 | biostudies-literature | 2018

REPOSITORIES: biostudies-literature

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Publications

On the Null Distribution of Bayes Factors in Linear Regression.

Zhou Quan Q Guan Yongtao Y

Journal of the American Statistical Association 20180608 523

We show that under the null, the 2 log(Bayes factor) is asymptotically distributed as a weighted sum of chi-squared random variables with a shifted mean. This claim holds for Bayesian multi-linear regression with a family of conjugate priors, namely, the normal-inverse-gamma prior, the g-prior, and the normal prior. Our results have three immediate impacts. First, we can compute analytically a p-value associated with a Bayes factor without the need of permutation. We provide a software package t ...[more]

PMID: 30386004

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Project description:In this work, we analyse factors explaining the distribution and range regression of Dupont's lark in Spain, the only European country in which this threatened alaudid is present. Dupont's lark is an extremely elusive and scarce species, distributed across a reduced and strongly fragmented range, showing a metapopulational structure with unknown dispersive and connective mechanisms. We used maximum entropy modelling (Maxent) on nearly 15,000 Dupont's lark observations (1985-2015) to assess the probability of presence at a 1 km resolution across its European range. Moreover, we tested the probability of extinction by comparing pre- and post-2000 observations by means of a GLM over a subset of cells with presence-absence data. We obtained strong model fitting (AUC = 0.919), in which species occurrence was explained by low values of plant productivity (NDVI), climate (high temperature range and medium annual precipitation), land use (increasing with sclerophyllous scrubland), flat topography and human disturbance (associated with low human population density). The species also tolerates dry farming, but not other farm types or forest cover. The probability map identified two main regions known as the species' core areas: the steppes of the Iberian System and the Ebro Valley. The North Plateau is characterised by a dispersed structure of small and very fragmented patches of suitable habitat, while a succession of discontinuous probability patches form an Eastern Corridor connecting the central core areas to the southernmost populations. Finally, the model identified small and isolated patches of high probability of presence along the eastern coastline. The species tends to occur in the best available areas but, at the same time, the model revealed a large area of suitable but unoccupied habitat. Our results correct the previous estimation of occupation area from 1,480 to 1,010.78 km2, a reduction of 26.22%. The current distribution of Dupont's lark is almost completely covered by Important Bird Areas (IBAs), highlighting their importance for bird conservation, but only 44.89% is included in Natura 2000 Special Protection Areas (SPAs). A comparison of pre- and post-2000 periods revealed a range contraction of 44%. Probability of extinction increased with higher temperature range and lower annual precipitation, and with decreases in population density, which suggests that this species is extremely vulnerable to both climate change and rural abandonment, due to its dependence on traditional grazing. These results suggest the need for a re-evaluation of the conservation status of Dupont's lark in Spain. They urge the preservation of not only current extant populations, but also the unoccupied suitable areas that could be critical for metapopulation structure, and the development of policies addressing the preservation of traditional grazing.

Dataset Information

On the Null Distribution of Bayes Factors in Linear Regression.

Publications

On the Null Distribution of Bayes Factors in Linear Regression.

Similar Datasets

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