A First Course in Bayesian Statistical Methods

Hoff, Peter D.

doi:10.1007/978-0-387-92407-6

Cited by 619 publications

(457 citation statements)

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“…Then, for every l−th locus, P l was drawn using the Gibbs sampler. Then, the parameters α, β, and γ were updated using the Metropolis-Hastings algorithm, in which new values were proposed using the reflective random walk (Hoff 2009). The final estimates (posterior means and quantiles) were obtained after 1,000,000 cycles, keeping every 250th update and disregarding the first 100,000 updates for burn-in.…”

Section: Analysis Of Outcrossing Ratesmentioning

confidence: 99%

Bayesian approach reveals confounding effects of population size and seasonality on outcrossing rates in a fragmented subalpine conifer

Chybicki

Dzialuk

2014

Tree Genetics & Genomes

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Mating systems have long been recognized as key factors determining genetic structure within and between populations. Outcrossing promotes genetic diversity and gene flow between populations, while inbreeding, on the other hand, decreases recombination rates, facilitating fixation of co-adapted genes. In small populations, selfing moderates pollen limitation because of low mate availability, but at the cost of increased inbreeding depression. These conflicts are of more than theoretical interest; they are critical for the management of endangered species. In order to help designing conservation strategies for the management of the gene pool of fragmented populations of Pinus cembra, a protected species in Poland, we have characterized pollen flow and mating structure using nuclear microsatellite markers. We demonstrated that P. cembra in the studied stands of the Tatra Mts. is characterized by an average outcrossing rate (t) of 0.72. Unlike with the existing approaches, using the newly developed Bayesian method, we found that population size and seasonal variation had confounding effects on outcrossing rates. In concordance with predictions, large populations showed significantly higher outcrossing rates (t=0.89) than smaller ones (t=0.51). Temporal variation revealed in the outcrossing rate might be linked with masting behavior of the species. On the other hand, we showed that outcrossing rates were not associated with a trunk diameter of a mother tree. Our study also demonstrated that biparental inbreeding is a significant component of mating system. However, we further show that pollen dispersal follows a fat-tailed distribution (with the average dispersal distance of 1,267 m) so that at least some long-distance pollen dispersal must be occurring.Overall, we conclude that the high inbreeding (both selfing and mating between relatives) found in P. cembra buffers for pollen limitation. We argue that small, isolated stands can be at risk of gene pool erosion, despite the potential for longdistance pollen and seed dispersal.

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Section: Analysis Of Outcrossing Ratesmentioning

confidence: 99%

Bayesian approach reveals confounding effects of population size and seasonality on outcrossing rates in a fragmented subalpine conifer

Chybicki

Dzialuk

2014

Tree Genetics & Genomes

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“…The samples obtained through this algorithm approximate the posterior distribution πθjd (Hoff, 2009). To minimize the effect of initial values and autocorrelation among samples, we discard an initial portion of the Markov chain and consider only every kth sample (thinning the chain).…”

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confidence: 99%

Uncertainty in Earthquake Source Imaging Due to Variations in Source Time Function and Earth Structure

Razafindrakoto

Martin

2014

Bulletin of the Seismological Society of America

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One way to improve the accuracy and reliability of kinematic earthquake source imaging is to investigate the origin of uncertainty and to minimize their effects. The difficulties in kinematic source inversion arise from the nonlinearity of the problem, nonunique choices in the parameterization, and observational errors. We analyze particularly the uncertainty related to the choice of the source time function (STF) and the variability in Earth structure. We consider a synthetic data set generated from a spontaneous dynamic rupture calculation. Using Bayesian inference, we map the solution space of peak slip rate, rupture time, and rise time to characterize the kinematic rupture in terms of posterior density functions. Our test to investigate the effect of the choice of STF reveals that all three tested STFs (isosceles triangle, regularized Yoffe with acceleration time of 0.1 and 0.3 s) retrieve the patch of high slip and slip rate around the hypocenter. However, the use of an isosceles triangle as STF artificially accelerates the rupture to propagate faster than the target solution. It additionally generates an artificial linear correlation between rupture onset time and rise time. These appear to compensate for the dynamic source effects that are not included in the symmetric triangular STF. The exact rise time for the tested STFs is difficult to resolve due to the small amount of radiated seismic moment in the tail of STF. To highlight the effect of Earth structure variability, we perform inversions including the uncertainty in the wavespeed only, and variability in both wavespeed and layer depth. We find that little difference is noticeable between the resulting rupture model uncertainties from these two parameterizations. Both significantly broaden the posterior densities and cause faster rupture propagation particularly near the hypocenter due to the major velocity change at the depth where the fault is located.Online Material: Figures of inverted rupture models, trade-off curve, and posterior probability density function.

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“…That is why, the prior distribution on ⌧ n and ⌧ s should be as minimally informative as possible [8]. To this end, one sets ↵ n = ↵ s = 1 and n = s !…”

Section: Choice Of the Prior Probability Distribution Of The Precisionsmentioning

confidence: 99%

Bayesian Formulations for Force Reconstruction Problems

Aucejo¹,

Smet²

2017

Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Abstract. To identify mechanical sources acting on a structure, Tikhonov-like regularizations are generally used. These approaches, however, only provide point estimates, meaning that the uncertainty about the regularized solution is not quantified. In practice, such information is essential to guarantee the quality of reconstructed sources. In this contribution, three possible Bayesian formulations of the source identification problem are presented and their limitations discussed. To assess the posterior uncertainty on the parameters appearing in each formulation given a simulated vibration field and a mechanical model, a Gibbs sampler is implemented. The proposed numerical validations highlight the practical interest of these formulations in terms of parameters estimations and posterior uncertainty quantification.

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A First Course in Bayesian Statistical Methods

Cited by 619 publications

References 0 publications

Bayesian approach reveals confounding effects of population size and seasonality on outcrossing rates in a fragmented subalpine conifer

Bayesian approach reveals confounding effects of population size and seasonality on outcrossing rates in a fragmented subalpine conifer

Uncertainty in Earthquake Source Imaging Due to Variations in Source Time Function and Earth Structure

Bayesian Formulations for Force Reconstruction Problems

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