scholarly journals Weighted Bayesian bootstrap for scalable posterior distributions

2020 ◽  
Author(s):  
Michael A. Newton ◽  
Nicholas G. Polson ◽  
Jianeng Xu
Keyword(s):  
Posterior Distributions ◽  
Bayesian Bootstrap

scholarly journals ACCIDENTAL EXPLOSIONS ON THE RAILWAY: SIMULATION‐BASED PREDICTION OF DAMAGE TO NEARBY BUILDINGS

Transport ◽  
2005 ◽  
Vol 20 (6) ◽  
pp. 265-273
Author(s):  
Egidijus R. Vaidogas
Keyword(s):  
Stochastic Simulation ◽  
Epistemic State ◽  
Posterior Distributions ◽  
Bayesian Bootstrap ◽  
Simulation Based ◽  
Potential Damage ◽  
Bayesian Prior

A procedure for estimating potential damage to buildings induced by accidental explosions on the railway is developed. By the damage failures of nearby structures due to actions generated by the accidental explosions are meant. This damage is measured in terms of probabilities of potential failures caused by explosions. The estimation of the damage probabilities is based on stochastic simulation of railway accidents involving an explosion. The proposed simulation‐based procedure quantifies epistemic (state‐of‐knowledge) uncertainties in the damage probabilities. These uncertainties are expressed in terms of Bayesian prior and posterior distributions. The foundation of the procedure is a computer intensive method known as the Bayesian bootstrap. It is used for approximating the posterior distributions of damage probabilities. The application of the Bayesian bootstrap makes the proposed procedure highly automatic and convenient for assessing structures subjected to the hazard of the accidental actions. In addition, it can be used for specifying safe distances between the railway and nearby buildings. Structures of these buildings can be designed for tolerable probabilities of failures induced by accidental explosions.

scholarly journals Genetic parameters for test-day model with random regressions for production traits of Czech Holstein cattle

2011 ◽  
Vol 50 (No. 4) ◽  
pp. 142-154 ◽  
Author(s):  
L. Zavadilová ◽  
J. Jamrozik ◽  
Schaeffer LR
Keyword(s):  
Milk Fat ◽  
Sampling Method ◽  
Random Regression ◽  
Model Parameters ◽  
Residual Variance ◽  
Posterior Distributions ◽  
Production Traits ◽  
Multiple Trait ◽  
Holstein Breed ◽  
Random Regression Model

Multiple-lactation random regression model was applied to test-day records of milk, fat and protein yields in the first three lactations of the Czech Holstein breed. Data included 9 583 cows, 89 584, 44 207 and 11 266 test-day records in the first, second and third lactation, respectively. Milk, fat and protein in the first three lactations were analysed separately and in a multiple-trait analysis. Linear model included herd-test date, fixed regressions within age-season class and two random effects: animal genetic and permanent environment modelled by regressions. Gibbs sampling method was used to generate samples from marginal posterior distributions of the model parameters. The single- and multiple-trait models provided similar results. Genetic and permanent environmental variances and heritability for particular days in milk were high at the beginning and at the end of lactation. The residual variance decreased throughout the lactation. The resulting heritability ranged from 0.13 to 0.52 and increased with parity.  

scholarly journals Parallel Markov chain Monte Carlo for non-Gaussian posterior distributions

Stat ◽  
2015 ◽  
Vol 4 (1) ◽  
pp. 304-319 ◽  
Author(s):  
Alexey Miroshnikov ◽  
Zheng Wei ◽  
Erin Marie Conlon
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Posterior Distributions ◽  
Non Gaussian

scholarly journals Rates of contraction of posterior distributions based on Gaussian process priors

2008 ◽  
Vol 36 (3) ◽  
pp. 1435-1463 ◽  
Author(s):  
A. W. van der Vaart ◽  
J. H. van Zanten
Keyword(s):  
Gaussian Process ◽  
Posterior Distributions

scholarly journals PAC-Bayes Bounds on Variational Tempered Posteriors for Markov Models

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 313
Author(s):  
Imon Banerjee ◽  
Vinayak A. Rao ◽  
Harsha Honnappa
Keyword(s):  
Markov Model ◽  
Markov Models ◽  
Model Misspecification ◽  
Dependence Structure ◽  
Posterior Distributions ◽  
Ergodic Properties ◽  
Variational Approximations ◽  
Popular View ◽  
Probably Approximately Correct ◽  
Risk Bounds

Datasets displaying temporal dependencies abound in science and engineering applications, with Markov models representing a simplified and popular view of the temporal dependence structure. In this paper, we consider Bayesian settings that place prior distributions over the parameters of the transition kernel of a Markov model, and seek to characterize the resulting, typically intractable, posterior distributions. We present a Probably Approximately Correct (PAC)-Bayesian analysis of variational Bayes (VB) approximations to tempered Bayesian posterior distributions, bounding the model risk of the VB approximations. Tempered posteriors are known to be robust to model misspecification, and their variational approximations do not suffer the usual problems of over confident approximations. Our results tie the risk bounds to the mixing and ergodic properties of the Markov data generating model. We illustrate the PAC-Bayes bounds through a number of example Markov models, and also consider the situation where the Markov model is misspecified.

The bootstrap and Bayesian bootstrap method in assessing bioequivalence

2009 ◽  
Vol 41 (5) ◽  
pp. 2246-2249 ◽  
Author(s):  
Wan Jianping ◽  
Zhang Kongsheng ◽  
Chen Hui
Keyword(s):  
Bootstrap Method ◽  
Bayesian Bootstrap

scholarly journals Bayesian Metric Multidimensional Scaling

2013 ◽  
Vol 21 (1) ◽  
pp. 125-140 ◽  
Author(s):  
Ryan Bakker ◽  
Keith T. Poole
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Bayesian Methods ◽  
Optimal Solution ◽  
Full Rank ◽  
Mcmc Methods ◽  
Ratio Scale ◽  
Posterior Distributions ◽  
Point Estimates ◽  
Inflection Points

In this article, we show how to apply Bayesian methods to noisy ratio scale distances for both the classical similarities problem as well as the unfolding problem. Bayesian methods produce essentially the same point estimates as the classical methods, but are superior in that they provide more accurate measures of uncertainty in the data. Identification is nontrivial for this class of problems because a configuration of points that reproduces the distances is identified only up to a choice of origin, angles of rotation, and sign flips on the dimensions. We prove that fixing the origin and rotation is sufficient to identify a configuration in the sense that the corresponding maxima/minima are inflection points with full-rank Hessians. However, an unavoidable result is multiple posterior distributions that are mirror images of one another. This poses a problem for Markov chain Monte Carlo (MCMC) methods. The approach we take is to find the optimal solution using standard optimizers. The configuration of points from the optimizers is then used to isolate a single Bayesian posterior that can then be easily analyzed with standard MCMC methods.

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