scholarly journals Remarks on consistency of posterior distributions

2008 ◽  
pp. 170-186 ◽  
Author(s):  
Taeryon Choi ◽  
R. V. Ramamoorthi
Keyword(s):  
Posterior Distributions

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.

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.

scholarly journals BAYESIAN INFERENCE FOR THE TANGENT PORTFOLIO

2018 ◽  
Vol 21 (08) ◽  
pp. 1850054 ◽  
Author(s):  
DAVID BAUDER ◽  
TARAS BODNAR ◽  
STEPAN MAZUR ◽  
YAREMA OKHRIN
Keyword(s):  
Bayesian Inference ◽  
Point Of View ◽  
Posterior Distributions ◽  
Conditional Distributions ◽  
Linear Combinations ◽  
Conjugate Priors ◽  
Mean And Variance ◽  
The Mean ◽  
Stochastic Representations ◽  
Mean Vector

In this paper, we consider the estimation of the weights of tangent portfolios from the Bayesian point of view assuming normal conditional distributions of the logarithmic returns. For diffuse and conjugate priors for the mean vector and the covariance matrix, we derive stochastic representations for the posterior distributions of the weights of tangent portfolio and their linear combinations. Separately, we provide the mean and variance of the posterior distributions, which are of key importance for portfolio selection. The analytic results are evaluated within a simulation study, where the precision of coverage intervals is assessed.

scholarly journals Accurate quantification of uncertainty in epidemic parameter estimates and predictions using stochastic compartmental models

2018 ◽  
Vol 28 (12) ◽  
pp. 3591-3608 ◽  
Author(s):  
Christoph Zimmer ◽  
Sequoia I Leuba ◽  
Ted Cohen ◽  
Reza Yaesoubi
Keyword(s):  
Stochastic Systems ◽  
Dynamic Models ◽  
Calibration Method ◽  
Compartmental Models ◽  
Prediction Intervals ◽  
Multiple Shooting ◽  
Parameter Estimates ◽  
Posterior Distributions ◽  
Calibration Methods ◽  
Google Search

Stochastic transmission dynamic models are needed to quantify the uncertainty in estimates and predictions during outbreaks of infectious diseases. We previously developed a calibration method for stochastic epidemic compartmental models, called Multiple Shooting for Stochastic Systems (MSS), and demonstrated its competitive performance against a number of existing state-of-the-art calibration methods. The existing MSS method, however, lacks a mechanism against filter degeneracy, a phenomenon that results in parameter posterior distributions that are weighted heavily around a single value. As such, when filter degeneracy occurs, the posterior distributions of parameter estimates will not yield reliable credible or prediction intervals for parameter estimates and predictions. In this work, we extend the MSS method by evaluating and incorporating two resampling techniques to detect and resolve filter degeneracy. Using simulation experiments, we demonstrate that an extended MSS method produces credible and prediction intervals with desired coverage in estimating key epidemic parameters (e.g. mean duration of infectiousness and R0) and short- and long-term predictions (e.g. one and three-week forecasts, timing and number of cases at the epidemic peak, and final epidemic size). Applying the extended MSS approach to a humidity-based stochastic compartmental influenza model, we were able to accurately predict influenza-like illness activity reported by U.S. Centers for Disease Control and Prevention from 10 regions as well as city-level influenza activity using real-time, city-specific Google search query data from 119 U.S. cities between 2003 and 2014.

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