scholarly journals On Default Priors for Robust Bayesian Estimation with Divergences

Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 29
Author(s):  
Tomoyuki Nakagawa ◽  
Shintaro Hashimoto
Keyword(s):  
Bayesian Estimation ◽  
Bayesian Methods ◽  
Posterior Distribution ◽  
Bayesian Framework ◽  
Moment Matching ◽  
Simulation Studies ◽  
Posterior Distributions ◽  
Prior Distributions ◽  
Matching Priors ◽  
Selection Of

This paper presents objective priors for robust Bayesian estimation against outliers based on divergences. The minimum γ-divergence estimator is well-known to work well in estimation against heavy contamination. The robust Bayesian methods by using quasi-posterior distributions based on divergences have been also proposed in recent years. In the objective Bayesian framework, the selection of default prior distributions under such quasi-posterior distributions is an important problem. In this study, we provide some properties of reference and moment matching priors under the quasi-posterior distribution based on the γ-divergence. In particular, we show that the proposed priors are approximately robust under the condition on the contamination distribution without assuming any conditions on the contamination ratio. Some simulation studies are also presented.

scholarly journals Bayesian Estimation of Explained Variance in ANOVA Designs

2019 ◽  
Author(s):  
Maarten Marsman ◽  
Lourens Waldorp ◽  
Fabian Dablander ◽  
Eric-Jan Wagenmakers
Keyword(s):  
Bayesian Estimation ◽  
Bayesian Methods ◽  
Posterior Distribution ◽  
Partial Correlation ◽  
Worked Examples ◽  
Multiple Correlation ◽  
Size Measure ◽  
Explained Variance ◽  
Correlation Coeffi

We propose to use the squared multiple correlation coeffi?cient as an eff?ect size measure for experimental ANOVA designs, and to use Bayesian methods to estimate its posterior distribution. We provide the expressions for the squared multiple, semipartial, and partial correlation coe?fficients corresponding to four commonly used ANOVA designs and illustrate our contribution with two worked examples.

Bayesian statistics

2010 ◽  
pp. 477-497
Author(s):  
Janet L. Peacock ◽  
Philip J. Peacock
Keyword(s):  
Bayesian Statistics ◽  
Bayesian Approach ◽  
Bayesian Methods ◽  
Posterior Distributions ◽  
Bayesian Analyses ◽  
Prior Distributions ◽  
Unknown Quantity ◽  
Frequentist Approach ◽  
Pros And Cons ◽  
The Bayesian Approach

Bayesian statistics 478 How Bayesian methods work 480 Prior distributions 482 Likelihood; posterior distributions 484 Summarizing and presenting results 486 Using Bayesian analyses in medicine 488 Software for Bayesian statistics 492 Reading Bayesian analyses in papers 494 Bayesian methods: a summary 496 In this chapter we describe the Bayesian approach to statistical analysis in contrast to the frequentist approach. We describe how Bayesian methods work including a description of prior and posterior distributions. We outline the role and choice of prior distributions and how they are combined with the data collected to provide an updated estimate of the unknown quantity being studied. We include examples of the use of Bayesian methods in medicine, and discuss the pros and cons of the Bayesian approach compared with the frequentist approach Finally, we give guidance on how to read and interpret Bayesian analyses in the medical literature....

scholarly journals Learning to Select Knowledge for Response Generation in Dialog Systems

2019 ◽  
Author(s):  
Rongzhong Lian ◽  
Min Xie ◽  
Fan Wang ◽  
Jinhua Peng ◽  
Hua Wu
Keyword(s):  
Posterior Distribution ◽  
Neural Model ◽  
Dialogue Systems ◽  
Posterior Distributions ◽  
Neural Models ◽  
Inference Process ◽  
Dialog Systems ◽  
Human Evaluation ◽  
End To End ◽  
Selection Of

End-to-end neural models for intelligent dialogue systems suffer from the problem of generating uninformative responses. Various methods were proposed to generate more informative responses by leveraging external knowledge. However,  few previous work has focused on selecting appropriate knowledge in the learning process. The inappropriate selection of knowledge could prohibit the model from learning to make full use of the knowledge. Motivated by this, we propose an end-to-end neural model which employs a novel knowledge selection mechanism where both prior and posterior distributions over knowledge are used to facilitate knowledge selection. Specifically, a posterior distribution over knowledge is inferred from both utterances and responses, and it ensures the appropriate selection of knowledge during the training process. Meanwhile, a prior distribution, which is inferred from utterances only,  is used to approximate the posterior distribution so that appropriate knowledge can be selected even without responses during the inference process. Compared with the previous work, our model can better incorporate appropriate knowledge in response generation. Experiments on both automatic and human evaluation verify the superiority of our model over previous baselines.

Numerical simulation studies of Cs3Bi2I9 perovskite solar device with optimal selection of electron and hole transport layers

Optik ◽  
2021 ◽  
Vol 231 ◽  
pp. 166417 ◽  
Author(s):  
Md Tohidul Islam ◽  
Md Rafsun Jani ◽  
Kazi Md Shorowordi ◽  
Zameer Hoque ◽  
Ali Mucteba Gokcek ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Hole Transport ◽  
Optimal Selection ◽  
Simulation Studies ◽  
Hole Transport Layers ◽  
Selection Of

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 Selection of X-chromosome Inactivation Model

2017 ◽  
Vol 16 ◽  
pp. 117693511774727 ◽  
Author(s):  
Jian Wang ◽  
Rajesh Talluri ◽  
Sanjay Shete
Keyword(s):  
X Chromosome ◽  
X Chromosome Inactivation ◽  
Association Test ◽  
Chromosome Inactivation ◽  
Simulation Studies ◽  
Nucleotide Polymorphisms ◽  
Unified Approach ◽  
Cancer Genetic ◽  
Single Nucleotide ◽  
Selection Of

To address the complexity of the X-chromosome inactivation (XCI) process, we previously developed a unified approach for the association test for X-chromosomal single-nucleotide polymorphisms (SNPs) and the disease of interest, accounting for different biological possibilities of XCI: random, skewed, and escaping XCI. In the original study, we focused on the SNP-disease association test but did not provide knowledge regarding the underlying XCI models. One can use the highest likelihood ratio (LLR) to select XCI models (max-LLR approach). However, that approach does not formally compare the LLRs corresponding to different XCI models to assess whether the models are distinguishable. Therefore, we propose an LLR comparison procedure (comp-LLR approach), inspired by the Cox test, to formally compare the LLRs of different XCI models to select the most likely XCI model that describes the underlying XCI process. We conduct simulation studies to investigate the max-LLR and comp-LLR approaches. The simulation results show that compared with the max-LLR, the comp-LLR approach has higher probability of identifying the correct underlying XCI model for the scenarios when the underlying XCI process is random XCI, escaping XCI, or skewed XCI to the deleterious allele. We applied both approaches to a head and neck cancer genetic study to investigate the underlying XCI processes for the X-chromosomal genetic variants.

scholarly journals A hierarchical Bayesian framework for force field selection in molecular dynamics simulations

2016 ◽  
Vol 374 (2060) ◽  
pp. 20150032 ◽  
Author(s):  
S. Wu ◽  
P. Angelikopoulos ◽  
C. Papadimitriou ◽  
R. Moser ◽  
P. Koumoutsakos
Keyword(s):  
Experimental Data ◽  
Molecular Dynamics ◽  
Force Field ◽  
Computational Cost ◽  
Md Simulations ◽  
Bayesian Framework ◽  
Underlying Structure ◽  
Hierarchical Bayesian ◽  
Wide Range ◽  
Selection Of

We present a hierarchical Bayesian framework for the selection of force fields in molecular dynamics (MD) simulations. The framework associates the variability of the optimal parameters of the MD potentials under different environmental conditions with the corresponding variability in experimental data. The high computational cost associated with the hierarchical Bayesian framework is reduced by orders of magnitude through a parallelized Transitional Markov Chain Monte Carlo method combined with the Laplace Asymptotic Approximation. The suitability of the hierarchical approach is demonstrated by performing MD simulations with prescribed parameters to obtain data for transport coefficients under different conditions, which are then used to infer and evaluate the parameters of the MD model. We demonstrate the selection of MD models based on experimental data and verify that the hierarchical model can accurately quantify the uncertainty across experiments; improve the posterior probability density function estimation of the parameters, thus, improve predictions on future experiments; identify the most plausible force field to describe the underlying structure of a given dataset. The framework and associated software are applicable to a wide range of nanoscale simulations associated with experimental data with a hierarchical structure.

Metropolis-Hastings Algorithms for DSGE Models

2015 ◽  
Author(s):  
Edward P. Herbst ◽  
Frank Schorfheide
Keyword(s):  
Random Walk ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Large Scale ◽  
Likelihood Function ◽  
Dsge Models ◽  
Posterior Distributions ◽  
Dsge Model ◽  
Alternative Proposal ◽  
Posterior Moments

This chapter talks about the most widely used method to generate draws from posterior distributions of a DSGE model: the random walk MH (RWMH) algorithm. The DSGE model likelihood function in combination with the prior distribution leads to a posterior distribution that has a fairly regular elliptical shape. In turn, the draws from a simple RWMH algorithm can be used to obtain an accurate numerical approximation of posterior moments. However, in many other applications, particularly those involving medium- and large-scale DSGE models, the posterior distributions could be very non-elliptical. Irregularly shaped posterior distributions are often caused by identification problems or misspecification. In lieu of the difficulties caused by irregularly shaped posterior surfaces, the chapter reviews various alternative MH samplers, which use alternative proposal distributions.

scholarly journals Robust Bayesian Regression with Synthetic Posterior Distributions

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 661 ◽  
Author(s):  
Shintaro Hashimoto ◽  
Shonosuke Sugasawa
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Bayesian Variable Selection ◽  
Bayesian Regression ◽  
Simulation Studies ◽  
Posterior Distributions ◽  
Linear Regression Models ◽  
Computation Algorithm ◽  
Shrinkage Priors ◽  
Variable Selection And Estimation

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not necessarily straightforward. We here propose a Bayesian approach to robust inference on linear regression models using synthetic posterior distributions based on γ-divergence, which enables us to naturally assess the uncertainty of the estimation through the posterior distribution. We also consider the use of shrinkage priors for the regression coefficients to carry out robust Bayesian variable selection and estimation simultaneously. We develop an efficient posterior computation algorithm by adopting the Bayesian bootstrap within Gibbs sampling. The performance of the proposed method is illustrated through simulation studies and applications to famous datasets.

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