Posterior probability

About: Posterior probability is a research topic. Over the lifetime, 13731 publications have been published within this topic receiving 475016 citations. The topic is also known as: posterior probability distribution & posterior distribution.

Bayesian Receiver Autonomous Integrity Monitoring Technique

Abstract: An integrity monitoring/failure detection and identification approach for GNSS positioning that is based on Bayesian model comparison theory is introduced. In the new method the user defines models for no-failure/failure cases and the most plausible model is chosen and used to estimate position. If a channel is contaminated and the corresponding model is chosen then the effect of this channel on the position estimate is attenuated. The posterior probability odds of two models can be used as a measure of how well the models can be distinguished from each other. In the proposed RAIMtechnique if none of the model plausibilities stands out from the others, the user is made aware of the situation as the case might be that the effect of a good channel is attenuated and the contaminated one is modeled as a good one. The performances of traditional RAIM/FDE and the new method are compared via simulations. Results of a test with real GPS data are also presented.

High posterior density ellipsoids of quantum states

Abstract: Regions of quantum states generalize the classical notion of error bars. High posterior density (HPD) credible regions are the most powerful of region estimators. However, they are intractably hard to construct in general. This paper reports on a numerical approximation to HPD regions for the purpose of testing a much more computationally and conceptually convenient class of regions: posterior covariance ellipsoids (PCEs). The PCEs are defined via the covariance matrix of the posterior probability distribution of states. Here it is shown that PCEs are near optimal for the example of Pauli measurements on multiple qubits. Moreover, the algorithm is capable of producing accurate PCE regions even when there is uncertainty in the model.

Multiple imputation with compatibility for high-dimensional data.

Abstract: Multiple Imputation (MI) is always challenging in high dimensional settings. The imputation model with some selected number of predictors can be incompatible with the analysis model leading to inconsistent and biased estimates. Although compatibility in such cases may not be achieved, but one can obtain consistent and unbiased estimates using a semi-compatible imputation model. We propose to relax the lasso penalty for selecting a large set of variables (at most n). The substantive model that also uses some formal variable selection procedure in high-dimensional structures is then expected to be nested in this imputation model. The resulting imputation model will be semi-compatible with high probability. The likelihood estimates can be unstable and can face the convergence issues as the number of variables becomes nearly as large as the sample size. To address these issues, we further propose to use a ridge penalty for obtaining the posterior distribution of the parameters based on the observed data. The proposed technique is compared with the standard MI software and MI techniques available for high-dimensional data in simulation studies and a real life dataset. Our results exhibit the superiority of the proposed approach to the existing MI approaches while addressing the compatibility issue.

Bayesian model selection in statistical construction of justification

Abstract: Argumentation mining involves identification of an attack relation between natural language sentences. Bayesian inference characterizing argument-based reasoning addresses this issue by calculating the posterior distribution over attack relations given acceptability statuses of arguments. This paper discusses the use of Bayesian model selection where graph-theoretic properties impose restrictions on the graphic structure of attack relations.

Selecting Data Adaptive Learner from Multiple Deep Learners using Bayesian Networks.

Abstract: A method to predict time-series using multiple deep learners and a Bayesian network is proposed. In this study, the input explanatory variables are Bayesian network nodes that are associated with learners. Training data are divided using K-means clustering, and multiple deep learners are trained depending on the cluster. A Bayesian network is used to determine which deep learner is in charge of predicting a time-series. We determine a threshold value and select learners with a posterior probability equal to or greater than the threshold value, which could facilitate more robust prediction. The proposed method is applied to financial time-series data, and the predicted results for the Nikkei 225 index are demonstrated.