Bayesian Inference Under Partial Prior Information

AbstractWe present a refined moving group membership diagnostics scheme based on Bayesian inference. Compared to the BANYAN II method, we improved the calculation by updating bona fide members of a moving group, field star treatment, and uniform spatial distribution of moving group members. Here, we present the detailed description of our method and the new results for Bayesian membership calculation. Comparison of our method with BANYAN II shows probability differences up to ~90%. We conclude that more cautious consideration is needed in moving group membership based on Bayesian inference.

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BAYESIAN INFERENCE, PRIOR INFORMATION ON VOLATILITY, AND OPTION PRICING: A MAXIMUM ENTROPY APPROACH

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024905002755 ◽

2005 ◽

Vol 08 (01) ◽

pp. 1-12 ◽

Cited By ~ 7

Author(s):

FRANCISCO VENEGAS-MARTÍNEZ

Keyword(s):

Bayesian Inference ◽

Option Pricing ◽

Maximum Entropy ◽

Bayesian Model ◽

Prior Information ◽

Bessel Functions ◽

Derivative Securities ◽

Expected Values ◽

Pricing Derivative Securities ◽

Approximate Formulas

This paper develops a Bayesian model for pricing derivative securities with prior information on volatility. Prior information is given in terms of expected values of levels and rates of precision: the inverse of variance. We provide several approximate formulas, for valuing European call options, on the basis of asymptotic and polynomial approximations of Bessel functions.

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A Bayesian Hyperparameter Inference for Radon-Transformed Image Reconstruction

International Journal of Biomedical Imaging ◽

10.1155/2011/870252 ◽

2011 ◽

Vol 2011 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Hayaru Shouno ◽

Madomi Yamasaki ◽

Masato Okada

Keyword(s):

Bayesian Inference ◽

Image Reconstruction ◽

Prior Information ◽

Additive White Gaussian Noise ◽

Estimation Accuracy ◽

Reconstruction Method ◽

Model Framework ◽

Poissonian Noise ◽

Observation Noise

We develop a hyperparameter inference method for image reconstruction from Radon transform which often appears in the computed tomography, in the manner of Bayesian inference. Hyperparameters are often introduced in Bayesian inference to control the strength ratio between prior information and the fidelity to the observation. Since the quality of the reconstructed image is controlled by the estimation accuracy of these hyperparameters, we apply Bayesian inference into the filtered back-projection (FBP) reconstruction method with hyperparameters inference and demonstrate that the estimated hyperparameters can adapt to the noise level in the observation automatically. In the computer simulation, at first, we show that our algorithm works well in the model framework environment, that is, observation noise is an additive white Gaussian noise case. Then, we also show that our algorithm works well in the more realistic environment, that is, observation noise is Poissonian noise case. After that, we demonstrate an application for the real chest CT image reconstruction under the Gaussian and Poissonian observation noises.

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Bayesian Inference in Auditing With Partial Prior Information Using Maximum Entropy Priors

Entropy ◽

10.3390/e20120919 ◽

2018 ◽

Vol 20 (12) ◽

pp. 919

Author(s):

María Martel-Escobar ◽

Francisco-José Vázquez-Polo ◽

Agustín Hernández-Bastida

Keyword(s):

Bayesian Inference ◽

Bayesian Analysis ◽

Maximum Entropy ◽

Prior Information ◽

Likelihood Function ◽

Bayes Theorem ◽

Main Interest ◽

Book Value ◽

Numerical Examples ◽

Modified Likelihood

Problems in statistical auditing are usually one–sided. In fact, the main interest for auditors is to determine the quantiles of the total amount of error, and then to compare these quantiles with a given materiality fixed by the auditor, so that the accounting statement can be accepted or rejected. Dollar unit sampling (DUS) is a useful procedure to collect sample information, whereby items are chosen with a probability proportional to book amounts and in which the relevant error amount distribution is the distribution of the taints weighted by the book value. The likelihood induced by DUS refers to a 201–variate parameter p but the prior information is in a subparameter θ linear function of p , representing the total amount of error. This means that partial prior information must be processed. In this paper, two main proposals are made: (1) to modify the likelihood, to make it compatible with prior information and thus obtain a Bayesian analysis for hypotheses to be tested; (2) to use a maximum entropy prior to incorporate limited auditor information. To achieve these goals, we obtain a modified likelihood function inspired by the induced likelihood described by Zehna (1966) and then adapt the Bayes’ theorem to this likelihood in order to derive a posterior distribution for θ . This approach shows that the DUS methodology can be justified as a natural method of processing partial prior information in auditing and that a Bayesian analysis can be performed even when prior information is only available for a subparameter of the model. Finally, some numerical examples are presented.

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Bayesian inference of private social network links using prior information and propagated data

Journal of Parallel and Distributed Computing ◽

10.1016/j.jpdc.2018.11.003 ◽

2019 ◽

Vol 125 ◽

pp. 72-80

Author(s):

Amirreza SeyedHassani ◽

Mohammad Sayad Haghighi ◽

Ahmad Khonsari

Keyword(s):

Social Network ◽

Bayesian Inference ◽

Prior Information ◽

Network Links

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Two case studies detailing Bayesian parameter inference for dynamic energy budget models

10.1101/259705 ◽

2018 ◽

Author(s):

Philipp H. Boersch-Supan ◽

Leah R. Johnson

Keyword(s):

Bayesian Inference ◽

Case Studies ◽

Energy Budget ◽

Open Source Software ◽

Prior Information ◽

Model Parameters ◽

Parameter Inference ◽

Dynamic Energy Budget ◽

Full Life Cycle ◽

Open Source Software Package

AbstractMechanistic representations of individual life-history trajectories are powerful tools for the prediction of organismal growth, reproduction and survival under novel environmental conditions. Dynamic energy budget (DEB) theory provides compact models to describe the acquisition and allocation of energy by organisms over their full life cycle. However, estimating DEB model parameters, and their associated uncertainties and covariances, is not trivial. Bayesian inference provides a coherent way to estimate parameter uncertainty, and propagate it through the model, while also making use of prior information to constrain the parameter space. We outline a Bayesian inference approach for energy budget models and provide two case studies – based on a simplified DEBkiss model, and the standard DEB model – detailing the implementation of such inference procedures using the open-source software package deBInfer. We demonstrate how DEB and DEBkiss parameters can be estimated in a Bayesian framework, but our results also highlight the difficulty of identifying DEB model parameters which serves as a reminder that fitting these models requires statistical caution.

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Towards modelling active sound localisation based on Bayesian inference in a static environment

Acta Acustica ◽

10.1051/aacus/2021039 ◽

2021 ◽

Vol 5 ◽

pp. 45

Author(s):

Glen McLachlan ◽

Piotr Majdak ◽

Jonas Reijniers ◽

Herbert Peremans

Keyword(s):

Bayesian Inference ◽

Statistical Inference ◽

Prior Information ◽

Multisensory Perception ◽

Active Listening ◽

Interesting Aspect ◽

Sound Localisation ◽

Recent Developments ◽

Staple Technique ◽

Self Motion

Over the decades, Bayesian statistical inference has become a staple technique for modelling human multisensory perception. Many studies have successfully shown how sensory and prior information can be combined to optimally interpret our environment. Because of the multiple sound localisation cues available in the binaural signal, sound localisation models based on Bayesian inference are a promising way of explaining behavioural human data. An interesting aspect is the consideration of dynamic localisation cues obtained through self-motion. Here we provide a review of the recent developments in modelling dynamic sound localisation with a particular focus on Bayesian inference. Further, we describe a theoretical Bayesian framework capable to model dynamic and active listening situations in humans in a static auditory environment. In order to demonstrate its potential in future implementations, we provide results from two examples of simplified versions of that framework.

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Using demographics toward efficient data classification in citizen science: a Bayesian approach

PeerJ Computer Science ◽

10.7717/peerj-cs.239 ◽

2019 ◽

Vol 5 ◽

pp. e239

Author(s):

Pietro De Lellis ◽

Shinnosuke Nakayama ◽

Maurizio Porfiri

Keyword(s):

Bayesian Inference ◽

Citizen Science ◽

Bayesian Approach ◽

Prior Information ◽

Data Accuracy ◽

Majority Voting ◽

Accurate Information ◽

Training Set ◽

Level Of Education ◽

Efficient Data

Public participation in scientific activities, often called citizen science, offers a possibility to collect and analyze an unprecedentedly large amount of data. However, diversity of volunteers poses a challenge to obtain accurate information when these data are aggregated. To overcome this problem, we propose a classification algorithm using Bayesian inference that harnesses diversity of volunteers to improve data accuracy. In the algorithm, each volunteer is grouped into a distinct class based on a survey regarding either their level of education or motivation to citizen science. We obtained the behavior of each class through a training set, which was then used as a prior information to estimate performance of new volunteers. By applying this approach to an existing citizen science dataset to classify images into categories, we demonstrate improvement in data accuracy, compared to the traditional majority voting. Our algorithm offers a simple, yet powerful, way to improve data accuracy under limited effort of volunteers by predicting the behavior of a class of individuals, rather than attempting at a granular description of each of them.

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Bayesian Inference for Acoustic Direction of Arrival Analysis Using Spherical Harmonics

Entropy ◽

10.3390/e21060579 ◽

2019 ◽

Vol 21 (6) ◽

pp. 579 ◽

Cited By ~ 4

Author(s):

Ning Xiang ◽

Christopher Landschoot

Keyword(s):

Bayesian Inference ◽

Spherical Harmonics ◽

Prior Information ◽

Microphone Array ◽

Sensor Arrays ◽

Analytical Models ◽

Sound Sources ◽

Directional Information ◽

Bayesian Formulation ◽

Acoustic Environments

This work applies two levels of inference within a Bayesian framework to accomplish estimation of the directions of arrivals (DoAs) of sound sources. The sensing modality is a spherical microphone array based on spherical harmonics beamforming. When estimating the DoA, the acoustic signals may potentially contain one or multiple simultaneous sources. Using two levels of Bayesian inference, this work begins by estimating the correct number of sources via the higher level of inference, Bayesian model selection. It is followed by estimating the directional information of each source via the lower level of inference, Bayesian parameter estimation. This work formulates signal models using spherical harmonic beamforming that encodes the prior information on the sensor arrays in the form of analytical models with an unknown number of sound sources, and their locations. Available information on differences between the model and the sound signals as well as prior information on directions of arrivals are incorporated based on the principle of the maximum entropy. Two and three simultaneous sound sources have been experimentally tested without prior information on the number of sources. Bayesian inference provides unambiguous estimation on correct numbers of sources followed by the DoA estimations for each individual sound sources. This paper presents the Bayesian formulation, and analysis results to demonstrate the potential usefulness of the model-based Bayesian inference for complex acoustic environments with potentially multiple simultaneous sources.

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Using Prior Information in Bayesian Inference—with Application to Fault Diagnosis

10.1063/1.2821293 ◽

2007 ◽

Author(s):

Anna Pernestål ◽

Mattias Nyberg ◽

Kevin H. Knuth ◽

Ariel Caticha ◽

Julian L. Center ◽

...

Keyword(s):

Bayesian Inference ◽

Fault Diagnosis ◽

Prior Information

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