scholarly journals Application of likelihood ratio and posterior probability density in sex estimation from level two fingerprint features among Hausa ethnic group

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Lawan Hassan Adamu ◽  
Magaji Garba Taura
Keyword(s):  
Probability Density ◽  
Ethnic Group ◽  
Likelihood Ratio ◽  
Posterior Probability ◽  
Sex Estimation ◽  
Posterior Probability Density

A Bayesian Framework of Computing and Updating Wavelet Parameter Distributions for Identifying Early Bearing Faults

2014 ◽  
Author(s):  
Peter W. Tse ◽  
Dong Wang
Keyword(s):  
Probability Density Function ◽  
Wavelet Analysis ◽  
Probability Density ◽  
Density Function ◽  
Posterior Probability ◽  
Fault Features ◽  
Bearing Failures ◽  
Posterior Probability Density ◽  
Posterior Probability Density Function ◽  
Parameter Distributions

Rolling element bearings are widely used in machines to support rotation shafts. Bearing failures may result in machine breakdown. In order to prevent bearing failures, early bearing faults are required to be identified. Wavelet analysis has proven to be an effective method for extracting early bearing fault features. Proper selection of wavelet parameters is crucial to wavelet analysis. In this paper, a Bayesian framework is proposed to compute and update wavelet parameter distributions. First, a smoothness index is used as the objective function because it has specific upper and lower bounds. Second, a general sequential Monte Carlo method is introduced to analytically derive the joint posterior probability density function of wavelet parameters. Last, approximately optimal wavelet parameters are inferred from the joint posterior probability density function. Simulated and real case studies are investigated to demonstrate that the proposed framework is effective in extracting early bearing fault features.

scholarly journals Implications for new physics in $$b\rightarrow s \mu \mu $$ transitions after recent measurements by Belle and LHCb

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Kamila Kowalska ◽  
Dinesh Kumar ◽  
Enrico Maria Sessolo
Keyword(s):  
Scalar Field ◽  
Probability Density ◽  
Posterior Probability ◽  
Bayes Factor ◽  
Nuisance Parameter ◽  
High Energy ◽  
New Physics ◽  
Data Set ◽  
Posterior Probability Density ◽  
Scalar Leptoquarks

Abstract We present a Bayesian analysis of the implications for new physics in semileptonic $$b\rightarrow s$$b→s transitions after including new measurements of $$R_K$$RK at LHCb and new determinations of $$R_{K^*}$$RK∗ and $$R_{K^{*+}}$$RK∗+ at Belle. We perform global fits with 1, 2, 4, and 8 input Wilson coefficients, plus one CKM nuisance parameter to take into account uncertainties that are not factorizable. We infer the 68% and 95.4% credibility regions of the marginalized posterior probability density for all scenarios and perform comparisons of models in pairs by calculating the Bayes factor given a common data set. We then proceed to analyzing a few well-known BSM models that can provide a high energy framework for the EFT analysis. These include the exchange of a heavy $$Z^{'}$$Z′ boson in models with heavy vector-like fermions and a scalar field, and a model with scalar leptoquarks. We provide predictions for the BSM couplings and expected mass values.

Structural damage detection based on variational Bayesian inference and delayed rejection adaptive Metropolis algorithm

2020 ◽  
pp. 147592172092125
Author(s):  
Xiaoyou Wang ◽  
Rongrong Hou ◽  
Yong Xia ◽  
Xiaoqing Zhou
Keyword(s):  
Bayesian Inference ◽  
Damage Detection ◽  
Probability Density ◽  
Structural Damage ◽  
Posterior Probability ◽  
Damage Index ◽  
Structural Damage Detection ◽  
Variational Bayesian ◽  
Variational Bayesian Inference ◽  
Posterior Probability Density

Existing studies on sparse Bayesian learning for structural damage detection usually assume that the posterior probability density functions follow standard distributions which facilitate to circumvent the intractable integration problem of the evidence by means of numerical sampling or analytical derivation. Moreover, the uncertainties of each mode are usually quantified as a common parameter to simplify the calculation. These assumptions may not be realistic in practice. This study proposes a sparse Bayesian method for structural damage detection suitable for standard and nonstandard probability distributions. The uncertainty corresponding to each mode is assumed as different. Variational Bayesian inference is developed and the posterior probability density functions of each unknown are individually derived. The parameters are found to follow the gamma distribution, whereas the distribution of the damage index cannot be directly obtained because of the nonlinear relationship in its posterior probability density function. The delayed rejection adaptive Metropolis algorithm is then adopted to generate numerical samples of the damage index. The coupled damage index and parameters in the variational Bayesian inference are successively calculated via an iterative process. A laboratory-tested frame is utilised to verify the effectiveness of the proposed method. The results indicate that the sparse damage can be accurately detected. The proposed method has the advantage of high accuracy and broad applicability.

scholarly journals Markov Chain Monte Carlo in a Dynamical System of Information Theoretic Particles

2021 ◽  
Author(s):  
Tokunbo Ogunfunmi ◽  
Manas Deb
Keyword(s):  
Dynamical System ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Potential Energy ◽  
Probability Density ◽  
Posterior Probability ◽  
Information Theoretic ◽  
Other Information ◽  
Posterior Probability Density

In Bayesian learning, the posterior probability density of a model parameter is estimated from the likelihood function and the prior probability of the parameter. The posterior probability density estimate is refined as more evidence becomes available. However, any non-trivial Bayesian model requires the computation of an intractable integral to obtain the probability density function (PDF) of the evidence. Markov Chain Monte Carlo (MCMC) is a well-known algorithm that solves this problem by directly generating the samples of the posterior distribution without computing this intractable integral. We present a novel perspective of the MCMC algorithm which views the samples of a probability distribution as a dynamical system of Information Theoretic particles in an Information Theoretic field. As our algorithm probes this field with a test particle, it is subjected to Information Forces from other Information Theoretic particles in this field. We use Information Theoretic Learning (ITL) techniques based on Rényi’s α-Entropy function to derive an equation for the gradient of the Information Potential energy of the dynamical system of Information Theoretic particles. Using this equation, we compute the Hamiltonian of the dynamical system from the Information Potential energy and the kinetic energy. The Hamiltonian is used to generate the Markovian state trajectories of the system.

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