A Bayesian regression model for circular data based on the projected normal distribution

2011 ◽  
Vol 11 (3) ◽  
pp. 185-201 ◽  
Author(s):  
Gabriel Nuñez-Antonio ◽  
Eduardo Gutiérrez-Peña ◽  
Gabriel Escarela
Keyword(s):  
Regression Model ◽  
Normal Distribution ◽  
Bayesian Regression ◽  
Circular Data ◽  
Projected Normal Distribution

scholarly journals Modelling complex geological circular data with the projected normal distribution and mixtures of von Mises distributions

Solid Earth ◽  
2014 ◽  
Vol 5 (2) ◽  
pp. 631-639 ◽  
Author(s):  
R. M. Lark ◽  
D. Clifford ◽  
C. N. Waters
Keyword(s):  
Normal Distribution ◽  
Circular Data ◽  
Data Sets ◽  
Statistical Distributions ◽  
Data Set ◽  
Geological Interpretation ◽  
The Earth ◽  
Von Mises ◽  
Special Case ◽  
Projected Normal Distribution

Abstract. Circular data are commonly encountered in the earth sciences and statistical descriptions and inferences about such data are necessary in structural geology. In this paper we compare two statistical distributions appropriate for complex circular data sets: the mixture of von Mises and the projected normal distribution. We show how the number of components in a mixture of von Mises distribution may be chosen, and how one may choose between the projected normal distribution and the mixture of von Mises for a particular data set. We illustrate these methods with a few structural geological data, showing how the fitted models can complement geological interpretation and permit statistical inference. One of our data sets suggests a special case of the projected normal distribution which we discuss briefly.

scholarly journals The similarity about the probability distributions of variables in the Bayesian regression model and application

2021 ◽  
Vol 5 (1) ◽  
pp. 1325-1339
Author(s):  
Hoa Thanh Le ◽  
Uyen Hoang Pham ◽  
An Thị Đỗ Nguyễn ◽  
Bao The Pham
Keyword(s):  
Probability Distribution ◽  
Regression Model ◽  
Normal Distribution ◽  
Stock Price ◽  
Probability Distributions ◽  
Random Variable ◽  
Bayesian Regression ◽  
Independent Variables ◽  
Classical Statistics ◽  
The Mean

The linear regression model as well as the time series model is applied in many fields, in which the mean of the dependent variable is one function of the mean of the independent variables. However, to consider the regression model following in the Classical Statistics (the Frequent Statistics), it means that the parameters are the constants, in many situations, the regression model does not describe the fluctuation of both the dependent variable and the independent variables. Therefore, we need to modify the parameters following the random variable form, not the constant form, like as the regression in Bayesian Statistics. The other side, when the parameters considered as the random variables, computations in the regression model becomes very complex, because we need to compute the product of the probability distributions. So, we must evaluate about to vary of the variables' probability distributions not only the normal distribution, the Student distribution t, the Poisson distribution, the binomial distribution… In this paper, we estimated the dependent variable's probability distribution form through the simple Bayesian regression model in cases having many the probability distribution forms of the independent variable. In addition, we apply the results to real stock price data, proving that the most appropriate probability distribution with the data is a mixture of probability distributions, not a single normal distribution.

scholarly journals HAMdetector: A Bayesian regression model that integrates information to detect HLA-associated mutations

2021 ◽  
Author(s):  
Daniel Habermann ◽  
Hadi Karimzadeh ◽  
Andreas Walker ◽  
Yang Li ◽  
Rongge Yang ◽  
...  
Keyword(s):  
Regression Model ◽  
Immune Escape ◽  
Point Mutations ◽  
Human Leukocyte ◽  
Relevant Information ◽  
Quantitative Information ◽  
Host Population ◽  
Bayesian Regression ◽  
Mhc I ◽  
Hla Alleles

Motivation: A key process in anti-viral adaptive immunity is that the Human Leukocyte Antigen system (HLA) presents epitopes as Major Histocompatibility Complex I (MHC I) protein-peptide complexes on cell surfaces and in this way alerts CD8+ cytotoxic T-Lymphocytes (CTLs). This pathway exerts strong selection pressure on viruses, favoring viral mutants that escape recognition by the HLA/CTL system, e.g. by point mutations that decrease binding of viral peptides to MHC I. Naturally, such immune escape mutations often emerge in highly variable viruses, e.g. HIV or HBV, as HLA-associated mutations (HAMs), specific to the host HLA alleles and its MHC I proteins. The reliable identification of HAMs is not only important for understanding viral genomes and their evolution, but it also impacts the development of broadly effective anti-viral treatments and vaccines against variable viruses. By their very nature HAMs are amenable to detection by statistical methods in paired sequence / HLA data. However, HLA alleles are very polymorphic in the human host population which makes the available data relatively sparse and noisy. Under these circumstances, one way to optimize HAM detection is to integrate all relevant information in a coherent model. Bayesian inference offers a principled approach to achieve this. Results: We present a new regression model for the detection of HAMs. As we choose a Bayesian approach we can include the novel sparsity-inducing priors, and we obtain easily interpretable quantitative information on HAM candidates. The basic model can be extended to include prior information relevant to HAM detection, which we demonstrate by integrating predictions of epitope affinities to MHC I, predictions of epitope peptide processing, and computation of phylogenetic background. This integrative method improves performance in HAM detection considerably over state-of-the-art methods.

Anomaly Detection in Video Surveillance via Gaussian Process

2015 ◽  
Vol 29 (06) ◽  
pp. 1555011 ◽  
Author(s):  
Nannan Li ◽  
Xinyu Wu ◽  
Huiwen Guo ◽  
Dan Xu ◽  
Yongsheng Ou ◽  
...  
Keyword(s):  
Anomaly Detection ◽  
Regression Model ◽  
Gaussian Process ◽  
Video Surveillance ◽  
Gaussian Process Regression ◽  
Bayesian Regression ◽  
Current Frame ◽  
Motion Patterns ◽  
Online Clustering ◽  
Efficient Calculation

In this paper, we propose a new approach for anomaly detection in video surveillance. This approach is based on a nonparametric Bayesian regression model built upon Gaussian process priors. It establishes a set of basic vectors describing motion patterns from low-level features via online clustering, and then constructs a Gaussian process regression model to approximate the distribution of motion patterns in kernel space. We analyze different anomaly measure criterions derived from Gaussian process regression model and compare their performances. To reduce false detections caused by crowd occlusion, we utilize supplement information from previous frames to assist in anomaly detection for current frame. In addition, we address the problem of hyperparameter tuning and discuss the method of efficient calculation to reduce computation overhead. The approach is verified on published anomaly detection datasets and compared with other existing methods. The experiment results demonstrate that it can detect various anomalies efficiently and accurately.

scholarly journals A Bayesian zero-inflated negative binomial regression model for the integrative analysis of microbiome data

Biostatistics ◽  
2019 ◽  
Author(s):  
Shuang Jiang ◽  
Guanghua Xiao ◽  
Andrew Y Koh ◽  
Jiwoong Kim ◽  
Qiwei Li ◽  
...  
Keyword(s):  
Regression Model ◽  
Negative Binomial ◽  
Human Microbiome ◽  
Simulated Data ◽  
Negative Binomial Regression ◽  
Bayesian Regression ◽  
Negative Binomial Regression Model ◽  
Disease States ◽  
Binomial Regression ◽  
Microbiome Data

Summary Microbiome omics approaches can reveal intriguing relationships between the human microbiome and certain disease states. Along with identification of specific bacteria taxa associated with diseases, recent scientific advancements provide mounting evidence that metabolism, genetics, and environmental factors can all modulate these microbial effects. However, the current methods for integrating microbiome data and other covariates are severely lacking. Hence, we present an integrative Bayesian zero-inflated negative binomial regression model that can both distinguish differentially abundant taxa with distinct phenotypes and quantify covariate-taxa effects. Our model demonstrates good performance using simulated data. Furthermore, we successfully integrated microbiome taxonomies and metabolomics in two real microbiome datasets to provide biologically interpretable findings. In all, we proposed a novel integrative Bayesian regression model that features bacterial differential abundance analysis and microbiome-covariate effects quantifications, which makes it suitable for general microbiome studies.

The Odd Log-Logistic Geometric Normal Regression Model with Applications

2019 ◽  
Vol 11 (01n02) ◽  
pp. 1950003
Author(s):  
Fábio Prataviera ◽  
Gauss M. Cordeiro ◽  
Edwin M. M. Ortega ◽  
Adriano K. Suzuki
Keyword(s):  
Regression Model ◽  
Normal Distribution ◽  
Regression Models ◽  
Empirical Distribution ◽  
Real Data ◽  
Likelihood Method ◽  
Standard Normal Distribution ◽  
Model Parameters ◽  
Diagnostic Measures ◽  
Standard Normal

In several applications, the distribution of the data is frequently unimodal, asymmetric or bimodal. The regression models commonly used for applications to data with real support are the normal, skew normal, beta normal and gamma normal, among others. We define a new regression model based on the odd log-logistic geometric normal distribution for modeling asymmetric or bimodal data with support in [Formula: see text], which generalizes some known regression models including the widely known heteroscedastic linear regression. We adopt the maximum likelihood method for estimating the model parameters and define diagnostic measures to detect influential observations. For some parameter settings, sample sizes and different systematic structures, various simulations are performed to verify the adequacy of the estimators of the model parameters. The empirical distribution of the quantile residuals is investigated and compared with the standard normal distribution. We prove empirically the usefulness of the proposed models by means of three applications to real data.

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