Bayesian Nonparametric Methods Research Articles

Bayesian Nonparametric Methods for Analyzing Ever-increasing Infinite Data

Bayesian Nonparametric Methods for Analyzing Ever-increasing Infinite Data

Application of non parametric Bayesian methods in high dimensional data

With the development of technology and the widespread collection of data, high-dimensional data analysis has become a research hotspot in many fields. Traditional parameter methods often face problems such as dimensional disasters in high-dimensional data analysis. Non parametric methods have broad application prospects in high-dimensional data because they do not rely on specific parameter distribution assumptions. The Bayesian rule is more suitable for dealing with noise and outliers in high-dimensional data because it takes uncertainty into account. Therefore, it is of great significance to combine non parametric methods with Bayesian methods for application research in high-dimensional data analysis. In this paper, the nonparametric Bayesian method was applied to the analysis of high-dimensional data, and the Dirichlet process Mixture model was used to cluster high-dimensional data. The regression analysis of high-dimensional data was carried out through the prediction model of nonparametric Bayesian regression. In this paper, the nonparametric Bayesian method based on Bayesian sparse linear model was used for feature selection of high-dimensional data. In order to determine the superiority of nonparametric Bayesian methods in high-dimensional data analysis, this paper conducted experiments on nonparametric Bayesian methods and traditional parametric methods in high-dimensional data analysis from five aspects of cluster analysis, classification analysis, regression analysis, feature selection and anomaly detection, and evaluated them through multiple indicators. This article explored the application of non parametric Bayesian methods in high-dimensional data analysis from these aspects through simulation experiments. The experimental results show that the clustering accuracy of the non parametric Bayesian clustering algorithm was 0.93, and the accuracy of the non parametric Bayesian classification algorithm was between 0.93 and 0.99; the coefficient of determination of nonparametric Bayesian regression algorithm was 0.98; the F1 values of non parametric Bayesian methods in anomaly detection ranged from 0.86 to 0.91, which was superior to traditional methods. Non parametric Bayesian methods have broad application prospects in high-dimensional data analysis, and can be applied in multiple fields such as clustering, classification, regression, etc.

Evidence of evolution of the black hole mass function with redshift

Aims. We investigate the observed distribution of the joint primary mass, mass ratio, and redshift of astrophysical black holes using the gravitational wave events detected by the LIGO-Virgo-KAGRA collaboration and included in the third gravitational wave transient catalogue. Methods. We reconstructed this distribution using Bayesian non-parametric methods, which are data-driven models able to infer arbitrary probability densities under minimal mathematical assumptions. Results. We find evidence that both the primary mass and mass-ratio distribution evolve with redshift: our analysis shows the presence of two distinct subpopulations in the primary mass−redshift plane, with the lighter population, ≲20 M⊙, disappearing at higher redshifts, z > 0.4. The mass-ratio distribution shows no support for symmetric binaries. Conclusions. The observed population of coalescing binary black holes evolves with look-back time, suggesting a trend in metallicity with redshift and/or the presence of multiple redshift-dependent formation channels.

A survey on Bayesian nonparametric learning for time series analysis

Time series analysis aims to understand underlying patterns and relationships in data to inform decision-making. As time series data are becoming more widely available across a variety of academic disciplines, time series analysis has become a rapidly growing field. In particular, Bayesian nonparametric (BNP) methods are gaining traction for their power and flexibility in modeling, predicting, and extracting meaningful information from time series data. The utility of BNP methods lies in their ability to encode prior information and represent complex patterns in the data without imposing strong assumptions about the underlying distribution or functional form. BNP methods for time series analysis can be applied to a breadth of problems, including anomaly detection, noise density estimation, and time series clustering. This work presents a comprehensive survey of the existing literature on BNP methods for time series analysis. Various temporal BNP models are discussed along with notable applications and possible approaches for inference. This work also highlights current research trends in the field and potential avenues for further development and exploration.

A Bayesian Nonparametric Modeling Approach to Settlement Patterns of Pastoralists Population in Kenya

Pastoralists' settlement patterns in Kenya have been studied for decades using various statistical and mathematical models. However, traditional models have often relied on restrictive assumptions, such as the normality of the data or the linearity of relationships. In this paper, we apply a Bayesian nonparametric approach to model the settlement patterns of pastoralists in Kenya, allowing for more flexible and realistic representations of the data. We first collected settlement data for pastoralists in Kenya and compiled a database of environmental covariates, such as distance to water sources, vegetation cover, and road networks. We then applied a Bayesian nonparametric clustering method to identify distinct settlement patterns and tested the performance of the model against other commonly used clustering techniques. Our results indicate that the Bayesian nonparametric approach outperforms other clustering techniques in terms of model fit and accuracy in identifying distinct settlement patterns. Additionally, we conducted a spatial regression analysis to investigate the relationship between settlement patterns and environmental covariates, revealing that distance to water sources and road networks are significant predictors of settlement patterns. Overall, our study highlights the usefulness of Bayesian nonparametric methods in modelling settlement patterns of pastoralists in Kenya and provides valuable insights into the relationship between environmental factors and settlement patterns.

Nonparametric failure time: Time-to-event machine learning with heteroskedastic Bayesian additive regression trees and low information omnibus Dirichlet process mixtures.

Many popular survival models rely on restrictive parametric, or semiparametric, assumptions that could provide erroneous predictions when the effects of covariates are complex. Modern advances in computational hardware have led to an increasing interest in flexible Bayesian nonparametric methods for time-to-event data such as Bayesian additive regression trees (BART). We propose a novel approach that we call nonparametric failure time (NFT) BART in order to increase the flexibility beyond accelerated failure time (AFT) and proportional hazard models. NFT BART has three key features: (1)a BART prior for the mean function of the event time logarithm; (2)a heteroskedastic BART prior to deduce a covariate-dependent variance function; and (3)a flexible nonparametric error distribution using Dirichlet process mixtures (DPM). Our proposed approach widens the scope of hazard shapes including nonproportional hazards, can be scaled up to large sample sizes, naturally provides estimates of uncertainty via the posterior and can be seamlessly employed for variable selection. We provide convenient, user-friendly, computer software that is freely available as a reference implementation. Simulations demonstrate that NFT BART maintains excellent performance for survival prediction especially when AFT assumptions are violated by heteroskedasticity. We illustrate the proposed approach on a study examining predictors for mortality risk in patients undergoing hematopoietic stem cell transplant (HSCT) for blood-borne cancer, where heteroskedasticity and nonproportional hazards are likelypresent.

Automatic Relevance Determination Kernel-Embedded Gaussian Process Regression for Sonar-Based Human Leg Localization with a Mobile Robot

Human leg localization problems involving sonar sensing can be posed as a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nonlinear regression problem</i> , and, nonparametric Bayesian methods, such as the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Gaussian process regression</i> (GPR) model, are potential solution candidates. In this work, to overcome the problem of irrelevant input features from the sonar range data, an advanced <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">automatic relevance determination</i> kernel structure is proposed to be used in the GPR model instead of the commonly used standard isotropic kernel. It is able to extract high-relevance input features even from partially trained data, thus offering a better generalization ability while improving the prediction rates and robustness significantly.

大数据中贝叶斯非参数方法的理论与应用研究

大数据中贝叶斯非参数方法的理论与应用研究

Hamiltonian sequential Monte Carlo with application to consumer choice behavior

The practical use of nonparametric Bayesian methods requires the availability of efficient algorithms for posterior inference. The inherently serial nature of traditional Markov chain Monte Carlo (MCMC) methods imposes limitations on their efficiency and scalability. In recent years, there has been a surge of research activity devoted to developing alternative implementation methods that target parallel computing environments. Sequential Monte Carlo (SMC), also known as a particle filter, has been gaining popularity due to its desirable properties. SMC uses a genetic mutation-selection sampling approach with a set of particles representing the posterior distribution of a stochastic process. We propose to enhance the performance of SMC by utilizing Hamiltonian transition dynamics in the particle transition phase, in place of random walk used in the previous literature. We call the resulting procedure Hamiltonian Sequential Monte Carlo (HSMC). Hamiltonian transition dynamics have been shown to yield superior mixing and convergence properties relative to random walk transition dynamics in the context of MCMC procedures. The rationale behind HSMC is to translate such gains to the SMC environment. HSMC will facilitate practical estimation of models with complicated latent structures, such as nonparametric individual unobserved heterogeneity, that are otherwise difficult to implement. We demonstrate the behavior of HSMC in a challenging simulation study and contrast its favorable performance with SMC and other alternative approaches. We then apply HSMC to a panel discrete choice model with nonparametric consumer heterogeneity, allowing for multiple modes, asymmetries, and data-driven clustering, providing insights for consumer segmentation, individual level marketing, and price micromanagement.

Shape modeling with spline partitions

Shape modelling (with methods that output shapes) is a new and important task in Bayesian nonparametrics and bioinformatics. In this work, we focus on Bayesian nonparametric methods for capturing shapes by partitioning a space using curves. In related work, the classical Mondrian process is used to partition spaces recursively with axis-aligned cuts, and is widely lied in multi-dimensional and relational data. The Mondrian process outputs hyper-rectangles. Recently, the random tessellation process was introduced as a generalization of the Mondrian process, partitioning a domain with non-axis aligned cuts in an arbitrary dimensional space, and outputting polytopes. Motivated by these processes, in this work, we propose a novel parallelized Bayesian nonparametric approach to partition a domain with curves, enabling complex data-shapes to be acquired. We apply our method to HIV-1-infected human macrophage image dataset, and also simulated datasets sets to illustrate our approach. We compare to support vector machines, random forests and state-of-the-art computer vision methods such as simple linear iterative clustering super pixel image segmentation. We develop an R package that is available at https://github.com/ShufeiGe/Shape-Modeling-with-Spline-Partitions.

Trends of extreme US weather events in the changing climate

Trends in extreme 100-y events of temperature and rainfall amounts in the continental United States are estimated, to see effects of climate change. This is a nontrivial statistical problem because climate change effects have to be extracted from "noisy" weather data within a limited time range. We use nonparametric Bayesian methods to estimate the trends of extreme events that have occurred between 1979 and 2019, based on data for temperature and rainfall. We focus on 100-y events for each month in [Formula: see text] geographical areas looking at hourly temperature and 5-d cumulative rainfall. Distribution tail models are constructed using extreme value theory (EVT) and data on 33-y events. This work shows it is possible to aggregate data from spatial points in diverse climate zones for a given month and fit an EVT model with the same parameters. This surprising result means there are enough extreme event data to see the trends in the 41-y record for each calendar month. The yearly trends of the risk of a 100-y high-temperature event show an average 2.1-fold increase over the last 41 y of data across all months, with a 2.6-fold increase for the months of July through October. The risk of high rainfall extremes increases in December and January 1.4-fold, but declines by 22% for the spring and summer months.

A Bayesian nonparametric method for detecting rapid changes in disease transmission

Whether an outbreak of infectious disease is likely to grow or dissipate is determined through the time-varying reproduction number, Rt. Real-time or retrospective identification of changes in Rt following the imposition or relaxation of interventions can thus contribute important evidence about disease transmission dynamics which can inform policymaking. Here, we present a method for estimating shifts in Rt within a renewal model framework. Our method, which we call EpiCluster, is a Bayesian nonparametric model based on the Pitman–Yor process. We assume that Rt is piecewise-constant, and the incidence data and priors determine when or whether Rt should change and how many times it should do so throughout the series. We also introduce a prior which induces sparsity over the number of changepoints. Being Bayesian, our approach yields a measure of uncertainty in Rt and its changepoints. EpiCluster is fast, straightforward to use, and we demonstrate that it provides automated detection of rapid changes in transmission, either in real-time or retrospectively, for synthetic data series where the Rt profile is known. We illustrate the practical utility of our method by fitting it to case data of outbreaks of COVID-19 in Australia and Hong Kong, where it finds changepoints coinciding with the imposition of non-pharmaceutical interventions. Bayesian nonparametric methods, such as ours, allow the volume and complexity of the data to dictate the number of parameters required to approximate the process and should find wide application in epidemiology. This manuscript was submitted as part of a theme issue on “Modelling COVID-19 and Preparedness for Future Pandemics”.

Bayesian Non-Parametric Thermal Thresholds for Helicoverpa armigera and Their Integration into a Digital Plant Protection System

The development of temperature-driven pest risk thresholds is a prerequisite for the buildup and implementation of smart plant protection solutions. However, the challenge is to convert short and abrupt phenology data with limited distributional information into ecological relevant information. In this work, we present a novel approach to analyze phenology data based on non-parametric Bayesian methods and develop degree-day (DD) risk thresholds for Helicoverpa armigera (Hübner) (Lepidoptera: Noctuidae) to be used in a decision support system for dry bean (Phaseolus vulgaris L.) production. The replication of each Bayesian bootstrap generates a posterior probability for each sampling set by considering that the prior unknown distribution of pest phenology is Dirichlet distribution. We computed R = 10,000 temperature-driven pest phenology replicates, to estimate the 2.5%, 50% and 95.5% percentiles (PC) of each flight generation peak in terms of heat summations. The related DD thresholds were: 114.04 (PC 2.5%) 131.8 (PC 50%) and 150.9 (PC 95.5%) for the first, 525.8 (PC 2.5%), 551.7 (PC 50%) and 577.6 (PC 95.5%) for the second and 992.7 (PC 2.5%), 1021.5 (PC 50%) and 1050 (PC 95.5%) for the third flight, respectively. The thresholds were evaluated by estimating the posterior differences between the predicted (2021) and observed (2022) phenology metrics and are in most cases in acceptable levels. The bootstrapped Bayesian risk thresholds have the advantage to be used in modeling short and noisy data sets providing tailored pest forecast without any parametric assumptions. In a second step the above thresholds were integrated to a sub-module of a digital weather-driven real time decision support system for precise pest management for dry bean crops. The system consists of a customized cloud based telemetric meteorological network, established over the border area of the Prespa National Park in Northern Greece, and delivers real time data and pest specific forecast to the end user.

Mediation analysis using Bayesian tree ensembles.

We present a general framework for causal mediation analysis using nonparametric Bayesian methods in the potential outcomes framework. Our model, which we refer to as the Bayesian causal mediation forests model, combines recent advances in Bayesian machine learning using decision tree ensembles, Bayesian nonparametric causal inference, and a Bayesian implementation of the g-formula for computing causal effects. Because of its strong performance on simulated data and because it greatly reduces researcher degrees of freedom, we argue that Bayesian causal mediation forests are highly attractive as a default approach. Of independent interest, we also introduce a new sensitivity analysis technique for mediation analysis with continuous outcomes that is widely applicable. We demonstrate our approach on both simulated and real data sets, and show that our approach obtains low mean squared error and close to nominal coverage of 95% interval estimates, even in highly nonlinear problems on which other methods fail. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Tracking the contribution of inductive bias to individualised internal models.

Internal models capture the regularities of the environment and are central to understanding how humans adapt to environmental statistics. In general, the correct internal model is unknown to observers, instead they rely on an approximate model that is continually adapted throughout learning. However, experimenters assume an ideal observer model, which captures stimulus structure but ignores the diverging hypotheses that humans form during learning. We combine non-parametric Bayesian methods and probabilistic programming to infer rich and dynamic individualised internal models from response times. We demonstrate that the approach is capable of characterizing the discrepancy between the internal model maintained by individuals and the ideal observer model and to track the evolution of the contribution of the ideal observer model to the internal model throughout training. In particular, in an implicit visuomotor sequence learning task the identified discrepancy revealed an inductive bias that was consistent across individuals but varied in strength and persistence.

The how and why of Bayesian nonparametric causal inference

AbstractSpurred on by recent successes in causal inference competitions, Bayesian nonparametric (and high‐dimensional) methods have recently seen increased attention in the causal inference literature. In this article, we present a comprehensive overview of Bayesian nonparametric applications to causal inference. Our aims are to (i) introduce the fundamental Bayesian nonparametric toolkit; (ii) discuss how to determine which tool is most appropriate for a given problem; and (iii) show how to avoid common pitfalls in applying Bayesian nonparametric methods in high‐dimensional settings. Unlike standard fixed‐dimensional parametric problems, where outcome modeling alone can sometimes be effective, we argue that most of the time it is necessary to model both the selection and outcome processes.This article is categorized under: Statistical and Graphical Methods of Data Analysis &gt; Analysis of High Dimensional Data Statistical and Graphical Methods of Data Analysis &gt; Nonparametric Methods Statistical and Graphical Methods of Data Analysis &gt; Bayesian Methods and Theory

Evaluating the measurement uncertainty at hydrogen refueling stations using a Bayesian non-parametric approach

The ability to evaluate measurement error at hydrogen refueling stations plays a vital role in the sustainability of the hydrogen vehicle industry. Most previous work in this application investigates the measurement accuracy of mass flow meters in controlled experiments, using testing equipment. The focus of our work is to estimate the measurement accuracy of fueling using data from hydrogen refueling stations collected under real operation. Accuracy is estimated by comparing the observed mass count readings with reference mass counts calculated using the pressure-volume-temperature method. To quantify the measurement uncertainty, we propose using Dirichlet process mixture models, a class of Bayesian non-parametric methods. The Dirichlet process mixture model approach is tested on five hydrogen refueling stations in real operation. Our results show that the model is able to capture the complex structure of the data and successfully estimate the probability distribution of measurement uncertainty. Our work demonstrates the effectiveness of the Bayesian non-parametric approach for evaluating the measurement uncertainty of hydrogen refueling stations.

A Bayesian Nonparametric Approach for Modeling SF-6D Health State Utility Scores

ObjectivesTypically, models that were used for health state valuation data have been parametric. Recently, many researchers have explored the use of nonparametric Bayesian methods in this field. In this article, we report on the results from using a nonparametric model to predict a Bayesian short-form 6-dimension (SF-6D) health state valuation algorithm along with estimating the effect of the individual characteristics on health state valuations. MethodsA sample of 126 Lebanese members from the American University of Beirut valued 49 SF-6D health states using the standard gamble technique. Results from applying the nonparametric model were reported and compared with those obtained using a standard parametric model. The covariates’ effect on health state valuations was also reported. ResultsThe nonparametric Bayesian model was found to perform better than the parametric model at (1) predicting health state values within the full estimation data and in an out-of-sample validation in terms of mean predictions, root mean squared error, and the patterns of standardized residuals and (2) allowing for the covariates’ effect to vary by health state. The findings also suggest a potential age effect with some gender effect. ConclusionsThe nonparametric model is theoretically more flexible and produces better utility predictions from the SF-6D than previously used classical parametric model. In addition, the Bayesian model is more appropriate to account the covariates’ effect. Further research is encouraged.

Time of Arrival Ranging and Localization Algorithm in Multi-Path and Non-Line-of-Sight Environments in OFDM System

Time of Arrival (TOA) is a widely used wireless cellular network ranging technology. How to perform accurate TOA estimation in multi-path and non-line-of-sight (NLOS) environments and then accurately calculating mobile terminal locations are two critical issues in positioning research. For NLOS identification, it can be performed in the TOA measurement part and the position calculation part, respectively. In this paper, for the above two steps, two schemes for mitigating NLOS errors are proposed. First of all, a TOA ranging method based on clustering theory is proposed to solve the problem of line of sight (LOS) path estimation in multi-path channels. We model TOA ranging as a Gaussian mixture model and illustrate how LOS and NLOS can be measured and identified based on non-parametric Bayesian methods when the wireless transmission environment is unknown. Moreover, for NLOS propagation channels, this paper proposes a user location estimator based on the maximum a posteriori (MAP) criterion. Combined with the TOA estimation and user location computation scheme proposed in this paper, the terminal's positioning accuracy is improved. Experiments show that the TOA measurement and localization algorithms presented in this paper have good robustness in complex wireless environments.

A novel method to generating two-sided class of probability distributions

We define a new two-sided class F of distributions and a generalized class by compounding this class with a baseline distribution G. The new model is called the general two-sided FG class. Some of its properties are provided. The proposed model is specialized taking the Weibull and exponential for F and G, respectively. For a new specialized distribution, we obtain the survival, quantiles and hazard rate. We estimate the parameters by maximum likelihood, Bayesian and parametric and non-parametric bootstrap methods. We conduct a simulation study to check the accuracy of the estimators. The classic and Bayesian approaches are illustrated by means of a real data set. We show that the proposed model fits better than the generalized two-sided exponential and generalized transmuted two-sided exponential distributions.