Bayesian Mixture Model Research Articles

Optimal stratification of survival data via Bayesian nonparametric mixtures

The stratified proportional hazards model represents a simple solution to take into account heterogeneity within the data while keeping the multiplicative effect of the predictors on the hazard function. Strata are typically defined a priori by resorting to the values of a categorical covariate. A general framework is proposed, which allows the stratification of a generic accelerated lifetime model, including, as a special case, the Weibull proportional hazards model. The stratification is determined a posteriori, taking into account that strata might be characterized by different baseline survivals, and also by different effects of the predictors. This is achieved by considering a Bayesian nonparametric mixture model and the posterior distribution it induces on the space of data partitions. An optimal stratification is then identified following a decision theoretic approach. In turn, stratum-specific inference is carried out. The performance of this method and its robustness to the presence of right-censored observations are investigated through an extensive simulation study. Further illustration is provided analysing a data set from the University of Massachusetts AIDS Research Unit IMPACT Study.

Bayesian mixture modelling for glass refractive index measurement

Glass is a common type of physical evidence in forensic science. Broken glass recovered from a suspect may have similar physical characteristics to glass collected at a crime scene and therefore can be used as evidence. Statistical treatment of this evidence involves computing a measure of the weight of evidence. This may be done in a Bayesian framework that incorporates information from the circumstances of the crime. One of the most crucial quantities in this calculation is the assessment of the relative rarity of the characteristics of the glass, essentially the probability distribution used to model the physical characteristics of recovered glass. Typical characteristics used in casework are the elemental composition of glass and the refractive index measurement. There is a considerable body of scientific literature devoted to the modelling of this information. For example a kernel density estimation has been used to model the background population of glass based on the refractive index measurement and a multivariate Gaussian finite mixture model has been used to model the elemental composition of glass. In this paper, we present an alternative approach, the Dirichlet Process Mixture Model, to model the glass refractive index measurement in a Bayesian methodology. A key advantage is that using this method allows us to model the probability density distribution of refractive index measurements in a more flexible way.

Dynamic Dirichlet process mixture model for identifying voting coalitions in the United Nations General Assembly human rights roll call votes

ABSTRACT Scholars have been interested in the politicization of humans rights within the United Nations for some time. However, previous research typically looks at simple associations between voting coalitions and observable variables, such as geographic location or membership in international organizations. Our study is the first attempt at estimating the latent coalition structure based on the voting data. We propose a Bayesian Dynamic Dirichlet Process Mixture (DDPM) model to identify voting coalitions based on roll call vote data across multiple time periods. We also propose post-processing methods for analyzing the outputs of the DDPM model. We apply these methods to the United Nations General Assembly (UNGA) human rights roll call vote data from 1992 to 2017. We identify human rights voting coalitions in the UNGA after the Cold War, and polarizing resolutions that divide countries into different coalitions.

Integrative learning for population of dynamic networks with covariates

Although there is a rapidly growing literature on dynamic connectivity methods, the primary focus has been on separate network estimation for each individual, which fails to leverage common patterns of information. We propose novel graph-theoretic approaches for estimating a population of dynamic networks that are able to borrow information across multiple heterogeneous samples in an unsupervised manner and guided by covariate information. Specifically, we develop a Bayesian product mixture model that imposes independent mixture priors at each time scan and uses covariates to model the mixture weights, which results in time-varying clusters of samples designed to pool information. The computation is carried out using an efficient Expectation-Maximization algorithm. Extensive simulation studies illustrate sharp gains in recovering the true dynamic network over existing dynamic connectivity methods. An analysis of fMRI block task data with behavioral interventions reveal sub-groups of individuals having similar dynamic connectivity, and identifies intervention-related dynamic network changes that are concentrated in biologically interpretable brain regions. In contrast, existing dynamic connectivity approaches are able to detect minimal or no changes in connectivity over time, which seems biologically unrealistic and highlights the challenges resulting from the inability to systematically borrow information across samples.

Do financial variables help predict the conditional distribution of the market portfolio?

This paper investigates predictability of the full density of market returns. The proposed model is a Bayesian nonparametric mixture model where the mixture weights are functions of predictors, allowing us to study predictability of the unknown and time-varying density of market returns, in contrast to the extant literature which essentially focuses on point forecasts of the predictive mean which contains no description of the associated uncertainty. We compare statistical and economic performance of the proposed model with a set of competing models. Despite little or no improvement in point forecasts, certain variables display significant out-of-sample predictive ability for the stock return density and increase economic value for investors when employed in portfolio decisions.

Investment Modelling Using Value at Risk Bayesian Mixture Modelling Approach and Backtesting to Assess Stock Risk

Background: Stock investment has been gaining momentum in the past years due to the development of technology. During the pandemic lockdown, people have invested more. One the one hand, stock investment has high potential profitability, but on the other, it is equally risky. Therefore, a value at risk (VaR) analysis is needed. One approach to calculate VaR is by using the Bayesian mixture model, which has been proven to be able to overcome heavy-tailed cases. Then, the VaR’s accuracy needs to be tested, and one of the ways is by using backtesting, such as the Kupiec test.Objective: This study aims to determine the VaR model of PT NFC Indonesia Tbk (NFCX) return data using Bayesian mixture modelling and backtesting. On a practical level, this study can provide information about the potential risks of investing that is grounded in empirical evidence.Methods: The data used was NFCX data retrieved from Yahoo Finance, which was then modelled with a mixture model based on the normal and Laplace distributions. After that, the VaR accuracy was calculated and then tested by using backtesting.Results: The test results showed that the VaR with the mixture Laplace autoregressive (MLAR) approach (2;[2],[4]) was accurate at 5% and 1% quantiles while mixture normal autoregressive MNAR (2;[2],[2,4]) was only accurate at 5% quantiles.Conclusion: The better performing NFCX VaR model for this study based on backtesting using Kupiec test is MLAR(2;[2],[4]).

A Bayesian nonparametric mixture model for grouping dependence structures and selecting copula functions

The demand for advanced dependence modeling arises in a variety of fields, including finance, insurance and health science. When analyzing dependent data, it is important but challenging to properly model the dependence structure in order to carry out valid and efficient inferences. Grouping the data according to the similarity in the dependence structure is necessary, especially for data of a small size. A copula-based model, indexed by copula selection indicators and dependence parameters, is introduced to delineate dependent data and group similar dependence structures. To conduct inference, a Bayesian nonparametric method with the prior distributions specified as a Dirichlet Process is proposed as a mixture of Dirichlet process mixture copula model (M-DPM-CM). Extensive simulation studies have been conducted to evaluate the performance of the proposed procedure, and the results show that the proposed M-DPM-CM can recover the true grouping structure and achieve high accuracy in copula model selection under various finite sample settings. The M-DPM-CM is applied to analyze the Vertebral Column dataset from UCI Machine Learning Repository.

Weakened magnetic braking supported by asteroseismic rotation rates of Kepler dwarfs

Studies using asteroseismic ages and rotation rates from star-spot rotation have indicated that standard age-rotation relations may break down roughly half-way through the main sequence lifetime, a phenomenon referred to as weakened magnetic braking. While rotation rates from spots can be difficult to determine for older, less active stars, rotational splitting of asteroseismic oscillation frequencies can provide rotation rates for both active and quiescent stars, and so can confirm whether this effect really takes place on the main sequence. We obtained asteroseismic rotation rates of 91 main sequence stars showing high signal-to-noise modes of oscillation. Using these new rotation rates, along with effective temperatures, metallicities and seismic masses and ages, we built a hierarchical Bayesian mixture model to determine whether the ensemble more closely agreed with a standard rotational evolution scenario, or one where weakened magnetic braking takes place. The weakened magnetic braking scenario was found to be 98.4% more likely for our stellar ensemble, adding to the growing body of evidence for this stage of stellar rotational evolution. This work represents the largest catalogue of seismic rotation on the main sequence to date, opening up possibilities for more detailed ensemble analysis of rotational evolution with Kepler.

A Bernoulli-Gamma hierarchical Bayesian model for daily rainfall forecasts

We consider stochastic weather models originally developed for rainfall simulations to build a hierarchical Bayesian mixture model for daily rainfall forecasts using endogenous and external information. We model daily rainfall as a seasonal-varying mixture of a Bernoulli distribution for rainfall occurrence and a gamma distribution for the rainfall amount. The model scheme allows the inclusion of predictors to reduce the bias and variance of the forecasts, while the hierarchical Bayesian framework promotes a better understanding and reduction in parameter uncertainties, especially for gauges with short records, as well as supports the estimation of regional parameters that could be employed for forecasts at ungauged sites. The model was tested using 47 years (1973–2019) of daily rainfall data from 60 gauges in South Korea. Climate indices derived from the low-level wind over the region were analyzed using Principal Component Analysis (PCA) and embodied into the model to enhance its forecast skills. The model structure was based on a detailed exploratory data analysis, which included the application of Self-Organizing Maps (SOM) to examine the spatio-temporal patterns of rainfall. Cross-validated results reveal improved skills over reference models based on climatology and persistence up to a three days lead time. The average gains in metrics such as the Brier and Winkler skill scores vary from 5% to 50%, while the average correlation skill between predictions and observations reach values up to 0.55. The gains beyond a three days lead time are marginal, but the underlying structure of the proposed model still encourages its use over the reference models, being a step forward in improving real-time daily rainfall forecasts for the region. It has also a great potential to be combined with weather model forecasts and applied in other places across the world.

Bayesian Mixture Modelling for Mortality Projection

Although a large number of mortality projection models have been proposed in the literature, relatively little attention has been paid to a formal assessment of the effect of model uncertainty. In this paper, we construct a Bayesian framework for embedding more than one mortality projection model and utilise the finite mixture model concept to allow for the blending of model structures. Under this framework, the varying features of different model structures can be exploited jointly and coherently to have a more detailed description of the underlying mortality patterns. We show that the proposed Bayesian approach performs well in fitting and forecasting Japanese mortality.

A Bayesian mixture model for changepoint estimation using ordinal predictors.

In regression models, predictor variables with inherent ordering, such ECOG performance status or novel biomarker expression levels, are commonly seen in medical settings. Statistically, it may be difficult to determine the functional form of an ordinal predictor variable. Often, such a variable is dichotomized based on whether it is above or below a certain cutoff. Other methods conveniently treat the ordinal predictor as a continuous variable and assume a linear relationship with the outcome. However, arbitrarily choosing a method may lead to inaccurate inference and treatment. In this paper, we propose a Bayesian mixture model to consider both dichotomous and linear forms for the variable. This allows for simultaneous assessment of the appropriate form of the predictor in regression models by considering the presence of a changepoint through the lens of a threshold detection problem. This method is applicable to continuous, binary, and survival outcomes, and it is easily amenable to penalized regression. We evaluated the proposed method using simulation studies and apply it to two real datasets. We provide JAGS code for easy implementation.

Large inter-stock differences in catch size-at-age of mature Atlantic salmon observed by using genetic individual origin assignment from catch data.

Genetic individual assignment of river stock of origin of mixed stock catch fish offers a tool to analyze size differences among river stocks. Data on the genetically identified river stock of origin of individual fish from commercial mixed stock catches were used to compare the catch size-at-age of mature Atlantic salmon catch fish (Salmo salar) from different rivers in the Baltic Sea. In this application of genetic mixed stock modeling, individual assignments of the river stock of origin were analyzed together with length- and weight-at-age data for individual catch fish. The use of four genetic stock identification based methods was compared for defining the length distributions of caught mature salmon in different river stocks. The catch data included information on maturing salmon in the northern Baltic Sea over the years 2000–2013. DNA microsatellite data on 17 loci and information on the smoltification age were used to assign spawners to their stock of origin. All of the compared methods for using probabilistic stock of origin data in our case yielded very similar estimates of the final mean length distributions of the stocks. The Bayesian mixture model yielded slightly more conservative estimates than the direct probability method, threshold method, or the modified probability method. The catch size between spawners of a same sex and age from river stocks differed significantly and the differences were large. The mean catch weight of 1-sea-winter old mature males in different rivers varied from 1.9 kg to 2.9 kg, from 5.1 kg to 7.5 kg for 2-sea-winter old males, from 5.0 kg to 7.2 kg for 2-sea-winter old females, and from 8.2 kg to 10.8 kg for 3-sea-winter-old females. The mean size of caught wild salmon spawners in each year-class was on average smaller than that of the hatchery-reared and sea ranched stocks.

Active Learning of Bayesian Probabilistic Movement Primitives

Learning from Demonstration permits non-expert users to easily and intuitively reprogram robots. Among approaches embracing this paradigm, probabilistic movement primitives (ProMPs) are a well-established and widely used method to learn trajectory distributions. However, providing or requesting useful demonstrations is not easy, as quantifying what constitutes a good demonstration in terms of generalization capabilities is not trivial. In this letter, we propose an active learning method for contextual ProMPs for addressing this problem. More specifically, we learn the trajectory distributions using a Bayesian Gaussian mixture model (BGMM) and then leverage the notion of epistemic uncertainties to iteratively choose new context query points for demonstrations. We show that this approach reduces the required number of human demonstrations. We demonstrate the effectiveness of the approach on a pouring task, both in simulation and on a real 7-DoF Franka Emika robot.

Bayesian infinite mixture models for wind speed distribution estimation

Wind energy, as a clean, environment-friendly, and inexhaustible renewable energy, has attracted significant attention, and wind speed distribution plays an important role in its development. Currently, various finite mixture distributions have been proposed to fit the empirical wind speed distribution. However, they have two disadvantages. First, different distribution components result in different fitting performances, and it is difficult to determine the optimal type of single distributions to construct a mixture model. Second, the number of distribution components has a significant effect on the final performance of the mixture model. It is well known that a mixture of Gaussian distributions (MoG) can fit any complex continuous distribution. To overcome the above-mentioned disadvantages, based on stick-breaking construction, this study extends the original MoG to two different types of infinite mixtures of Gaussian distributions (IMoG) with different prior parameter distributions. These distributions are called IMoG-I and IMoG-II. The proposed models not only have superior fitting performance but also determine the optimal number of Gaussian components automatically. The results show that both IMoG-I and IMoG-II perform better than single, heterogeneous, and homogeneous mixture distributions. In most cases, the coefficient of determination-based criterion can reach its maximum of 1. In addition, the optimal number of Gaussian components varies with different datasets. When modeling different wind speed distributions in this study, they are all less than 10. The proposed wind speed distribution estimation models are good choices for unknown areas with complex wind regimes.

Ant Colony System Optimization for Spatiotemporal Modelling of Combined EEG and MEG Data.

Electroencephalography/Magnetoencephalography (EEG/MEG) source localization involves the estimation of neural activity inside the brain volume that underlies the EEG/MEG measures observed at the sensor array. In this paper, we consider a Bayesian finite spatial mixture model for source reconstruction and implement Ant Colony System (ACS) optimization coupled with Iterated Conditional Modes (ICM) for computing estimates of the neural source activity. Our approach is evaluated using simulation studies and a real data application in which we implement a nonparametric bootstrap for interval estimation. We demonstrate improved performance of the ACS-ICM algorithm as compared to existing methodology for the same spatiotemporal model.

A Comparison of Statistical Tools for Identifying Modality in Body Mass Distributions

The assessment of modality or \bumps in distributions is of in- terest to scientists in many areas. We compare the performance of four statistical methods to test for departures from unimodality in simulations, and further illustrate the four methods using well-known ecological datasets on body mass published by Holling in 1992 to illustrate their advantages and disadvantages. Silverman's kernel density method was found to be very conservative. The excess mass test and a Bayesian mixture model approach showed agreement among the data sets, whereas Hall and York's test pro- vided strong evidence for the existence of two or more modes in all data sets. The Bayesian mixture model also provided a way to quantify the un- certainty associated with the number of modes. This work demonstrates the inherent richness of animal body mass distributions but also the diculties for characterizing it, and ultimately understanding the processes underlying them.

Biologically Enhanced Genome-Wide Association Study Provides Further Evidence for Candidate Loci and Discovers Novel Loci That Influence Risk of Anterior Cruciate Ligament Rupture in a Dog Model.

Anterior cruciate ligament (ACL) rupture is a common condition that disproportionately affects young people, 50% of whom will develop knee osteoarthritis (OA) within 10 years of rupture. ACL rupture exhibits both hereditary and environmental risk factors, but the genetic basis of the disease remains unexplained. Spontaneous ACL rupture in the dog has a similar disease presentation and progression, making it a valuable genomic model for ACL rupture. We leveraged the dog model with Bayesian mixture model (BMM) analysis (BayesRC) to identify novel and relevant genetic variants associated with ACL rupture. We performed RNA sequencing of ACL and synovial tissue and assigned single nucleotide polymorphisms (SNPs) within differentially expressed genes to biological prior classes. SNPs with the largest effects were on chromosomes 3, 5, 7, 9, and 24. Selection signature analysis identified several regions under selection in ACL rupture cases compared to controls. These selection signatures overlapped with genome-wide associations with ACL rupture as well as morphological traits. Notable findings include differentially expressed ACSF3 with MC1R (coat color) and an association on chromosome 7 that overlaps the boundaries of SMAD2 (weight and body size). Smaller effect associations were within or near genes associated with regulation of the actin cytoskeleton and the extracellular matrix, including several collagen genes. The results of the current analysis are consistent with previous work published by our laboratory and others, and also highlight new genes in biological pathways that have not previously been associated with ACL rupture. The genetic associations identified in this study mirror those found in human beings, which lays the groundwork for development of disease-modifying therapies for both species.

Exploring Class Enumeration in Bayesian Growth Mixture Modeling Based on Conditional Medians

Growth mixture modeling is a popular analytic tool for longitudinal data analysis. It detects latent groups based on the shapes of growth trajectories. Traditional growth mixture modeling assumes that outcome variables are normally distributed within each class. When data violate this normality assumption, however, it is well documented that the traditional growth mixture modeling mislead researchers in determining the number of latent classes as well as in estimating parameters. To address nonnormal data in growth mixture modeling, robust methods based on various nonnormal distributions have been developed. As a new robust approach, growth mixture modeling based on conditional medians has been proposed. In this article, we present the results of two simulation studies that evaluate the performance of the median-based growth mixture modeling in identifying the correct number of latent classes when data follow the normality assumption or have outliers. We also compared the performance of the median-based growth mixture modeling to the performance of traditional growth mixture modeling as well as robust growth mixture modeling based on t distributions. For identifying the number of latent classes in growth mixture modeling, the following three Bayesian model comparison criteria were considered: deviance information criterion, Watanabe-Akaike information criterion, and leave-one-out cross validation. For the median-based growth mixture modeling and t-based growth mixture modeling, our results showed that they maintained quite high model selection accuracy across all conditions in this study (ranged from 87 to 100%). In the traditional growth mixture modeling, however, the model selection accuracy was greatly influenced by the proportion of outliers. When sample size was 500 and the proportion of outliers was 0.05, the correct model was preferred in about 90% of the replications, but the percentage dropped to about 40% as the proportion of outliers increased to 0.15.

Anomaly Detection in Health Insurance Claims Using Bayesian Quantile Regression

Research has shown that current health expenditure in most countries, especially in sub-Saharan Africa, is inadequate and unsustainable. Yet, fraud, abuse, and waste in health insurance claims by service providers and subscribers threaten the delivery of quality healthcare. It is therefore imperative to analyze health insurance claim data to identify potentially suspicious claims. Typically, anomaly detection can be posited as a classification problem that requires the use of statistical methods such as mixture models and machine learning approaches to classify data points as either normal or anomalous. Additionally, health insurance claim data are mostly associated with problems of sparsity, heteroscedasticity, multicollinearity, and the presence of missing values. The analyses of such data are best addressed by adopting more robust statistical techniques. In this paper, we utilized the Bayesian quantile regression model to establish the relations between claim outcome of interest and subject-level features and further classify claims as either normal or anomalous. An estimated model component is assumed to inherently capture the behaviors of the response variable. A Bayesian mixture model, assuming a normal mixture of two components, is used to label claims as either normal or anomalous. The model was applied to health insurance data captured on 115 people suffering from various cardiovascular diseases across different states in the USA. Results show that 25 out of 115 claims (21.7%) were potentially suspicious. The overall accuracy of the fitted model was assessed to be 92%. Through the methodological approach and empirical application, we demonstrated that the Bayesian quantile regression is a viable model for anomaly detection.

Gene expression profiling (GEP) to identify metabolic gene signature predictive of recurrence after surgery in stage III clear-cell renal cell carcinoma (ccRCC).

355 Background: Management of patients with localized or locally advanced renal cell cancer (RCC) involves surgical resection. However, 20-40% of all localized kidney cancer patients experience a recurrence. Adjuvant treatment in high-risk kidney cancer has not proven to successfully improve overall survival (OS) and the only drug approved so far in this setting is vascular endothelial growth factor (VEGF) inhibitor, sunitinib. As multiple trials are evaluating drugs including immune checkpoint inhibitors in patients with high risk localized clear cell RCC, there is an urgent need to identify biomarkers to help with therapeutic decisions as well as for risk stratification. Here we present analysis pertaining to genes involved in metabolic reprogramming in kidney cancer. Methods: A deep transcriptomic analysis of patients with stage III ccRCC in the TCGA KIRC Firehose Legacy cohort was undertaken. Caucasian males with stage III ccRCC in the TCGA cohort for whom recurrence data was available with a minimum follow-up of 2 years were identified for the analysis. Expression profiles of differentially expressed genes were clustered using the Bayesian infinite mixture model and samples clustered using average linkage hierarchical clustering based on pairwise Pearson’s correlations as the measure of similarity. Enrichment analysis of up- and down-regulated genes was performed using logistic regression. R package was used to generate Kaplan-Meier curves and assess statistical significance of differences in overall and disease-free survival using log-rank test. Results: The cohort evaluated for this study included Caucasian male patients that remained disease free for at least 24 months after surgery (n = 22) and patients whose cancer recurred within 24 months (n = 20). We identified metabolic genes, encoding subunits of mitochondrial electron transport chain as well as malate aspartate shuttle (MAS), where loss of coordinated co-expression between these genes identified patients at risk of recurrence after surgery. The gene signature stratified the 42 patients into three subtypes: significantly enriched for a) recurrence (subtype 1), for b) disease free status (subtype 2) and b) intermediate (subtype 3). Work is underway to combine the use of individual gene expression and ratios of gene expression within the signature to optimize prognostic biomarkers for localized ccRCC. Conclusions: In this analysis, we have identified a novel metabolic gene signature which can help identify patients with localized ccRCC at high risk of recurrence after surgery to guide aggressive therapy. These findings require further validation in tumors collected from patients with stage III ccRCC.