Bayesian Mixture Model Approach Research Articles

Bayesian mixture model approach to quantifying the empirical nuclear saturation point

Bayesian mixture model approach to quantifying the empirical nuclear saturation point

A Bayesian finite mixture model approach to evaluate dichotomization method for correlated ELISA tests

In diagnostic accuracy studies, a commonly employed approach involves dichotomizing continuous data and subsequently analyzing them using a Bayesian latent class model (BLCM), often relying on binomial or multinomial distributions, rather than preserving their continuous nature. However, this procedure can inadvertently lead to less reliable outcomes due to the inherent loss of information when converting the original continuous measurements into binary values. Through comprehensive simulations, we demonstrated the limitations and disadvantages of dichotomizing continuous biomarkers from two correlated tests. Our findings highlighted notable disparities between the true values and the model estimates as a result of dichotomization. We discovered the crucial significance of selecting a reference test with high diagnostic accuracy in test evaluation in order to obtain reliable estimates of test accuracy and prevalences. Our study served as a call to action for veterinary researchers to exercise caution when utilizing dichotomization.

Incorporating Prior Data in Quantitative Benefit-Risk Assessments: Case Study of a Bayesian Method.

Multiple criteria decision analysis (MCDA) and stochastic multi-criteria acceptability analysis (SMAA) in their current implementation cannot incorporate prior or external information on benefits and risks. We demonstrate how to incorporate prior data using a Bayesian mixture model approach while conducting quantitative benefit-risk assessments (qBRA) for medical products. We implemented MCDA and SMAA in a Bayesian framework. To incorporate information from a prior study, we use mixture priors on each benefit and risk attribute that mixes information from a previous study with a vague prior distribution. The degree of borrowing is varied using a mixing proportion parameter. A demonstration case study for qBRA using the supplementary New Drug Application (sNDA) filing for Rivaroxaban for the indication of reduction in the risk of major thrombotic vascular events in patients with peripheral artery disease (PAD) was used to illustrate the method. Net utility scores, obtained from the randomized controlled trial data to support the sNDA, from the MCDA for Rivaraxoban and comparator were 0.48 and 0.56, respectively, with Rivaroxaban being the preferred alternative only 33% of the time. We show that with only 30% borrowing from a previous RCT, the MCDA and SMAA results are favorable for Rivaroxaban, accounting for the seemingly aberrant results on all-cause death in the trial data used to support the sNDA. Our method to formally incorporate prior data in MCDA and SMAA is easy to use and interpret. Software in the form of an RShiny App is available here: https://sai-dharmarajan.shinyapps.io/BayesianMCDA_SMAA/ .

A Bayesian Mixture Model Approach to Disparity Testing

A Bayesian Mixture Model Approach to Disparity Testing

Identifying Subpopulations of Cells in Single-Cell Transcriptomic Data: A Bayesian Mixture Modeling Approach to Zero Inflation of Counts.

In the study of single-cell RNA-seq (scRNA-Seq) data, a key component of the analysis is to identify subpopulations of cells in the data. A variety of approaches to this have been considered, and although many machine learning-based methods have been developed, these rarely give an estimate of uncertainty in the cluster assignment. To allow for this, probabilistic models have been developed, but scRNA-Seq data exhibit a phenomenon known as dropout, whereby a large proportion of the observed read counts are zero. This poses challenges in developing probabilistic models that appropriately model the data. We develop a novel Dirichlet process mixture model that employs both a mixture at the cell level to model multiple populations of cells and a zero-inflated negative binomial mixture of counts at the transcript level. By taking a Bayesian approach, we are able to model the expression of genes within clusters, and to quantify uncertainty in cluster assignments. It is shown that this approach outperforms previous approaches that applied multinomial distributions to model scRNA-Seq counts and negative binomial models that do not take into account zero inflation. Applied to a publicly available data set of scRNA-Seq counts of multiple cell types from the mouse cortex and hippocampus, we demonstrate how our approach can be used to distinguish subpopulations of cells as clusters in the data, and to identify gene sets that are indicative of membership of a subpopulation.

Inferring the age and sex of ancient potters from fingerprint ridge densities: A data-driven, Bayesian mixture modelling approach

The density of epidermal ridges in a fingerprint varies predictably by age and sex. Archaeologists are therefore interested in using recovered fingerprints to learn about the ancient people who produced them. Recent studies focus on estimating the age and sex of individuals by measuring their fingerprints with one of two similar metrics: mean ridge breadth (MRB) or ridge density (RD). Yet these attempts face several critical problems: expected values for adult females and adolescent males are inherently indistinguishable, and inter-assemblage variation caused by biological and technological differences cannot be easily estimated. Each of these factors greatly decreases the accuracy of predictions based on individual prints, and together they condemn this strategy to relative uselessness. However, information in fingerprints from across an assemblage can be pooled to generate a more accurate depiction of potter demographics. We present a new approach to epidermal ridge density analysis using Bayesian mixture models with the following key benefits:•Age and sex are estimated more accurately than existing methods by incorporating a data-driven understanding of how demographics and ridge density covary.•Uncertainty in demographic estimates is automatically quantified and included in output.•The Bayesian framework can be easily adapted to fit the unique needs of different researchers.

Repetition learning is neither a continuous nor an implicit process

Learning advances through repetition. A classic paradigm for studying this process is the Hebb repetition effect: Immediate serial recall performance improves for lists presented repeatedly as compared to nonrepeated lists. Learning in the Hebb paradigm has been described as a slow but continuous accumulation of long-term memory traces over repetitions [e.g., Page & Norris, Phil. Trans. R. Soc. B 364, 3737-3753 (2009)]. Furthermore, it has been argued that Hebb repetition learning requires no awareness of the repetition, thereby being an instance of implicit learning [e.g., Guérard etal., Mem. Cogn. 39, 1012-1022 (2011); McKelvie, J. Gen. Psychol.114, 75-88 (1987)]. While these assumptions match the data from a group-level perspective, another picture emerges when analyzing data on the individual level. We used a Bayesian hierarchical mixture modeling approach to describe individual learning curves. In two preregistered experiments, using a visual and a verbal Hebb repetition task, we demonstrate that 1) individual learning curves show an abrupt onset followed by rapid growth, with a variable time for the onset of learning across individuals, and that 2) learning onset was preceded by, or coincided with, participants becoming aware of the repetition. These results imply that repetition learning is not implicit and that the appearance of a slow and gradual accumulation of knowledge is an artifact of averaging over individual learning curves.

Identifying sub-populations of cells in single cell transcriptomic data - a Bayesian mixture modelling approach to zero-inflation of counts

Identifying sub-populations of cells in single cell transcriptomic data - a Bayesian mixture modelling approach to zero-inflation of counts

Identifying sub-populations of cells in single cell transcriptomic data - a Bayesian mixture model approach to zero-inflation of counts

Identifying sub-populations of cells in single cell transcriptomic data - a Bayesian mixture model approach to zero-inflation of counts

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 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.

A Hierarchical Bayesian Mixture Model Approach for Analysis of Resting-State Functional Brain Connectivity: An Alternative to Thresholding.

This article proposes a Bayesian hierarchical mixture model to analyze functional brain connectivity where mixture components represent “positively connected” and “non-connected” brain regions. Such an approach provides a data-informed separation of reliable and spurious connections in contrast to arbitrary thresholding of a connectivity matrix. The hierarchical structure of the model allows simultaneous inferences for the entire population as well as for each individual subject. A new connectivity measure, the posterior probability of a given pair of brain regions of a specific subject to be connected given the observed correlation of regions' activity, can be computed from the model fit. The posterior probability reflects the connectivity of a pair of regions relative to the overall connectivity pattern of an individual, which is overlooked in traditional correlation analyses. This article demonstrates that using the posterior probability might diminish the effect of spurious connections on inferences, which is present when a correlation is used as a connectivity measure. In addition, simulation analyses reveal that the sparsification of the connectivity matrix using the posterior probabilities might outperform the absolute thresholding based on correlations. Therefore, we suggest that posterior probability might be a beneficial measure of connectivity compared with the correlation. The applicability of the introduced method is exemplified by a study of functional resting-state brain connectivity in older adults.

A fully Bayesian mixture model approach for identifying noncompliance in a regulatory tobacco clinical trial.

Identifying noncompliance in a randomized trial is challenging, but could be improved by leveraging biomarker data to identify participants that did not comply with their assigned treatment. For randomized trials of very low nicotine content (VLNC) cigarettes, the biomarker of total nicotine equivalents (TNE) could be used to identify noncompliance. Compliant participants should have lower levels of TNEs than participants that did not comply and smoked normal nicotine content cigarettes, resulting in a mixture of compliant and noncompliant participants at each dose level. Thresholds of TNE could then be identified from the compliant groups at each dose level and used to determine which study participants were compliant. Furthermore, proposed biological relationships of TNE with nicotine dose could be incorporated into improve the efficiency of estimation, but may introduce bias if misspecified. To account for multiple modeling assumptions across dose levels, we explore model averaging via reversible jump markov chain monte carlo (MCMC) within each dose level to take advantage of improvements in efficiency when the proposed relationship is true and to downweight the biological model when it is misspecified. In simulation studies, we demonstrate that model averaging in the presence of a correct biological relationship results in a decrease in the mean square error (MSE) of up to 85%, but downweights the model in dose levels where the relationship is not appropriate. We apply our approach to data from a randomized trial of VLNC cigarettes to estimate TNE thresholds and probability of compliance curves as a function of TNEs for each nicotine dose used in the trial.

HALO7D II: The Halo Velocity Ellipsoid and Velocity Anisotropy with Distant Main-sequence Stars

Abstract The Halo Assembly in Lambda Cold Dark Matter: Observations in 7 Dimensions (HALO7D) data set consists of Keck II/DEIMOS spectroscopy and Hubble Space Telescope–measured proper motions of Milky Way halo main-sequence turnoff stars in the CANDELS fields. In this paper, the second in the HALO7D series, we present the proper motions for the HALO7D sample. We discuss our measurement methodology, which makes use of a Bayesian mixture modeling approach for creating the stationary reference frame of distant galaxies. Using the 3D kinematic HALO7D sample, we estimate the parameters of the halo velocity ellipsoid, , and the velocity anisotropy β. Using the full HALO7D sample, we find at kpc. We also estimate the ellipsoid parameters for our sample split into three apparent magnitude bins; the posterior medians for these estimates of β are consistent with one another. Finally, we estimate β in each of the individual HALO7D fields. We find that the velocity anisotropy β can vary from field-to field, which suggests that the halo is not phase-mixed at . We explore the β variation across the skies of two stellar halos from the Latte suite of FIRE-2 simulations, finding that both simulated galaxies show β variation over a range similar to that of the variation observed across the four HALO7D fields. The accretion histories of the two simulated galaxies result in different β variation patterns; spatially mapping β is thus a way forward in characterizing the accretion history of the Galaxy.

Halo mass estimates from the globular cluster populations of 175 low surface brightness galaxies in the Fornax cluster

The halo masses $M_{halo}$ of low surface brightness (LSB) galaxies are critical measurements for understanding their formation processes. One promising method to estimate a galaxy's $M_{halo}$ is to exploit the empirical scaling relation between $M_{halo}$ and the number of associated globular clusters ($N_{\mathrm{GC}}$). We use a Bayesian mixture model approach to measure $N_{\mathrm{GC}}$ for 175 LSB ($23\leq\left\langle \mu_{e,r} \right\rangle [\mathrm{mag\ arcsec}^{-2}]\leq 28$) galaxies in the Fornax cluster using the Fornax Deep Survey (FDS) data; this is the largest sample of low mass galaxies so-far analysed for this kind of study. The proximity of the Fornax cluster means that we can measure galaxies with much smaller physical sizes ($0.3\leq r_{e,r}\ [\mathrm{kpc}]\leq 9.5$) compared to previous studies of the GC systems of LSB galaxies, probing stellar masses down to $M_{*}\sim10^{5}\mathrm{M_{\odot}}$. The sample also includes \nudg\ ultra-diffuse galaxies (UDGs), with projected $r$-band half-light radii greater than 1.5 kpc. Our results are consistent with an extrapolation of the $M_{*}-M_{halo}$ relation predicted from abundance matching. In particular, our UDG measurements are consistent with dwarf sized halos, having typical masses between $10^{10}$ and $10^{11}\mathrm{M_{\odot}}$. Overall, our UDG sample is statistically indistinguishable from smaller LSB galaxies in the same magnitude range. We do not find any candidates likely to be as rich as some of those found in the Coma cluster. We suggest that environment might play a role in producing GC-rich LSB galaxies.

A Bayesian mixture modelling approach for spatial proteomics.

Analysis of the spatial sub-cellular distribution of proteins is of vital importance to fully understand context specific protein function. Some proteins can be found with a single location within a cell, but up to half of proteins may reside in multiple locations, can dynamically re-localise, or reside within an unknown functional compartment. These considerations lead to uncertainty in associating a protein to a single location. Currently, mass spectrometry (MS) based spatial proteomics relies on supervised machine learning algorithms to assign proteins to sub-cellular locations based on common gradient profiles. However, such methods fail to quantify uncertainty associated with sub-cellular class assignment. Here we reformulate the framework on which we perform statistical analysis. We propose a Bayesian generative classifier based on Gaussian mixture models to assign proteins probabilistically to sub-cellular niches, thus proteins have a probability distribution over sub-cellular locations, with Bayesian computation performed using the expectation-maximisation (EM) algorithm, as well as Markov-chain Monte-Carlo (MCMC). Our methodology allows proteome-wide uncertainty quantification, thus adding a further layer to the analysis of spatial proteomics. Our framework is flexible, allowing many different systems to be analysed and reveals new modelling opportunities for spatial proteomics. We find our methods perform competitively with current state-of-the art machine learning methods, whilst simultaneously providing more information. We highlight several examples where classification based on the support vector machine is unable to make any conclusions, while uncertainty quantification using our approach provides biologically intriguing results. To our knowledge this is the first Bayesian model of MS-based spatial proteomics data.

A Bayesian mixture modeling approach for public health surveillance.

SummarySpatial monitoring of trends in health data plays an important part of public health surveillance. Most commonly, it is used to understand the etiology of a public health issue, to assess the impact of an intervention, or to provide detection of unusual behavior. In this article, we present a Bayesian mixture model for public health surveillance, which is able to provide estimates of the disease risk in space and time, and also to detect areas with unusual behavior. The model is designed to deal with a range of spatial and temporal patterns in the data, and with time series of different lengths. We carry out a simulation study to assess the performance of the model under different scenarios, and we compare it against a recently proposed Bayesian model for short time series. Finally, the proposed model is used for surveillance of road traffic accidents data in England over the years 2005–2015.

Characterizing sex ratios of sea turtle populations: A Bayesian mixture modeling approach applied to juvenile loggerheads (Caretta caretta)

Sex ratio is fundamental to the demography of animal populations. For sea turtles, the operational sex ratio (i.e., that of breeding adults) can be inferred from juvenile sex ratio. In this study, we characterize sex ratio of n = 1401 juvenile loggerhead sea turtles (Caretta caretta) sampled from foraging grounds in North Carolina, USA. For a subset (n = 170), sex was confirmed by laparoscopy, and for the remaining individuals, sex was classified probabilistically using a mixture regression model. The model predicted plasma testosterone concentration as a function of sex, which was treated as a latent variable, and of other potential covariates, namely water temperature and carapace length. Furthermore, it quantified uncertainty in the sex classification of each individual. For the full data set, the predicted sex ratio was 81% female. Using the subset of turtles with known sex and a leave-one-out validation approach, we found the model to have classification accuracy of 94%. We further used that subset to examine how many laparoscopies are sufficient for accurate classification of turtles with unknown sex, in an attempt to provide guidance for other studies. We found diminishing returns as sample size increased, and recommend 100–140 turtles as a sufficient range.

Impact of whole-genome duplication events on diversification rates in angiosperms.

Polyploidy or whole-genome duplication (WGD) pervades the evolutionary history of angiosperms. Despite extensive progress in our understanding of WGD, the role of these events in promoting diversification is still not well understood. We seek to clarify the possible association between WGD and diversification rates in flowering plants. Using a previously published phylogeny spanning all land plants (31,749 tips) and WGD events inferred from analyses of the 1000 Plants (1KP) transcriptome data, we analyzed the association of WGDs and diversification rates following numerous WGD events across the angiosperms. We used a stepwise AIC approach (MEDUSA), a Bayesian mixture model approach (BAMM), and state-dependent diversification analyses (MuSSE) to investigate patterns of diversification. Sister-clade comparisons were used to investigate species richness after WGDs. Based on the density of 1KP taxon sampling, 106 WGDs were unambiguously placed on the angiosperm phylogeny. We identified 334-530 shifts in diversification rates. We found that 61 WGD events were tightly linked to changes in diversification rates, and state-dependent diversification analyses indicated higher speciation rates for subsequent rounds of WGD. Additionally, 70 of 99 WGD events showed an increase in species richness compared to the sister clade. Forty-six of the 106 WGDs analyzed appear to be closely associated with upshifts in the rate of diversification in angiosperms. Shifts in diversification do not appear more likely than random within a four-node lag phase following a WGD; however, younger WGD events are more likely to be followed by an upshift in diversification than older WGD events.

Modelling habitat and planning surveillance using Landsat imagery: a case study using Imported Red Fire ants

This paper presents a Bayesian mixture model approach for detecting areas of habitat that are suitable for S. invicta infestation, aiding the ongoing surveillance for early detection of these exotic pests. We show that Landsat imagery is an affordable and valuable tool to assist in determining an informed surveillance strategy. In this paper, we use Landsat band 3 (visible red), Landsat band 6 (mid infrared) and a soil brightness index, in various combinations, to assess the probability that the area associated with each pixel is habitable terrain, either in a multivariate analysis, or as a univariate spatial temporal model. The multivariate analysis allows researchers to create meaningful clusters that reflect the sometimes complex combinations of conditions of conditions that form suitable habitat, rather then relying on single derived indices.