Bayesian Bootstrap Research Articles

Predicting blind-use test (BUT) results from sensory testing using Bayesian bootstrapping

Predicting blind-use test (BUT) results from sensory testing using Bayesian bootstrapping

The Bayesian Phylogenetic Bootstrap, Application to Short Trees and Branches.

Felsenstein's bootstrap is the most commonly used method to measure branch support in phylogenetics. Current sequencing technologies can result in massive sampling of taxa (e.g. SARS-CoV-2). In this case, the sequences are very similar, the trees are short, and the branches correspond to a small number of mutations (possibly 0). Nevertheless, these trees contain a strong signal, with unresolved parts but a low rate of false branches. With such data, Felsenstein's bootstrap is not satisfactory. Due to the frequentist nature of bootstrap sampling, the expected support of a branch corresponding to a single mutation is ∼63%, even though it is highly likely to be correct. Here we propose a Bayesian version of the phylogenetic bootstrap in which sites are assigned uninformative prior probabilities. The branch support can then be interpreted as a posterior probability. We do not view the alignment as a small subsample of a large sample of sites, but rather as containing all available information (e.g., as with complete viral genomes, which are becoming routine). We give formulas for expected supports under the assumption of perfect phylogeny, in both the frequentist and Bayesian frameworks, where a branch corresponding to a single mutation now has an expected support of ∼90%. Simulations show that these theoretical results are robust to realistic data. Analyses on low-homoplasy viral and non-viral datasets show that Bayesian bootstrap support is easier to interpret, with high supports for branches very likely to be correct. As homoplasy increases, the two supports become closer and strongly correlated.

Methodological considerations in calculating the minimal clinically important change score for the core outcome measures index (COMI): insights from a large single-centre spine surgery registry.

The Minimal Clinically Important Change (MCIC) is used in conjunction with Patient-Reported Outcome Measures (PROMs) to determine the clinical relevance of changes in health status. MCIC measures a change within the same person or group over time. This study aims to evaluate the variability in computing MCIC for the Core Outcome Measure Index (COMI) using different methods. Data from a spine centre in Switzerland were used to evaluate variations in MCIC for the COMI score. Distribution-based and anchor-based methods (predictive and nonpredictive) were applied. Bayesian bootstrap estimated confidence intervals. From 27,003 cases, 9821 met the inclusion criteria. Distribution-based methods yielded MCIC values from 0.4 to 1.4. Anchor-based methods showed more variability, with MCIC values from 1.5 to 4.9. Predictive anchor-based methods also provided variable MCIC values for improvement (0.3-2.4), with high sensitivity and specificity. MCIC calculation methods produce varying values, emphasizing careful method selection. Distribution-based methods likely measure minimal detectable change, while non-predictive anchor-based methods can yield high MCIC values due to group averaging. Predictive anchor-based methods offer more stable and clinically relevant MCIC values for improvement but are affected by prevalence and reliability corrections.

Quantifying population-level neural tuning functions using Ricker wavelets and the Bayesian bootstrap

BackgroundExperience changes visuo-cortical tuning. In humans, re-tuning has been studied during aversive generalization learning, in which the similarity of generalization stimuli (GSs) with a conditioned threat cue (CS+) is used to quantify tuning functions. Previous work utilized pre-defined tuning shapes (generalization and sharpening patterns). This approach may constrain the ways in which re-tuning can be characterized since the tuning patterns may not match the prototypical functions. New methodThe present study proposes a flexible and data-driven method for precisely quantifying changes in tuning based on the Ricker wavelet function and the Bayesian bootstrap. This method was applied to EEG and psychophysics data from an aversive generalization learning paradigm. ResultsThe Ricker wavelet model fitted the steady-state visual event potentials (ssVEP), alpha-band power, and detection accuracy data well. A Morlet wavelet function was used for comparison and fit the data better in some situations, but was more challenging to interpret. The pattern of re-tuning in the EEG data, predicted by the Ricker model, resembled the shapes of the best fitting a-priori patterns. Comparison with existing methodsAlthough the re-tuning shape modeled by the Ricker function resembled the pre-defined shapes, the Ricker approach led to greater Bayes factors and more interpretable results compared to a-priori models. The Ricker approach was more easily fit and led to more interpretable results than a Morlet wavelet model. ConclusionThis work highlights the promise of the current method for capturing the precise nature of visuo-cortical tuning, unconstrained by the implementation of a-priori models.

Empirical Inferences Under Bayesian Framework to Identify Cellwise Outliers

Outliers are typically identified using frequentist methods. The data are classified as “outliers” or “not outliers” based on a test statistic that measures the magnitude of the difference between a value and the majority part of the data. The threshold for a data value to be an outlier is typically defined by the user. However, a subjective choice of the threshold increases the uncertainty associated with outlier status for each data value. A cellwise outlier detection algorithm named FuzzyHRT is used to automate the editing process in repeated surveys. This algorithm uses Bienaymé–Chebyshev’s inequality and fuzzy logic to detect four different types of outliers resulting from format inconsistencies, historical, tail, and relational anomalies. However, fuzzy logic is not suited for probabilistic reasoning behind the identification of anomalous cells. Bayesian methods are well suited for quantifying the uncertainty associated with the identification of outliers. Although, as suggested by the literature, there exist well-developed Bayesian methods for record-level outlier detection, Bayesian methods for identifying outliers within individual records (i.e., at the cell level) remain unexplored. This paper presents two approaches from the Bayesian perspective to study the uncertainty associated with identifying outliers. A Bayesian bootstrap approach is explored to study the uncertainty associated with the output scores from the FuzzyHRT algorithm. Empirical likelihoods in a Bayesian setting are also considered for probabilistic reasoning behind the identification of anomalous cells. NASS survey data for livestock and major crop yield (such as corn) are considered for comparing the performances of the two proposed approaches with recent cellwise outlier methods.

Grid-Based Bayesian Bootstrap Approach for Real-Time Detection of Abnormal Vessel Behaviors From AIS Data in Maritime Logistics

Grid-Based Bayesian Bootstrap Approach for Real-Time Detection of Abnormal Vessel Behaviors From AIS Data in Maritime Logistics

Inverse uncertainty quantification for stochastic systems by resampling. Applications to modeling of alcohol consumption and infection by HIV

A random differential equation, or stochastic differential equation with parametric uncertainty, is a classical differential equation whose input values (coefficients, initial conditions, etc.) are random variables. Given data, the probability distributions of the input random parameters must be appropriately inferred, before proceeding to simulate the model’s output. This task is called inverse uncertainty quantification. In this paper, the goal is to study the applicability of the Bayesian bootstrap to draw inferences on the posterior distributions of the parameters, by resampling the residuals of the deterministic least-squares optimization with Dirichlet weights. The method is based on repeated deterministic calibrations. Thus, to alleviate the curse of dimensionality, the technique may be combined with the principle of maximum entropy for densities, when there are some parameters that are not optimized deterministically. For illustration of the methodology, two case studies on important health topics are conducted, with stochastic fitting to data. The first one, on past alcohol consumption in Spain, taking social contagion into account. The second one, on HIV evolution considering CD4+ T cells and viral load, with a patient in clinical follow-up. All these applied models are built from a compartmental viewpoint, with a randomized basic reproduction number that controls the long-term behavior of the system.

Monte Carlo inference for semiparametric Bayesian regression

Data transformations are essential for broad applicability of parametric regression models. However, for Bayesian analysis, joint inference of the transformation and model parameters typically involves restrictive parametric transformations or nonparametric representations that are computationally inefficient and cumbersome for implementation and theoretical analysis, which limits their usability in practice. This paper introduces a simple, general, and efficient strategy for joint posterior inference of an unknown transformation and all regression model parameters. The proposed approach directly targets the posterior distribution of the transformation by linking it with the marginal distributions of the independent and dependent variables, and then deploys a Bayesian nonparametric model via the Bayesian bootstrap. Crucially, this approach delivers (1) joint posterior consistency under general conditions, including multiple model misspecifications, and (2) efficient Monte Carlo (not Markov chain Monte Carlo) inference for the transformation and all parameters for important special cases. These tools apply across a variety of data domains, including real-valued, positive, and compactly-supported data. Simulation studies and an empirical application demonstrate the effectiveness and efficiency of this strategy for semiparametric Bayesian analysis with linear models, quantile regression, and Gaussian processes. The R package SeBR is available on CRAN.

Source analysis of low frequency seismicity at Mt. Vesuvius by a hybrid moment tensor inversion

Seismicity at Mt. Vesuvius has been relatively weak in the last decades. While the occurrence of shallow volcano-tectonic (VT) events at Mt. Vesuvius is well known, the occurrence of deeper low frequency events (LF) was only recently recognized. Previous source studies only targeted VT events, which were found to have quite heterogeneous focal mechanisms. In this paper, we perform for the first time the source inversion of LF seismicity at Mt. Vesuvius, analysing 27 LF events recorded from 2012 to 2021 with the aim to investigate their source processes. Given the challenges of analysing weak LF earthquakes, we implement a specific moment tensor (MT) inversion approach that combines the fit of displacement seismograms in the time domain and amplitude spectra in the frequency domain. The inversion is simultaneously performed for the source depth and moment tensor components in the 2–7 and 2–5 Hz frequency band, assuming either a full or deviatoric MT representation. Source parameter uncertainties are estimated by using a Bayesian bootstrapping scheme. Our results confirm a larger depth of LF events compared to VTs and show a strong heterogeneity of the LF seismic sources, which present various rupture types, different orientations and heterogeneous, whilst poorly resolved, non-double-couple components. The MT variability is qualitatively confirmed by significant differences among the recorded waveforms. The heterogeneity of both VT and LF source processes is attributed to complex source processes in a highly fractured seismogenic volume submitted to a heterogeneous stress field.

An interactive 3D atlas of sentinel lymph nodes in breast cancer developed using SPECT/CT

BackgroundThe identification and assessment of sentinel lymph nodes (SLNs) in breast cancer is important for optimised patient management. The aim of this study was to develop an interactive 3D breast SLN atlas and to perform statistical analyses of lymphatic drainage patterns and tumour prevalence.MethodsA total of 861 early-stage breast cancer patients who underwent preoperative lymphoscintigraphy and SPECT/CT were included. Lymphatic drainage and tumour prevalence statistics were computed using Bayesian inference, non-parametric bootstrapping, and regression techniques. Image registration of SPECT/CT to a reference patient CT was carried out on 350 patients, and SLN positions transformed relative to the reference CT. The reference CT was segmented to visualise bones and muscles, and SLN distributions compared with the European Society for Therapeutic Radiology and Oncology (ESTRO) clinical target volumes (CTVs). The SLN atlas and statistical analyses were integrated into a graphical user interface (GUI).ResultsDirect lymphatic drainage to the axilla level I (anterior) node field was most common (77.2%), followed by the internal mammary node field (30.4%). Tumour prevalence was highest in the upper outer breast quadrant (22.9%) followed by the retroareolar region (12.8%). The 3D atlas had 765 SLNs from 335 patients, with 33.3–66.7% of axillary SLNs and 25.4% of internal mammary SLNs covered by ESTRO CTVs.ConclusionThe interactive 3D atlas effectively displays breast SLN distribution and statistics for a large patient cohort. The atlas is freely available to download and is a valuable educational resource that could be used in future to guide treatment.

Quantifying Population-level Neural Tuning Functions Using Ricker Wavelets and the Bayesian Bootstrap.

Experience changes the tuning of sensory neurons, including neurons in retinotopic visual cortex, as evident from work in humans and non-human animals. In human observers, visuo-cortical re-tuning has been studied during aversive generalization learning paradigms, in which the similarity of generalization stimuli (GSs) with a conditioned threat cue (CS+) is used to quantify tuning functions. This work utilized pre-defined tuning shapes reflecting prototypical generalization (Gaussian) and sharpening (Difference-of-Gaussians) patterns. This approach may constrain the ways in which re-tuning can be characterized, for example if tuning patterns do not match the prototypical functions or represent a mixture of functions. The present study proposes a flexible and data-driven method for precisely quantifying changes in neural tuning based on the Ricker wavelet function and the Bayesian bootstrap. The method is illustrated using data from a study in which university students (n = 31) performed an aversive generalization learning task. Oriented gray-scale gratings served as CS+ and GSs and a white noise served as the unconditioned stimulus (US). Acquisition and extinction of the aversive contingencies were examined, while steady-state visual event potentials (ssVEP) and alpha-band (8-13 Hz) power were measured from scalp EEG. Results showed that the Ricker wavelet model fitted the ssVEP and alpha-band data well. The pattern of re-tuning in ssVEP amplitude across the stimulus gradient resembled a generalization (Gaussian) shape in acquisition and a sharpening (Difference-of-Gaussian) shape in an extinction phase. As expected, the pattern of re-tuning in alpha-power took the form of a generalization shape in both phases. The Ricker-based approach led to greater Bayes factors and more interpretable results compared to prototypical tuning models. The results highlight the promise of the current method for capturing the precise nature of visuo-cortical tuning functions, unconstrained by the exact implementation of prototypical a-priori models.

Strong uniform laws of large numbers for bootstrap means and other randomly weighted sums

This article establishes novel strong uniform laws of large numbers for randomly weighted sums such as bootstrap means. By leveraging recent advances, these results extend previous work in their general applicability to a wide range of weighting procedures and in their flexibility with respect to the effective bootstrap sample size. In addition to the standard multinomial bootstrap and the m-out-of-n bootstrap, our results apply to a large class of randomly weighted sums involving negatively orthant dependent (NOD) weights, including the Bayesian bootstrap, jackknife, resampling without replacement, simple random sampling with over-replacement, independent weights, and multivariate Gaussian weighting schemes. Weights are permitted to be non-identically distributed and possibly even negative. Our proof technique is based on extending a proof of the i.i.d. strong uniform law of large numbers to employ strong laws for randomly weighted sums; in particular, we exploit a recent Marcinkiewicz–Zygmund strong law for NOD weighted sums.

A Network Analysis of Digital Clock Drawing for Command and Copy Conditions.

Graphomotor and time-based variables from the digital Clock Drawing Test (dCDT) characterize cognitive functions. However, no prior publications have quantified the strength of the associations between digital clock variables as they are produced. We hypothesized that analysis of the production of clock features and their interrelationships, as suggested, will differ between the command and copy test conditions. Older adults aged 65+ completed a digital clock drawing to command and copy conditions. Using a Bayesian hill-climbing algorithm and bootstrapping (10,000 samples), we derived directed acyclic graphs (DAGs) to examine network structure for command and copy dCDT variables. Although the command condition showed moderate associations between variables (= 0.34) relative to the copy condition ( = 0.25), the copy condition network had more connections (18/18 versus 15/18 command). Network connectivity across command and copy was most influenced by five of the 18 variables. The direction of dependencies followed the order of instructions better in the command condition network. Digitally acquired clock variables relate to one another but differ in network structure when derived from command or copy conditions. Continued analyses of clock drawing production should improve understanding of quintessential normal features to aid in early neurodegenerative disease detection.

Brothers in arms: the value of coalitions in sanctions regimes

Abstract This paper examines the impact of coalitions on the economic costs of the 2012 Iran and 2014 Russia sanctions. By estimating and simulating a quantitative general equilibrium trade model under different coalition setups, we (1) dissect welfare losses for sanctions senders and target; (2) compare prospective coalition partners; (3) investigate ‘optimal’ coalitions that maximize payoff from sanctions; (4) provide bounds for sanctions potential, that is, the maximum welfare change attainable when sanctions are scaled vertically up to an embargo, and horizontally up to a global regime. Relative to unilateral action, we find that coalitions magnify welfare losses imposed while their impact on domestic welfare loss incurred depends on the design and sectoral dimension of sanctions. Hypothetical cooperation of large developing economies such as China additionally raises the deterrent force of coalitions. Additionally, we quantify transfers that equalize welfare losses across coalition members to further demonstrate asymmetries in the relative economic burden of sanctions. In all scenarios, we implement a novel Bayesian bootstrap procedure that generates confidence bands for simulation outcomes.

Comparison of estimation and prediction methods for a zero-inflated geometric INAR(1) process with random coefficients

This study explores zero-inflated count time series models used to analyze data sets with characteristics such as overdispersion, excess zeros, and autocorrelation. Specifically, we investigate the ZIGINAR RC ( 1 ) process, a first-order stationary integer-valued autoregressive model with random coefficients and a zero-inflated geometric marginal distribution. Our focus is on examining various estimation and prediction techniques for this model. We employ estimation methods, including Whittle, Taper Spectral Whittle, Maximum Empirical Likelihood, and Sieve Bootstrap estimators for parameter estimation. Additionally, we propose forecasting approaches, such as median, Bayesian, and Sieve Bootstrap methods, to predict future values of the series. We assess the performance of these methods through simulation studies and real-world data analysis, finding that all methods perform well, providing 95% highest predicted probability intervals that encompass the observed data. While Bayesian and Bootstrap methods require more time for execution, their superior predictive accuracy justifies their use in forecasting.

Spatial patterns of β-diversity under cumulative pressures in the Western Mediterranean Sea

Understanding the spatial dynamics of biodiversity is an essential issue in marine ecology and requires combining information at local and regional scales. β-diversity is an important measure of biodiversity that informs on the differences in community composition between sites and, thus, in the species turnover in the community structure. In this study, we analysed and predicted the spatial patterns of β-diversity for fishes, invertebrates and the demersal assemblage along the Iberian Mediterranean coast. We used Bayesian Bootstrap Generalized Dissimilarity Models (BBGDMs) to study the effects of environment and human pressures on the β-diversity of invertebrate, fishes and the entire demersal assemblage from 1994 to 2015 using different time windows to account for temporal variability. Then, we used these relationships to predict the spatial patterns of β-diversity in the whole Iberian Mediterranean coast. Our results highlighted that the regional spatial patterns of β-diversity were best described by bathymetry and a cumulative index of coastal impacts. We identified specific regions with the highest β-diversity in the study area, which were complementary to hotspots of species richness and presented different degree of overlapping with existent marine protected areas. Overall, our study illustrates that by modelling spatial turnover using β-diversity we can better understand and predict spatial variation of biodiversity and the effects of particular variables, providing relevant information to end-users and policy makers for designing specific spatial conservation and management strategies.

New mycoparasitic species in the genera Niveomyces and Pseudoniveomyces gen. nov. (Hypocreales: Cordycipitaceae), with sporothrix-like asexual morphs, from Thailand-SUPP

Supplementary files:<br />Fig. S1. The best phylogenetic tree from Bayesian inference based on ITS. The statistical support values, namely Bayesian posterior probability (PP; > 0.70) and maximum likelihood-based bootstrap (BS; > 70 %), are shown above the nodes (PP/BS).<br />Fig. S2. The best phylogenetic tree from Bayesian inference based on LSU. The statistical support values, namely Bayesian posterior probability (PP; > 0.70) and maximum likelihood-based bootstrap (BS; > 70 %), are shown above the nodes (PP/BS).<br />Fig. S3. The best phylogenetic tree from Bayesian inference based on TEF1. The statistical support values, namely Bayesian posterior probability (PP; > 0.70) and maximum likelihood-based bootstrap (BS; > 70 %), are shown above the nodes (PP/BS).<br />Fig. S4. The best phylogenetic tree from Bayesian inference based on RPB1. The statistical support values, namely Bayesian posterior probability (PP; > 0.70) and maximum likelihood-based bootstrap (BS; > 70 %), are shown above the nodes (PP/BS).<br />Fig. S5. The best phylogenetic tree from Bayesian inference based on RPB2. The statistical support values, namely Bayesian posterior probability (PP; > 0.70) and maximum likelihood-based bootstrap (BS; > 70 %), are shown above the nodes (PP/BS).

Parametric Bootstrap Confidence Interval Estimation for the Percentile and Difference between the Percentiles of Delta-Lognormal Distributions with Application to Rainfall Data in Thailand

In Thailand, flooding often occurs during the summer monsoon when many tropical storms affect the country. The motivation of this study was to plan for and mitigate the damage caused by flooding in the future. The confidence interval (CI) for the percentile of a precipitation dataset can be used to estimate the intensity of rainfall in a particular area whereas the CI for the difference between the percentiles of two datasets can be used to compare the rainfall intensities in two areas. To this end, the performances of several approaches to estimate the CI for the percentile and difference between the percentiles of delta-lognormal distributions were constructed and compared. These estimates were constructed based on the Bayesian (BS) and parametric bootstrap (PB) approaches, as well as two fiducial generalized confidence interval (FGCI) approaches. The performances of the methods were evaluated using Monte Carlo simulation, the results of which indicate that the PB approach for both CIs performed the best in all scenarios tested. Its suitability was confirmed via two illustrative examples using daily rainfall datasets for Chiang Mai and Lampang provinces in Thailand.

Sex-based differences in odds of motor vehicle crash injury outcomes

ObjectiveSeveral studies have documented the relative risk or odds of injury and fatality for females versus males in motor vehicle crashes (Parenteau et al. 2013, Forman et al. 2019, Brumbelow and Jermakian, 2022; Noh et al. 2022). Though, none combined National Automotive Sampling System–Crashworthiness Data System (NASS-CDS) and Crash Investigation Sampling System (CISS). The aim of this study was to document the relative odds of various injury outcomes for females versus males while considering a broad range of crash types, pre-crash and crash variables, and occupant characteristics. MethodsMultivariable logistic regression was carried out to study the odds of injury for females versus males. A select imputation method (Hot Deck, Approximate Bayesian Bootstrap) was applied as part of efforts to create multivariable logistic regression models for 25 different injury outcomes associated with occupants (age 13 years and older) involved in passenger vehicle crashes published in NASS-CDS (2000 to 2015) and CISS (2017–2021). Both pre-crash (n=7) and crashworthiness (n=22) predictor variables were considered, but only significant variables at p≤0.10 level were retained in final models. Six crash-type models were produced for each injury outcome; one that included all crashes, one for each of four different planar crash types (frontal, near-side, far-side, rear), and one for crashes involving rollover. These six sets of crash-type models were expanded further to include a model version that included both pre-crash/environment and crashworthiness predictor variables and one model limited to crashworthiness predictors only. Different than other recent studies, all crash types, occupant restraint conditions, and seating positions were considered. Occupant sex was retained in all models to facilitate female versus male injury outcome odds ratio (OR) assessments. ResultsFemale versus male injury OR estimates for 300 unique models are presented. Females had significantly higher odds of injury than males in 36 models (OR>1.0, p-value ≤0.05). This contrasts with 43 models where females had significantly lower odds (OR<1.0, p≤0.05). For the remaining 221 models, there was a near even split in how often the odds of injury were non-significantly higher (n=103) and non-significantly lower (n=114) for females as compared to males (p>0.05). In four cases, the OR estimate was 1.00. Amongst the results, there was a trend for females to have higher odds of AIS 2+ injuries (MAIS 2+ OR=1.75 and 1.69 for Full and Crashworthiness models, respectively for the All Crashes dataset). These increases included higher estimates for lower extremity injuries in frontal crashes, consistent with earlier studies (e.g., Forman et al. 2019). However, for certain AIS 2+ (neck, thorax) and AIS 3+ injuries (head, neck, thorax), females had significantly lower odds of injury (p≤0.05). The trends for reduced odds of injury for females were most prevalent in non-frontal crash models.

Embedded multilevel regression and poststratification: Model-based inference with incomplete auxiliary information.

Health disparity research often evaluates health outcomes across demographic subgroups. Multilevel regression and poststratification (MRP) is a popular approach for small subgroup estimation as it can stabilize estimates by fitting multilevel models and adjust for selection bias by poststratifying on auxiliary variables, which are population characteristics predictive of the analytic outcome. However, the granularity and quality of the estimates produced by MRP are limited by the availability of the auxiliary variables' joint distribution; data analysts often only have access to the marginal distributions. To overcome this limitation, we embed the estimation of population cell counts needed for poststratification into the MRP workflow: embedded MRP (EMRP). Under EMRP, we generate synthetic populations of the auxiliary variables before implementing MRP. All sources of estimation uncertainty are propagated with a fully Bayesian framework. Through simulation studies, we compare different methods of generating the synthetic populations and demonstrate EMRP's improvements over alternatives on the bias-variance tradeoff to yield valid subpopulation inferences of interest. We apply EMRP to the Longitudinal Survey of Wellbeing and estimate food insecurity prevalence among vulnerable groups in New York City. We find that all EMRP estimators can correct for the bias in classical MRP while maintaining lower standard errors and narrower confidence intervals than directly imputing with the weighted finite population Bayesian bootstrap (WFPBB) and design-based estimates. Performances from the EMRP estimators do not differ substantially from each other, though we would generally recommend using the WFPBB-MRP for its consistently high coverage rates.