Marginal Probability Research Articles

A Partitioned Poisson Multi-Bernoulli Filter

The Poisson multi-Bernoulli (PMB) filter offers an elegant Bayesian formulation for multi-target tracking by approximating the complex PMBM density as a PMB density. This approximation allows for more efficient computation and simpler implementation while maintaining reasonable accuracy. However, approximating the posterior density involves a certain degree of tracking accuracy loss, and different approximation methods may result in different types of tracking accuracy losses. To address this problem, this paper proposes a partitioned PMB (PPMB) filter that decomposes the multi-target tracking problem to smaller sub-problems, which can synthesize the advantages of different approximations to avoid tracking accuracy loss. Furthermore, to address the issue of tracking lost for close-spaced and undetected targets, an improved measurement oriented multi-Bernoulli Poisson (IMOMB/P) filter is also proposed, which utilizes more accurate marginal association probabilities. Simulation results demonstrate that the proposed PPMB filter outperforms existing PMB filters, such as the MOMB/P and track oriented multi-Bernoulli (TOMB) filters, thus showing promising application prospects.

The protective role of postoperative radiation therapy in low and intermediate grade major salivary gland malignancies: A study of the Canadian Head and Neck Collaborative Research Initiative.

The objective of this study was to examine the utility of postoperative radiation for low and intermediate grade cancers of the parotid and submandibular glands. The authors conducted a retrospective, Canadian-led, international, multi-institutional analysis of a patient cohort with low or intermediate grade salivary gland cancer of the parotid or submandibular gland who were treated from 2010 until 2020 with or without postoperative radiation therapy. A multivariable, marginal Cox proportional hazards regression analysis was performed to quantify the association between locoregional recurrence (LRR) and receipt of postoperative radiation therapy while accounting for patient-level factors and the clustering of patients by institution. In total, 621 patients across 14 tertiary care centers were included in the study; of these, 309 patients (49.8%) received postoperative radiation therapy. Tumor histologies included 182 (29.3%) acinic cell carcinomas, 312 (50.2%) mucoepidermoid carcinomas, and 137 (20.5%) other low or intermediate grade primary salivary gland carcinomas. Kaplan-Meier LRR-free survival at 10years was 89.0% (95% confidence interval [CI], 84.9%-93.3%). In multivariable Cox regression analysis, postoperative radiation therapy was independently associated with a lower hazard of LRR (adjusted hazard ratio, 0.53; 95% CI, 0.29-0.97). The multivariable model estimated that the marginal probability of LRR within 10years was 15.4% without radiation and 8.8% with radiation. The number needed to treat was 16 patients (95% CI, 14-18 patients). Radiation therapy had no benefit in patients who had early stage, low-grade salivary gland cancer without evidence of nodal disease and negative margins. Postoperative radiation therapy may reduce LLR in some low and intermediate grade salivary gland cancers with adverse features, but it had no benefit in patients who had early stage, low-grade salivary gland cancer with negative margins.

Multi-Modality Fusion & Inductive Knowledge Transfer Underlying Non-Sparse Multi-Kernel Learning and Distribution Adaption.

With the development of sensors, more and more multimodal data are accumulated, especially in biomedical and bioinformatics fields. Therefore, multimodal data analysis becomes very important and urgent. In this study, we combine multi-kernel learning and transfer learning, and propose a feature-level multi-modality fusion model with insufficient training samples. To be specific, we firstly extend kernel Ridge regression to its multi-kernel version under the lp-norm constraint to explore complementary patterns contained in multimodal data. Then we use marginal probability distribution adaption to minimize the distribution differences between the source domain and the target domain to solve the problem of insufficient training samples. Based on epilepsy EEG data provided by the University of Bonn, we construct 12 multi-modality & transfer scenarios to evaluate our model. Experimental results show that compared with baselines, our model performs better on most scenarios.

On the Fence: The Impact of Education on Support for Electric Fencing to Prevent Conflict between Humans and Baboons in Kommetjie, South Africa.

Few studies test whether education can help increase support for wildlife management interventions. This mixed methods study sought to test the importance of educating a community on the use of a baboon-proof electric fence to mitigate negative interactions between humans and Chacma baboons (Papio ursinus) in a residential suburb of the City of Cape Town, South Africa. An educational video on the welfare, conservation and lifestyle benefits of a baboon-proof electric fence was included in a short online survey. The positioning of the video within the survey was randomised either to fall before or after questions probing the level of support for an electric fence. The results showed that watching the video before most survey questions increased the average marginal probability of supporting an electric fence by 15 percentage points. The study also explored whether the educational video could change people's minds. Those who saw the video towards the end of the survey were questioned again about the electric fence. Many changed their minds after watching the video, with support for the fence increasing from 36% to 50%. Of these respondents, the results show that being female raised the average marginal probability of someone changing their mind in favour of supporting the fence by 19%. Qualitative analysis revealed that support for or against the fence was multi-layered and that costs and concern for baboons were not the only relevant factors influencing people's choices. Conservation often needs to change people's behaviours. We need to know what interventions are effective. We show in the real world that an educational video can be effective and can moderately change people's opinions and that women are more likely to change their position in light of the facts than men. This study contributes to the emerging literature on the importance of education in managing conservation conflicts and the need for evidence-based interventions.

Математичне моделювання стохастичної динаміки взаємодії студентів різних спеціальностей в процесі інтегрованого навчання

The article proposes the concept of assessing the level of optimal load modes in terms of tasks (flow of tasks) for two groups of students in the process of integrated education in the specialty 126 "Information systems and technologies" and specialty 022 "Web design", by using the toolkit of Markov chains and equations Kolmogorov. The proposed approach allows you to reproduce the dynamics of states and the results of the mutual influence of two social groups, which are represented by a contingent of students in the context of processing the flow of tasks. Possible options for research may include comparing the level of productivity of each group, the influence of factors affecting their work, as well as the calculation of probabilities of states of social groups over time and marginal probabilities.

Polynomial Propagation of Moments in Stochastic Differential Equations

We address the problem of approximating the moments of the solution, , of an Itô stochastic differential equation (SDE) with drift and diffusion terms over a time grid . In particular, we assume an explicit numerical scheme for the generation of sample paths and then obtain recursive equations that yield any desired noncentral moment of as a function of the initial condition . The core of the methodology is the decomposition of the numerical solution into a “central part” and an “effective noise” term. The central term is computed deterministically from the ordinary differential equation (ODE) that results from eliminating the diffusion term in the SDE, while the effective noise accounts for the stochastic deviation from the numerical solution of the ODE. For simplicity, we describe the proposed methodology based on an Euler–Maruyama integrator, but other explicit numerical schemes can be exploited in the same way. We also apply the moment approximations to construct estimates of the 1-dimensional marginal probability density functions of based on a Gram–Charlier expansion. Both for the approximation of moments and 1-dimensional densities, we describe how to handle the cases in which the initial condition is fixed (i.e., for some deterministic and known ) or random. In the latter case, we resort to polynomial chaos expansion (PCE) schemes in order to approximate the target moments. The methodology has been inspired by the PCE and differential algebra methods used for uncertainty propagation in astrodynamics problems. Hence, we illustrate its application for the quantification of uncertainty in a 2-dimensional Keplerian orbit perturbed by a Wiener noise process.

Income gradient in psychotherapy use and psychotropic drug purchases: A longitudinal register study in Finnish employed population

ObjectiveWe examined the income gradient changes in the use of long-term rehabilitative psychotherapy and psychotropic drug purchases in men and women during a 9-year follow-up. MethodsWe used register data from a random sample of the working-age population (18–64 years) with information on annual income, psychotherapy use and psychotropic drug purchases from 2011 to 2019 (N = 736 613, 49.7% women). Sex-stratified generalized estimating equations logistic regression models with predicted marginal probabilities were used to examine change in the treatment use rates over time for income quartiles. ResultsTreatment rates increased during the follow-up, with men having lower rates than women. There were no significant differences in psychotherapy use rates between the income quartiles during the follow-up in men. A small income gradient in women (the wealthiest group with the highest use rate) remained stable throughout the follow-up. As for psychotropic drug purchases, the rates increased more among the poorest income quartile compared to the wealthiest quartile in both men and women. In the last year of the follow-up, the initial income gradient (wealthiest group having the highest psychotropic drug purchase rate) had become reversed, and the poorest group had the highest psychotropic drug purchase rate. ConclusionIn psychotherapy use, no income gradient was found in men, while a stable income gradient was found in women. Psychotropic drug purchases have previously been more common in the wealthiest groups, but more recently among the poorest. The findings indicate that gender and income have distinct relationships with the treatment modality over time.

Prediction and Mapping of Intraprostatic Tumor Extent with Artificial Intelligence

BackgroundMagnetic resonance imaging (MRI) underestimation of prostate cancer extent complicates the definition of focal treatment margins. ObjectiveTo validate focal treatment margins produced by an artificial intelligence (AI) model. Design, setting, and participantsTesting was conducted retrospectively in an independent dataset of 50 consecutive patients who had radical prostatectomy for intermediate-risk cancer. An AI deep learning model incorporated multimodal imaging and biopsy data to produce three-dimensional cancer estimation maps and margins. AI margins were compared with conventional MRI regions of interest (ROIs), 10-mm margins around ROIs, and hemigland margins. The AI model also furnished predictions of negative surgical margin probability, which were assessed for accuracy. Outcome measurements and statistical analysisComparing AI with conventional margins, sensitivity was evaluated using Wilcoxon signed-rank tests and negative margin rates using chi-square tests. Predicted versus observed negative margin probability was assessed using linear regression. Clinically significant prostate cancer (International Society of Urological Pathology grade ≥2) delineated on whole-mount histopathology served as ground truth. Results and limitationsThe mean sensitivity for cancer-bearing voxels was higher for AI margins (97%) than for conventional ROIs (37%, p < 0.001), 10-mm ROI margins (93%, p = 0.24), and hemigland margins (94%, p < 0.001). For index lesions, AI margins were more often negative (90%) than conventional ROIs (0%, p < 0.001), 10-mm ROI margins (82%, p = 0.24), and hemigland margins (66%, p = 0.004). Predicted and observed negative margin probabilities were strongly correlated (R2 = 0.98, median error = 4%). Limitations include a validation dataset derived from a single institution's prostatectomy population. ConclusionsThe AI model was accurate and effective in an independent test set. This approach could improve and standardize treatment margin definition, potentially reducing cancer recurrence rates. Furthermore, an accurate assessment of negative margin probability could facilitate informed decision-making for patients and physicians. Patient summaryArtificial intelligence was used to predict the extent of tumors in surgically removed prostate specimens. It predicted tumor margins more accurately than conventional methods.

Non-parametric simulation of random field samples from incomplete measurements using generative adversarial networks

ABSTRACT Random field theory is an effective tool for modelling spatial or temporal variability and uncertainty in natural phenomena, and it has been widely applied in many areas such as structural dynamics, geology, hydrology, and meteorology. Conventional methods of random field simulations are often parametric, in which explicit function forms for trend function, auto-correlation function, and marginal probability density function (PDF) should be selected, together with their corresponding parameters estimated from measurements. Complete random field measurements with many data points are indispensable for selection of the appropriate function forms and accurate estimates of their corresponding parameters. However, the measurements in practice are often incomplete. Without sufficient measurement data, the random field samples (RFSs) generated by conventional methods might contain unexpected uncertainty and might be misleading. To tackle this problem, a purely non-parametric random field simulation method is developed in this study that generates RFSs directly from incomplete measurement data using generative adversarial networks (GAN). Statistical analysis is performed to estimate statistical properties from the generated RFSs, including mean, standard deviation (SD), autocovariance function (AF), and cumulative density function (CDF). The results show that the proposed method properly simulates RFSs from incomplete measurement data in a purely data-driven manner.

Fruit and vegetable consumption across population segments: evidence from a national household survey

BackgroundThe 2002 World Health Report documented that low fruit and vegetable intake are among the top ten risk factors contributing to attributable mortality and up to three million lives could be saved each year by adequate consumption of F&V across the globe, leading an examination of behavioral preferences of the individual and family social, environmental, and behavioral factors that constitute perceived barriers to fruit and vegetable consumption.ObjectiveThe study examines factors affecting the choice of eating fruits and vegetables by household members and calculates eating frequency probabilities of different population-origin associated with personal attributes and behavior.MethodTurkish Health Survey (THS) 2019 data from the Turkish Statistical Institute (TSI) national representative household panel is applied. Estimating a random-effect bivariate probit model of fruit and vegetable choice, we calculated marginal probabilities of choosing fruits and vegetables, the joint probability of choosing both, and conditional probabilities between choosing to eat either, detecting consumption synergy.ResultsThe role of uncontrolled variables in choosing to eat fruits and vegetable (F&V) differs between the decision of an average family and the decision of individual family members. The attitude is positive for an average family and contrasts with the negative attitude among some family members. Most individual and family attributes inversely affect fruit and vegetable choice across different groups, while a positive relationship exists between the likelihood of fruit and vegetable choice and attributes such as age, marital status, education, weight, having health insurance, income, and time and forms of physical activity.Conclusion and recommendationInstead of a general policy for the implementation of a healthy and balanced nutrition program to improve fruit and vegetable eating frequency, it appears more effective to adopt programs with distinct characteristics that segregate society into different cohorts. We suggest appropriate policies and offer suitable approaches to reach targeted groups.

Joint trans-dimensional inversion for water-column sound speed and seabed geoacoustic models.

This letter considers joint estimation of the water-column sound-speed profile (SSP) and seabed geoacoustic model through Bayesian inversion of ocean-acoustic data. The inversion is formulated in terms of separate trans-dimensional models for the water column (as an unknown number of nodes of a piecewise-continuous SSP) and seabed (as an unknown number of uniform layers) to intrinsically parameterize each according to the information content of the data. The inversion estimates marginal posterior probability profiles, quantifying the resolution of water-column and seabed structure. To validate the proposed method, modal-dispersion data from the New England Mud Patch, collected using hand-deployable systems, are considered.

Artificial Bee Colony Based Iterative Heuristic Signal Detection Technique for Optical Wireless Communications

In this paper, we consider a problem of optical signal detection and present a novel artificial bee colony (ABC) based heuristic approach for optical spectrum sensing in a free-space optical wireless network that overcomes channel impairment due to noise uncertainty. In particular, we propose a generic ABC-based optimization framework in conjunction with eigenvalue-based detection (EVD). The uniqueness of the proposed algorithm is that it is executed iteratively by comparing various local solutions until an optimum solution is obtained. The channel is characterized as correlated multivariate fading and the received signal is quantified as a continuous waveform wideband detector. We derive the joint statistic of the correlated multivariate channel fading in the multiple-input multiple-output (MIMO) optical network. Subsequently, the marginal probability density function of the channel coefficients is obtained. For comparison purposes with existing optical spectrum sensing techniques, noise uncertainty is considered. It is demonstrated from simulations that the proposed ABC-EVD spectrum sensing yields performance improvement and the analytical results derived are verified. From the comparative study, it is also found that the proposed scheme outperforms existing optical spectrum sensing techniques, particularly in a regime of low signal-to-noise ratio. When compared to EVD, it is shown that, at a received signal-to-noise ratio of -15 dB, the performance gain achieved in terms of the probability of detection is 15% higher over the entire range of target probability of false alarm. When compared with the ED technique, the proposed technique outperforms it with approximately 50% higher probability of detection at the noise uncertainty of 1 dB and received SNR of -10 dB. The proposed algorithm offers fast convergence, strong robustness, and high flexibility.

Maximum entropy copula for bivariate drought analysis

Copula functions are widely used to derive multivariate probability distributions in hydrometeorology. One of the key steps in the copula method is the derivation of marginal distributions of individual variables which can be accomplished using the principle of maximum entropy where the distribution parameters are estimated from the specified constraints. This study, investigated two drought variables (severity and duration) by coupling the principle of maximum entropy with parametric and empirical copulas. So, homogeneous climatic zones were first identified by applying the fuzzy clustering method to data from 39 synoptic stations in Iran and then drought severity and duration were determined with the standardized precipitation index. These two variables were scaled and their marginal probability distribution functions were derived using the principle of maximum entropy as well as empirically. Then, the joint probability distribution of drought severity and duration was determined using maximum entropy-copula, and parametric and empirical copulas. Thereafter, bivariate conditional return periods were determined for each homogeneous region. Results showed that 1) univariate and bivariate distributions can be obtained by maximizing entropy; 2) the dependence structure via Spearman's rho, which directly affects the Lagrange parameters of entropy copula, was a controlling factor to optimize the objective function; 3) for a given set of constraints, the maximum entropy copula is independent of the types of marginals; 4)The entropy-entropy copula (with entropy marginals) is considered a better method than alternatives, because it has a similar result to the parametric methods while it only needs to fit a single model.

Multiple testing with covariate adjustment in experimental economics

SummaryThis paper provides a framework for testing multiple null hypotheses simultaneously using experimental data in which simple random sampling is used to assign treatment status to units. Using general results from the multiple testing literature, we develop under weak assumptions a procedure that (i) asymptotically controls the familywise error rate—the probability of one or more false rejections—and (ii) is asymptotically balanced in that the marginal probability of rejecting any true null hypothesis is approximately equal in large samples. Our procedure improves upon classical methods by incorporating information about the joint dependence structure of the test statistics when determining which null hypotheses to reject, leading to gains in power. An important point of departure from prior work is that we exploit observed, baseline covariates to obtain further gains in power. The precise way in which we incorporate these covariates is based on recent results from the statistics literature in order to ensure that inferences are typically more powerful in large samples.

A statistical moment-based spectral approach to the chance-constrained stochastic optimal control of epidemic models

This paper presents a spectral approach to the uncertainty management in epidemic models through the formulation of chance-constrained stochastic optimal control problems. Specifically, a statistical moment-based polynomial expansion is used to calculate surrogate models of the stochastic state variables of the problem that allow for the efficient computation of their main statistics as well as their marginal and joint probability density functions at each time instant, which enable the uncertainty management in the epidemic model. Moreover, the surrogate models are employed to perform the corresponding sensitivity and risk analyses. The proposed methodology provides the designers of the optimal control policies with the capability to increase the predictability of the outcomes by adding suitable chance constraints to the epidemic model and formulating a proper cost functional. The chance-constrained optimal control of a COVID-19 epidemic model is considered in order to illustrate the practical application of the proposed methodology.

Discussion of “Specifying prior distributions in reliability applications”

Discussion of “Specifying prior distributions in reliability applications”

The use of transesophageal echocardiography to predict surgical complexity scoring system for degenerative mitral valve repair.

For severe mitral valve (MV) degenerative disease, repair is recommended. Prediction of repair complexity and referral to high volume centers can increase rates of successful repair. This study sought to demonstrate that TEE is a feasible imaging modality to predict the complexity of surgical MV repair. Two hundred TEE examinations of patients who underwent MV repair (2009-2011) were retrospectively reviewed and scored by two cardiac anesthesiologists. TEE scores were compared to surgical complexity scores, which were previously assigned based on published methods. Kappa values were reported for the agreement of TEE and surgical scores. McNemar's tests were used to test the homogeneity of the marginal probabilities of different scoring categories. TEE scores were slightly lower (2[1,3]) than surgical scores (3[1,4]). The agreement was 66% between the scoring methods, with a moderate kappa (.46). Using surgical scores as the gold standard, 70%, 71%, and 46% of simple, intermediate and complex surgical scores, respectively, were correctly scored by TEE. P1, P2, P3, and A2 prolapse were easiest to identify with TEE and had the highest agreement with surgical scoring (P1 agreement 79% with kappa .55, P2 96% [kappa .8], P3 77% [kappa .51], A2 88% [kappa .6]). The lowest agreement between the two scores occurred with A1 prolapse (kappa .05) and posteromedial commissure prolapse (kappa .14). In the presence of significant disagreement, TEE scores were more likely to be of higher complexity than surgical. McNemar's test was significant for prolapse of P1 (p=.005), A1 (p=.025), A2 (p=.041), and the posteromedial commissure (p<.0001). TEE-based scoring is feasible for prediction of the complexity of MV surgical repair, thus allowing for preoperative stratification.

Generalization of Cointegration Arbitrage Based on GARCH Model, Improved by Marginal Probability Distribution

As the Russia Ukraine War broke out in February, 2022, a series of international sanctions led to a panic among international hot moneys and slumps in global stock markets. For such a volatile market, hedging strategy is in a position to avoid risks. In finance, the correlation among financial derivative is always a topical issue and investors are concerned about the statistical methods to model the volatility. Recent years, the rapid development in data science makes it possible to record and manipulate massive data of financial derivative series, of which activates statistical arbitrage, a hedging strategy by pairs trading. The most widespread method in practice is cointegration arbitrage and many experiments show that it can always generate positive profits. This paper introduces the backgrounds of statistical arbitrage and relative definitions in cointegration arbitrage like time series, stationary, autocorrelation process, integration and cointegration. Based on the features of financial derivative series, this paper also illustrates error correction model, ARCH model and GARCH model. Finally, this paper shows the current strategy of cointegration arbitrage and raises some improvement by marginal probability distribution.

Distributions of random variables involved in discrete censored δ-shock models

AbstractSuppose that a system is affected by a sequence of random shocks that occur over certain time periods. In this paper we study the discrete censored $\delta$ -shock model, $\delta \ge 1$ , for which the system fails whenever no shock occurs within a $\delta$ -length time period from the last shock, by supposing that the interarrival times between consecutive shocks are described by a first-order Markov chain (as well as under the binomial shock process, i.e., when the interarrival times between successive shocks have a geometric distribution). Using the Markov chain embedding technique introduced by Chadjiconstantinidis et al. (Adv. Appl. Prob.32, 2000), we study the joint and marginal distributions of the system’s lifetime, the number of shocks, and the number of periods in which no shocks occur, up to the failure of the system. The joint and marginal probability generating functions of these random variables are obtained, and several recursions and exact formulae are given for the evaluation of their probability mass functions and moments. It is shown that the system’s lifetime follows a Markov geometric distribution of order $\delta$ (a geometric distribution of order $\delta$ under the binomial setup) and also that it follows a matrix-geometric distribution. Some reliability properties are also given under the binomial shock process, by showing that a shift of the system’s lifetime random variable follows a compound geometric distribution. Finally, we introduce a new mixed discrete censored $\delta$ -shock model, for which the system fails when no shock occurs within a $\delta$ -length time period from the last shock, or the magnitude of the shock is larger than a given critical threshold $\gamma &gt;0$ . Similarly, for this mixed model, we study the joint and marginal distributions of the system’s lifetime, the number of shocks, and the number of periods in which no shocks occur, up to the failure of the system, under the binomial shock process.

Causal relationships between the gut microbiome, blood lipids, and heart failure: a Mendelian randomization analysis.

Studies have linked gut microbiome and heart failure (HF). However, their causal relationships and potential mediating factors have not been well defined. To investigate the causal relationships between the gut microbiome and HF and the mediating effect of potential blood lipids by using genetics. We performed a bidirectional and mediation Mendelian randomization (MR) study using summary statistics from the genome-wide association studies of gut microbial taxa (Dutch Microbiome Project, n = 7,738), blood lipids (UK Biobank, n = 115,078), and a meta-analysis of HF (115,150 cases and 1,550,331 controls). We applied the inverse-variance weighted estimation method as the primary method, with several other estimators as complementary methods. The multivariable MR approach based on Bayesian model averaging (MR-BMA) was used to prioritize the most likely causal lipids. Six microbial taxa are suggestively associated with HF causally. The most significant taxon was the species Bacteroides dorei (odds ratio = 1.059, 95% confidence interval [CI] = 1.022 - 1.097, P value = 0.0017). The MR-BMA analysis showed that apolipoprotein B (ApoB) was the most likely causal lipid for HF (the marginal inclusion probability = 0.717, P value = 0.005). The mediation MR analysis showed that ApoB mediated the causal effects of species Bacteroides dorei on HF (proportion mediated = 10.1%, 95% CI = 0.2% - 21.6%, P value = 0.031). The study suggested a causal relationship between specific gut microbial taxa and HF and that ApoB might mediate this relationship as the primary lipid determinant of HF.