Parameter Inference Research Articles

Modelling Role of Protective and Nonprotective HLA Allele Inducing Different HIV Infection Outcomes

Human immunodeficiency virus (HIV) infects CD4+ cells and causes progressive immune function failure, and CD8+ cells lyse infected CD4+ cell via recognising peptide presented by human leukocyte antigens (HLA). Variations in HLA allele lead to observed different HIV infection outcomes. Within-host HIV dynamics involves virus replication within infected cells and lysing of infected cells by CD8+ cells, but how variations in HLA alleles determine different infection outcomes was far from clear. Here, we used mathematical modelling and parameter inference with a new analysis of published virus inhibition assay data to estimate CD8+ cell lysing efficiency, and found that lysing efficiency fall in the gap between low bound (0.1–0.2 day−1 (Elemans et al. in PLoS Comput Biol 8(2):e1002381, 2012)) and upper boundary (6.5–8.4 day−1 (Wick et al. in J Virol 79(21):13579–13586, 2005)). Our outcomes indicate that both lysing efficiency and viral inoculum size jointly determine observed different infection outcomes. Low lysing rate associated with non-protective HLA alleles leads to monostable viral kinetic to high viral titre and oscillatory viral kinetics. High lysing rate associated with protective HLA alleles leads monostable viral kinetic to low viral titre and bistable viral kinetics; at a specific interval of CD8+ cell counts, small viral inoculum sizes are inhibited but not large viral inoculum sizes remain infectious. Further, with CD8+ cell recruitment, HIV kinetics always exhibit oscillatory kinetics, but lysing rate is negatively correlated with range of CD8+ cell count. Our finding highlights role of HLA allele determining different infection outcomes, thereby providing a potential mechanistic explanation for observed good and bad HIV infection outcomes induced by protective HLA allele.

Robust point and variance estimation for meta‐analyses with selective reporting and dependent effect sizes

Abstract Meta‐analysis produces a quantitative synthesis of evidence‐based knowledge, shaping not only research trends but also policies and practices in biology. However, two statistical issues, selective reporting and statistical dependence, can severely distort meta‐analytic parameter estimation and inference. Here, we re‐analyse 448 meta‐analyses to demonstrate a new two‐step procedure to deal with two common challenges in biological meta‐analyses that often occur simultaneously: publication bias and non‐independence. First, we employ bias‐robust weighting schemes under the generalized least square estimator to obtain average effect sizes that are more robust to selective reporting. We then use cluster‐robust variance estimation to account for statistical dependence, reducing bias in estimating standard errors and ensuring valid statistical inference. The first step of our approach demonstrates comparable performance in estimating average effect sizes to the existing publication‐bias adjustment methods in the presence of selective reporting. This equivalence holds across two publication bias selection processes. The second step achieves estimates of standard errors consistent with the multilevel meta‐analytic model, a benchmark method with adequate control of Type I error rates for multiple, statistically dependent effect sizes. Re‐analyses of 448 meta‐analyses show that ignoring these two issues tends to overestimate effect sizes by an average of 110% and underestimate standard errors by 120%. To facilitate implementation, we have developed a website including a step‐by‐step tutorial. Complementing current meta‐analytic workflows with the proposed method as a sensitivity analysis can facilitate a transition to a more robust approach in quantitative evidence synthesis.

The effect of the Solar System Ephemeris on the search for the nano-Hz gravitational wave background

ABSTRACT The detection of the nano-Hz gravitational-wave background (GWB) is one of the main targets of Pulsar timing arrays (PTAs). The detection can be achieved via searching for a common signal with quadrapolar correlation between pulsar pairs. Errors in the Solar-System ephemeris (SSE) can induce dipolar correlations in PTA data, which may affect the results of GWB searches, especially when the data quality is not high enough to constrain the correlation pattern. We investigate the effect of unmodelled SSE errors on GWB searches with PTAs, using simulations with properties based on the European Pulsar Timing Array data set. When the GWB signal is strong, SSE errors have little effect on the GWB search results, including parameter inference and model selection. When the GWB signal is weak, SSE errors can lead to overestimation of the GWB amplitude. However, model comparison would show strong support for dipolar correction, which implies the source of the common signal to be SSE-related and helps avoid its misidentification as a GWB signal. This indicates that SSE error is unlikely to be the main source of the common signal detected recently with real PTA data. We also use simulations to test the ability of the SSE model LINIMOSS in absorbing SSE-error signals and leaving the GWB signal intact. We show that marginalizing LINIMOSS planetary parameters with infinite priors is good at absorbing SSE errors, but may also lead to improper absorption of a GWB signal. Caution is therefore required when setting appropriate limits on the priors of SSE parameters.

Different Statistical Inference Algorithms for the New Pareto Distribution Based on Type-II Progressively Censored Competing Risk Data with Applications

In this research, the statistical inference of unknown lifetime parameters is proposed in the presence of independent competing risks using a progressive Type-II censored dataset. The lifetime distribution associated with a failure mode is assumed to follow the new Pareto distribution, with consideration given to two distinct competing failure reasons. Maximum likelihood estimators (MLEs) for the unknown model parameters, as well as reliability and hazard functions, are derived, noting that they are not expressible in closed form. The Newton–Raphson, expectation maximization (EM), and stochastic expectation maximization (SEM) methods are employed to generate maximum likelihood (ML) estimations. Approximate confidence intervals for the unknown parameters, reliability, and hazard rate functions are constructed using the normal approximation of the MLEs and the normal approximation of the log-transformed MLEs. Additionally, the missing information principle is utilized to derive the closed form of the Fisher information matrix, which, in turn, is used with the delta approach to calculate confidence intervals for reliability and hazards. Bayes estimators are derived under both symmetric and asymmetric loss functions, with informative and non-informative priors considered, including independent gamma distributions for informative priors. The Monte Carlo Markov Chain sampling approach is employed to obtain the highest posterior density credible intervals and Bayesian point estimates for unknown parameters and reliability characteristics. A Monte Carlo simulation is conducted to assess the effectiveness of the proposed techniques, with the performances of the Bayes and maximum likelihood estimations examined using average values and mean squared errors as benchmarks. Interval estimations are compared in terms of average lengths and coverage probabilities. Real datasets are considered and examined for each topic to provide illustrative examples.

Hierarchical Bayesian Integrated Modeling of Age- and Sex-Structured Wildlife Population Dynamics

AbstractBiodiversity of large wild mammals is declining at alarming rates worldwide. It is therefore imperative to develop effective population conservation and recovery strategies. Population dynamics models can provide insights into processes driving declines of particular populations of a species and their relative importance. But there are insufficient tools, namely population dynamics models for wild herbivores, for characterizing their decline and for guiding conservation and management actions. Therefore, we have developed a model which can serve as a tool to fill that void. Specifically, we develop an integrated Bayesian state-space population dynamics model for wildlife populations and illustrate it using a topi population inhabiting the Greater Mara-Serengeti Ecosystem in Kenya and Tanzania. The model integrates ground demographic survey with aerial survey monitoring data. It incorporates population age and sex structure and life history traits and strategies and relates birth rates, age-specific survival rates and sex ratios with meteorological covariates, prior population density, environmental seasonality and predation risk. It runs on a monthly time step, enabling accurate characterization of reproductive seasonality, phenology, synchrony and prolificacy of births, juvenile and adult recruitments. Model performance is evaluated using balanced bootstrap sampling and by comparing model predictions with empirical aerial population size estimates. The hierarchical Bayesian model is implemented using MCMC methods for parameter estimation, prediction and inference and reproduces several well-known features of the Mara topi population, including striking and persistent population decline, seasonality of births, juvenile and adult recruitments. It is general and can be readily adapted for other wildlife species and extended to incorporate several additional useful features. Supplementary materials accompanying this paper appear on-line.

Fast Parameter Inference on Pulsar Timing Arrays with Normalizing Flows.

Pulsar timing arrays perform Bayesian posterior inference with expensive Markov chain MonteCarlo (MCMC) methods. Given a dataset of ∼10-100 pulsars and O(10^{3}) timing residuals each, producing a posterior distribution for the stochastic gravitational wave background (SGWB) can take days to a week. The computational bottleneck arises because the likelihood evaluation required for MCMC is extremely costly when considering the dimensionality of the search space. Fortunately, generating simulated data is fast, so modern simulation-based inference techniques can be brought to bear on the problem. In this Letter, we demonstrate how conditional normalizing flows trained on simulated data can be used for extremely fast and accurate estimation of the SGWB posteriors, reducing the sampling time from weeks to a matter of seconds.

Cosmology with Multiple Galaxies

Recent works have discovered a relatively tight correlation between Ωm and the properties of individual simulated galaxies. Because of this, it has been shown that constraints on Ωm can be placed using the properties of individual galaxies while accounting for uncertainties in astrophysical processes such as feedback from supernovae and active galactic nuclei. In this work, we quantify whether using the properties of multiple galaxies simultaneously can tighten those constraints. For this, we train neural networks to perform likelihood-free inference on the value of two cosmological parameters (Ωm and σ 8) and four astrophysical parameters using the properties of several galaxies from thousands of hydrodynamic simulations of the CAMELS project. We find that using properties of more than one galaxy increases the precision of the Ωm inference. Furthermore, using multiple galaxies enables the inference of other parameters that were poorly constrained with one single galaxy. We show that the same subset of galaxy properties are responsible for the constraints on Ωm from one and multiple galaxies. Finally, we quantify the robustness of the model and find that without identifying the model range of validity, the model does not perform well when tested on galaxies from other galaxy formation models.

A Machine Learning Boosted Data Reduction Methodology for Translaminar Fracture of Structural Composites

AbstractThis work explored a machine learning (ML) algorithm as a fast data reduction method for translaminar fracture energy in composite laminates. The method was validated with translaminar fracture tests on compact tension (CT) specimens on AS4/8552 and IM7/8552 cross-ply lay-ups. Experimental fracture energy and R-curves for both materials were determined using the most common data reduction methods, such as the compliance calibration (CC), the area (AM) and the Irwin relationship (IM). Our new data reduction method uses a surrogate model based on an artificial neural network (ANN) trained with synthetic data generated with the cohesive crack finite element model. Such a surrogate model maps the cohesive properties with the corresponding load–displacement, crack-displacement and energy-displacement curves with interrogation times in the order of 20 ms and relative errors in the load–displacement and crack growth less than 2%. Such performance enabled its encapsulation to approximate the inverse problem to infer the cohesive parameters with the maximum likelihood estimator (MLE) directly from the experimental load–displacement and crack-displacement curves. The results demonstrated the ability of the model to deliver cohesive parameter inference directly from the macroscopic tests carried out at the laboratory level.

Efficient parameter estimation for ODE models of cellular processes using semi-quantitative data.

Quantitative dynamical models facilitate the understanding of biological processes and the prediction of their dynamics. The parameters of these models are commonly estimated from experimental data. Yet, experimental data generated from different techniques do not provide direct information about the state of the system but a nonlinear (monotonic) transformation of it. For such semi-quantitative data, when this transformation is unknown, it is not apparent how the model simulations and the experimental data can be compared. We propose a versatile spline-based approach for the integration of a broad spectrum of semi-quantitative data into parameter estimation. We derive analytical formulas for the gradients of the hierarchical objective function and show that this substantially increases the estimation efficiency. Subsequently, we demonstrate that the method allows for the reliable discovery of unknown measurement transformations. Furthermore, we show that this approach can significantly improve the parameter inference based on semi-quantitative data in comparison to available methods. Modelers can easily apply our method by using our implementation in the open-source Python Parameter EStimation TOolbox (pyPESTO) available at https://github.com/ICB-DCM/pyPESTO.

A Spatial Semantic Feature Extraction Method for Urban Functional Zones Based on POIs

Accurately extracting semantic features of urban functional zones is crucial for understanding urban functional zone types and urban functional spatial structures. Points of interest provide comprehensive information for extracting the semantic features of urban functional zones. Many researchers have used topic models of natural language processing to extract the semantic features of urban functional zones from points of interest, but topic models cannot consider the spatial features of points of interest, which leads to the extracted semantic features of urban functional zones being incomplete. To consider the spatial features of points of interest when extracting semantic features of urban functional zones, this paper improves the Latent Dirichlet Allocation topic model and proposes a spatial semantic feature extraction method for urban functional zones based on points of interest. In the proposed method, an assumption (that points of interest belonging to the same semantic feature are spatially correlated) is introduced into the generation process of urban functional zones, and then, Gibbs sampling is combined to carry out the parameter inference process. We apply the proposed method to a simulated dataset and the point of interest dataset for Chaoyang District, Beijing, and compare the semantic features extracted by the proposed method with those extracted by the Latent Dirichlet Allocation. The results show that the proposed method sufficiently considers the spatial features of points of interest and has a higher capability of extracting the semantic features of urban functional zones than the Latent Dirichlet Allocation.

A Bayesian cure rate regression model using Hamiltonian Monte Carlo methods

In this paper, we propose a flexible cure rate survival model by assuming the number of competing causes, related to the event of interest, to follow generalized Poisson distribution. The generalized Poisson distribution has several important properties, e.g. it can effectively model both underdispersed (mean > variance) and overdispersed (mean < variance) mechanisms present in the data. Further, it includes the promotion time cure model as a special case. In this work, for a non-cure subject, we model the time to event of interest with the piecewise exponential distribution. We emphasize that the piecewise exponential distribution has a greater flexibility to model failure times, and can be considered as a distribution-free alternative to the parametric distributions based assumptions. Inferences for the model parameters are considered via full Bayesian analysis. Further, a detailed simulation study is performed with different parameter settings, sample sizes and censoring percentages to study the behavior of the estimators. Finally, a data set from the medical area is analyzed for further illustration.

An application of the Bayesian network model based on the EN-ESL-GA algorithm: Exploring the predictors of heart disease in middle-aged and elderly people in China.

The morbidity and mortality of heart disease are increasing in middle-aged and elderly people in China. It is necessary to explore relationships and interactive associations between heart disease and its risk factors in order to prevent heart disease. To establish a Bayesian network model of heart disease and its influencing factors in middle-aged and elderly people in China, and explore the applicability of the elite-based structure learner using genetic algorithm based on ensemble learning (EN-ESL-GA) algorithm in etiology analysis and disease prediction. Based on the 2013 national tracking survey data from China Health and Retirement Longitudinal Study (CHARLS) database, EN-ESL-GA algorithm was used to learn the Bayesian network structure. Then we input the data and the learned network structure into the Netica software for parameter learning and inference analysis. The Bayesian network model based on the EN-ESL-GAalgorithm can effectively excavate the complex network relationships and interactive associations between heart disease and its risk factors in middle-aged and elderly people in China. The Bayesian network model based on the EN-ESL-GA algorithm has good applicability and application prospect in the prediction of diseases prevalence risk.

Spatial Prediction of Diameter Distributions for the Alpine Protection Forests in Ebensee, Austria, Using ALS/PLS and Spatial Distributional Regression Models

A novel Bayesian spatial distributional regression model is presented to predict forest structural diversity in terms of the distributions of the stem diameter at breast height (DBH) in the protection forests in Ebensee, Austria. The distributional regression approach overcomes the limitations and uncertainties of traditional regression modeling, in which the conditional mean of the response is regressed against explanatory variables. The distributional regression addresses the complete conditional response distribution, instead. In total 36,338 sample trees were measured via a handheld mobile personal laser scanning system (PLS) on 273 sample plots each having a 20 m radius. Recent airborne laser scanning (ALS) data were used to derive regression covariates from the normalized digital vegetation height model (DVHM) and the digital terrain model (DTM). Candidate models were constructed that differed in their linear predictors of the two gamma distribution parameters. In the distributional regression approach, covariates can enter the model in a flexible form, such as via nonlinear smooth curves, cyclic smooths, or spatial effects. Supported by Bayesian diagnostics DIC and WAIC, nonlinear smoothing splines outperformed linear parametric slope coefficients, and the best implementation of spatial structured effects was achieved by a Gaussian process smooth. Model fitting and posterior parameter inference was achieved by using full Bayesian methodology and MCMC sampling algorithms implemented in the R-package BAMLSS. With BAMLSS, spatial interval predictions of the DBH distribution at any new geo-locations were enabled via straightforward access to the posterior predictive distributions of the model terms and by offering simple plug-in solutions for new covariate values. A cross-validation analysis validated the robustness of the proposed method’s parameter estimation and out-of-sample prediction. Spatial predictions of stem count proportions per DBH classes revealed that regeneration of smaller trees was lacking in certain areas of the protection forest landscape. Therefore, the intensity of final felling needs to be increased to reduce shading from the dense, overmature shelter trees and to promote sunlight for the young regeneration trees.

Improving crop yield estimation by unified model parameters and state variable with Bayesian inference

Data assimilation techniques integrating crop growth models and remote sensing technologies offer a feasible approach for large-scale crop yield estimation. Previous research has primarily focused on either recalibrate the uncertain model parameters or updating model state variables independently using remotely sensed observations. In this study, we developed a two-step inference algorithm that couples the parameter inference and the state update, to solve the joint posterior distribution of uncertain parameters and state variables given the remote sensing observations. An Observing Simulation System (OSS) experiment was first performed based on the WOFOST crop model to validate the effectiveness of the parameter inference method. The results indicate that, the parameter inference method successfully improved the estimation of different types of model parameters and enhanced yield estimation. Furthermore, leaf area index (LAI) retrieved from Sentinel-2 was assimilated into the WOFOST model to simulate winter wheat yield at the plot scale in the northeastern part of Henan Province. The results demonstrated that the proposed two-step inference algorithm can more effectively correct model simulation biases and improve winter wheat yield estimation accuracy (R²=0.58, MAPE=12.75 %, and RMSE=1112 kg·ha⁻¹), outperforming the standard EnKF algorithm (R²=0.51, MAPE=14.62 %, RMSE=1328 kg·ha⁻¹). Overall, attributed to its unified approach to estimating both model parameters and state variables, the proposed two-step inference algorithm shows promising application prospects for data assimilation-based crop yield estimation.

Advanced Copula-Based Models for Type II Censored Data: Applications in Industrial and Medical Settings

Copula models are increasingly recognized for their ability to capture complex dependencies among random variables. In this study, we introduce three innovative bivariate models utilizing copula functions: the XLindley (XL) distribution with Frank, Gumbel, and Clayton copulas. The results highlight the fundamental characteristics and effectiveness of these newly introduced bivariate models. Statistical inference for the distribution parameters is conducted using a Type II censored sampling design. This employs maximum likelihood and Bayesian estimation techniques. Asymptotic and credible confidence intervals are calculated, and numerical analysis is performed using the Markov Chain Monte Carlo method. The proposed methodology’s applicability is illustrated by analyzing several real-world datasets. The initial dataset examines burr formation occurrences and consists of two observation sets. Additionally, the second and third datasets contain medical information. The second dataset focuses on diabetic nephropathy, while the third dataset explores infection and recurrence time among kidney patients.

A Lightweight Method for Graph Neural Networks Based on Knowledge Distillation and Graph Contrastive Learning

Graph neural networks (GNNs) are crucial tools for processing non-Euclidean data. However, due to scalability issues caused by the dependency and topology of graph data, deploying GNNs in practical applications is challenging. Some methods aim to address this issue by transferring GNN knowledge to MLPs through knowledge distillation. However, distilled MLPs cannot directly capture graph structure information and rely only on node features, resulting in poor performance and sensitivity to noise. To solve this problem, we propose a lightweight optimization method for GNNs that combines graph contrastive learning and variable-temperature knowledge distillation. First, we use graph contrastive learning to capture graph structural representations, enriching the input information for the MLP. Then, we transfer GNN knowledge to the MLP using variable temperature knowledge distillation. Additionally, we enhance both node content and structural features before inputting them into the MLP, thus improving its performance and stability. Extensive experiments on seven datasets show that the proposed KDGCL model outperforms baseline models in both transductive and inductive settings; in particular, the KDGCL model achieves an average improvement of 1.63% in transductive settings and 0.8% in inductive settings when compared to baseline models. Furthermore, KDGCL maintains parameter efficiency and inference speed, making it competitive in terms of performance.

On Modi-Exponential Distribution under Conventional Type-I and Type-II Censoring

In this article, a new Modi-Exponential distribution is considered under Type-I and Type-II censoring. Some statistical and reliability characteristics of the distribution are specified. Statistical inferences of the Modi-Exponential parameters based on Type-I and Type-II censored data are discussed. The maximum likelihood estimation method is used for estimation of unknown parameters along with reliability characteristics. Asymptotic confidence intervals are also obtained for interval estimation. Monte-Carlo Simulation study is performed to study the performances of estimators. Further, two real data sets are provided to illustrate the results.. KEYWORDS :Censoring, Maximum likelihood estimation, Confidence bounds, Simulation.

SEMIPARAMETRIC BIVARIATE HIERARCHICAL STATE SPACE MODEL WITH APPLICATION TO HORMONE CIRCADIAN RELATIONSHIP.

The adrenocorticotropic hormone and cortisol play critical roles in stress regulation and the sleep-wake cycle. Most research has been focused on how the two hormones regulate each other in terms of short-term pulses. Few studies have been conducted on the circadian relationship between the two hormones and how it differs between normal and abnormal groups. The circadian patterns are difficult to model as parametric functions. Directly extending univariate functional mixed effects models would result in a large dimensional problem and a challenging nonparametric inference. In this article, we propose a semi-parametric bivariate hierarchical state space model, in which each hormone profile is modeled by a hierarchical state space model, with nonparametric population-average and subject-specific components. The bivariate relationship is constructed by concatenating two latent independent subject-specific random functions specified by a design matrix, leading to a parametric inference on the correlation. We propose a computationally efficient state-space EM algorithm for estimation and inference. We apply the proposed method to a study of chronic fatigue syndrome and fibromyalgia and discover an erratic regulation pattern in the patient group in contrast to a circadian regulation pattern conforming to the day-night cycle in the control group.

Model Falsification from a Bayesian Viewpoint with Applications to Parameter Inference and Model Selection of Dynamical Systems

Model Falsification from a Bayesian Viewpoint with Applications to Parameter Inference and Model Selection of Dynamical Systems

Two-stage stochastic model updating approach based on Bayesian framework and hybrid multi-population migrant genetic–Metropolis–Hastings algorithm for heavy-haul railway bridges

This study proposes a stochastic model updating approach using an improved multi-population migrant genetic algorithm (MMGA) with the Metropolis–Hastings (MH) algorithm based on the Bayesian inference approach. To enhance the search capacity of the genetic algorithm (GA), the MMGA introduces heuristic: the promotion and elimination mechanisms of urban population migration. The stochastic model updating approach includes two stages. The optimal values identified by the MMGA without considering the parameter uncertainties in the first stage are used as the initial values for the MH algorithm to accelerate Bayesian inference for uncertain parameters in the second stage. A practical application, the Yellow River Bridge with a heavy-haul railway line, demonstrates that the proposed approach offers an increased probability of gaining the global optimum, and predictions of displacements and frequencies provided by the updated finite element model are comparable to those obtained from the field tests.