Sampling Importance Resampling Research Articles

Development and comparison of model-integrated evidence approaches for bioequivalence studies with pharmacokinetic end points.

By applying nonlinear mixed-effect (NLME) models, model-integrated evidence (MIE) approaches are able to analyze bioequivalence (BE) data with pharmacokinetic end points that have sparse sampling, which is problematic for non-compartmental analysis (NCA). However, MIE approaches may suffer from inflation of type I error due to underestimation of parameter uncertainty and to the assumption of asymptotic normality. In this study, we developed a MIE BE analysis method that is based on a pre-defined model and consists of several steps including model fitting, uncertainty assessment, simulation, and BE determination. The presented MIE approach has several improvements compared with the previously reported model-integrated methods: (1) treatment, sequence, and period effects are only added to absorption parameters (such as relative bioavailability and rate of absorption) instead of all PK parameters; (2) a simulation step is performed to generate confidence intervals of the pharmacokinetic metrics for BE assessment; and (3) in an effort to maintain type I error, two more advanced parameter uncertainty evaluation approaches are explored, a nonparametric (case resampling) bootstrap, and sampling importance resampling (SIR). To evaluate the developed method and compare the uncertainty assessment methods, simulation experiments were performed for BE studies using a two-way crossover design with different amounts of information (sparse to rich designs) and levels of variability. Based on the simulation results, the method using SIR for parameter uncertainty quantification controls type I error at the nominal level of 0.05 (i.e., the significance level set for BE evaluation) even for studies with small sample size and/or sparse sampling. As expected, our MIE approach for BE assessment exhibited higher power than the NCA-based method, especially as the data becomes sparser and/or more variable.

Assimilation of Sentinel‐Based Leaf Area Index for Modeling Surface‐Ground Water Interactions in Irrigation Districts

AbstractVegetation‐related processes, such as evapotranspiration (ET), irrigation water withdrawal, and groundwater recharge, are influencing surface water (SW)—groundwater (GW) interaction in irrigation districts. Meanwhile, conventional numerical models of SW‐GW interaction are not developed based on satellite‐based observations of vegetation indices. In this paper, we propose a novel methodology for multivariate assimilation of Sentinel‐based leaf area index (LAI) as well as in‐situ records of streamflow. Moreover, the GW model is initially calibrated based on water table observations. These observations are assimilated into the SWAT‐MODFLOW model to accurately analyze the advantage of considering high‐resolution LAI data for SW‐GW modeling. We develop a data assimilation (DA) framework for SWAT‐MODFLOW model using the particle filter based on the sampling importance resampling (PF‐SIR). Parameters of MODFLOW are calibrated using the parameter estimation (PEST) algorithm and based on in‐situ observation of the GW table. The methodology is implemented over the Mahabad Irrigation Plain, located in the Urmia Lake Basin in Iran. Some DA scenarios are closely examined, including univariate LAI assimilation (L‐DA), univariate streamflow assimilation (S‐DA), and multivariate streamflow‐LAI assimilation (SL‐DA). Results show that the SL‐DA scenario results in the best estimations of streamflow, LAI, and GW level, compared to other DA scenarios. The streamflow DA does not improve the accuracy of LAI estimation, while the LAI assimilation scenario results in significant improvements in streamflow simulation, where, compared to the open loop run, the (absolute) bias decreases from 75% to 6%. Moreover, S‐DA, compared to L‐DA, underestimates irrigation water use and demand as well as potential and actual crop yield.

Evaluation of model-integrated evidence approaches for pharmacokinetic bioequivalence studies using model averaging methods.

Conventional approaches for establishing bioequivalence (BE) between test and reference formulations using non-compartmental analysis (NCA) may demonstrate low power in pharmacokinetic (PK) studies with sparse sampling. In this case, model-integrated evidence (MIE) approaches for BE assessment have been shown to increase power, but may suffer from selection bias problems if models are built on the same data used for BE assessment. This work presents model averaging methods for BE evaluation and compares the power and type I error of these methods to conventional BE approaches for simulated studies of oral and ophthalmic formulations. Two model averaging methods were examined: bootstrap model selection and weight-based model averaging with parameter uncertainty from three different sources, either from a sandwich covariance matrix, a bootstrap, or from sampling importance resampling (SIR). The proposed approaches increased power compared with conventional NCA-based BE approaches, especially for the ophthalmic formulation scenarios, and were simultaneously able to adequately control type I error. In the rich sampling scenario considered for oral formulation, the weight-based model averaging method with SIR uncertainty provided controlled type I error, that was closest to the target of 5%. In sparse-sampling designs, especially the single sample ophthalmic scenarios, the type I error was best controlled by the bootstrap model selection method.

Variance-reduced sampling importance resampling

The sampling importance resampling method is widely utilized in various fields, such as numerical integration and statistical simulation. In this paper, two modified methods are presented by incorporating two variance reduction techniques commonly used in Monte Carlo simulation, namely antithetic sampling and Latin hypercube sampling, into the process of sampling importance resampling method, respectively. Theoretical evidence is provided to demonstrate that the proposed methods significantly reduce estimation errors compared to the original approach. Furthermore, the effectiveness and advantages of the proposed methods are validated through both numerical studies and real data analysis.

A time-to-event modelling of sputum conversion within two months after antituberculosis initiation among drug-susceptible smear positive pulmonary tuberculosis patients: Implementation of internal and external validation

Delayed sputum conversion has been associated with a higher risk of treatment failure or relapse among drug susceptible smear-positive pulmonary tuberculosis patients. Several contributing factors have been identified in many studies, but the results varied across regions and countries. Therefore, the current study aimed to develop a predictive model that explained the factors affecting time to sputum conversion within two months after initiating antituberculosis agents among Malaysian with drug-susceptible smear-positive pulmonary tuberculosis patients. Retrospective data of pulmonary tuberculosis patients followed up at a tertiary hospital in the Northern region of Malaysia from 2013 until 2018 were collected and analysed. Nonlinear mixed-effect modelling software (NONMEM 7.3.0) was used to develop parametric survival models. The final model was further validated using Kaplan-Meier-visual predictive check (KM-VPC) approach, kernel-based hazard rate estimation method and sampling-importance resampling (SIR) method. A total of 224 patients were included in the study, with 34.4 % (77/224) of the patients remained positive at the end of 2 months of the intensive phase. Gompertz hazard function best described the data. The hazard of sputum conversion decreased by 39 % and 33 % for moderate and advanced lesions as compared to minimal baseline of chest X-ray severity, respectively (adjusted hazard ratio (aHR), 0.61; 95 % confidence intervals (95 % CI), (0.44–0.84) and 0.67, 95 % CI (0.53–0.84)). Meanwhile, the hazard also decreased by 59 % (aHR, 0.41; 95 % CI, (0.23–0.73)) and 48 % (aHR, 0.52; 95 % CI, (0.35–0.79)) between active and former drug abusers as compared to non-drug abuser, respectively. The successful development of the internally and externally validated final model allows a better estimation of the time to sputum conversion and provides a better understanding of the relationship with its predictors.

Particle Filter based on Jaya optimisation for Bayesian updating of nonlinear models

Particle filter (PF) is a powerful and commonly used filtering technique based on Sequential Monte Carlo framework. The main challenge in using PF for nonlinear state and parameter estimation is the degeneracy of particles. Although resampling techniques can solve this to some extent, it would still result in particle impoverishment when a limited number of particles are used thereby affecting the accuracy. Hence, a hybrid metaheuristic optimisation algorithm that combines the PF with Jaya optimisation, (PF-JAYA) has been proposed and implemented for joint state and parameter estimation for geotechnical engineering problems. The performance of PF-JAYA has been compared against the traditional Particle Filter with Sampling Importance Resampling (PF-SIR) technique. The synthetic examples show that PF-JAYA outperforms PF-SIR in terms of accuracy, rate of convergence, parameter identification and particle diversity. Furthermore, the performance of PF-JAYA is independent of the choice of prior distribution and due to its superior convergence proves to be efficient when working with sparse monitoring information. The performance of PF-JAYA on Bayesian updating of state and parameters of an elastoplastic model for a synthetic embankment case has also been evaluated where, along with PF-SIR, the Ensemble Kalman Filter (EnKF) is also chosen for comparison. Finally a further evaluation using the Lorenz ‘63 model, shows the superior performance of PF-JAYA in terms of accuracy and precision over the classical Data Assimilation techniques.

Sequential estimation of high temperatures of liquid metals by using particle filter methods

This work follows up our previous studies dedicated to the estimation of the transient temperature of niobium and 100c6 steel samples, in ranges that include solid and liquid phases, as well as phase changes. In the experimental setup, a metallic sample of few millimeters is aerodynamically levitated and then heated by a powerful laser, while a collimator focused on the sample collects the radiative flux that is split towards five pyrometers of different wavelengths. The measured spectral fluxes are used in an inverse analysis to estimate the sample temperature. Difficulties in the inverse problem solution related to the dependence of the sample emittance with temperature and wavelength could be overcome by reducing the number of model parameters using a simple linear variation of the emittance with respect to the wavelength. In this work the transient temperature of the sample is estimated sequentially by solving a state estimation problem with two algorithms of the particle filter method, namely: the Sampling Importance Resampling (SIR) and Auxiliary Sampling Importance Resampling (ASIR) algorithms. Results obtained with these algorithms and the radiative spectral fluxes exhibited small discrepancies with respect to the temperature measurements of a reference bichromatic pyrometer.

Sampling Importance Resampling Algorithm with Nonignorable Missing Response Variable Based on Smoothed Quantile Regression

The presence of nonignorable missing response variables often leads to complex conditional distribution patterns that cannot be effectively captured through mean regression. In contrast, quantile regression offers valuable insights into the conditional distribution. Consequently, this article places emphasis on the quantile regression approach to address nonrandom missing data. Taking inspiration from fractional imputation, this paper proposes a novel smoothed quantile regression estimation equation based on a sampling importance resampling (SIR) algorithm instead of nonparametric kernel regression methods. Additionally, we present an augmented inverse probability weighting (AIPW) smoothed quantile regression estimation equation to reduce the influence of potential misspecification in a working model. The consistency and asymptotic normality of the empirical likelihood estimators corresponding to the above estimating equations are proven under the assumption of a correctly specified parameter working model. Furthermore, we demonstrate that the AIPW estimation equation converges to an IPW estimation equation when a parameter working model is misspecified, thus illustrating the robustness of the AIPW estimation approach. Through numerical simulations, we examine the finite sample properties of the proposed method when the working models are both correctly specified and misspecified. Furthermore, we apply the proposed method to analyze HIV—CD4 data, thereby exploring variations in treatment effects and the influence of other covariates across different quantiles.

Vision-based particle filtering for quad-copter attitude estimation using multirate delayed measurements.

In this paper, the problem of attitude estimation of a quad-copter system equipped with a multi-rate camera and gyroscope sensors is addressed through extension of a sampling importance re-sampling (SIR) particle filter (PF). Attitude measurement sensors, such as cameras, usually suffer from a slow sampling rate and processing time delay compared to inertial sensors, such as gyroscopes. A discretized attitude kinematics in Euler angles is employed where the gyroscope noisy measurements are considered the model input, leading to a stochastic uncertain system model. Then, a multi-rate delayed PF is proposed so that when no camera measurement is available, the sampling part is performed only. In this case, the delayed camera measurements are used for weight computation and re-sampling. Finally, the efficiency of the proposed method is demonstrated through both numerical simulation and experimental work on the DJI Tello quad-copter system. The images captured by the camera are processed using the ORB feature extraction method and the homography method in Python-OpenCV, which is used to calculate the rotation matrix from the Tello's image frames.

Statistical testing under distributional shifts

AbstractWe introduce statistical testing under distributional shifts. We are interested in the hypothesis P*∈H0 for a target distribution P*, but observe data from a different distribution Q*. We assume that P* is related to Q* through a known shift τ and formally introduce hypothesis testing in this setting. We propose a general testing procedure that first resamples from the observed data to construct an auxiliary data set (similarly to sampling importance resampling) and then applies an existing test in the target domain. We prove that if the size of the resample is of order o(n) and the resampling weights are well behaved, this procedure inherits the pointwise asymptotic level and power from the target test. If the map τ is estimated from data, we maintain the above guarantees under mild conditions on the estimation. Our results extend to finite sample level, uniform asymptotic level, a different resampling scheme, and statistical inference different from testing. Testing under distributional shifts allows us to tackle a diverse set of problems. We argue that it may prove useful in contextual bandit problems and covariate shift, show how it reduces conditional to unconditional independence testing and provide example applications in causal inference.

Mathematical modelling of a glucose-insulin system for type 2 diabetic patients in Chad

In this paper, we focus on modelling the glucose-insulin system for the purpose of estimating glucagon, insulin, and glucose in the liver in the internal organs of the human body. A three-compartmental mathematical model is proposed. The model parameters are estimated using a nonlinear inverse optimization problem and data collected in Chad. In order to identify insulin and glucose in the liver for type 2 diabetic patients, the Sampling Importance Resampling (SIR) particle filtering algorithm is used and implemented through discretization of the developed mathematical model. The proposed mathematical model allows further investigation of the dynamic behavior of hepatic glucose, insulin, and glucagon in internal organs for type 2 diabetic patients. During periods of hyperglycemia (i.e., after meal ingestion), whereas insulin secretion is increased, glucagon secretion is reduced. The results are in agreement with empirical and clinical data and they are clinically consistent with physiological responses.

Focusing on the front end: A framework for incorporating uncertainty in biological parameters in model ensembles of integrated stock assessments

Uncertainty in population status estimates from stock assessments is important for providing a comprehensive picture of current knowledge of a stock. The use of model ensembles to encapsulate model uncertainty has become increasingly prevalent. The uncertainty of biological parameters that are often fixed in stock assessment models can be quantified for presentation of management advice through model ensembles. An ensemble can be created by randomly drawing values from the likely parameter space using a Monte-Carlo/bootstrap (MCB ensemble) or fixed at either a high, medium, or low value that encapsulates the variability in the parameter and applied in a full factorial grid across the fixed parameters (factorial ensemble). We calculated the management advice from MCB ensembles of various sizes and a 243 model factorial ensemble for Southwest Pacific swordfish (Xiphias gladius) and compared reference points which included model uncertainty only, model and estimation uncertainty, or both uncertainties weighted by sampling importance resampling. Median reference points were significantly different between the two ensemble types with the factorial ensemble having a significantly larger estimate of model uncertainty than the MCB ensemble. Stock assessments with fixed biological parameters can characterize uncertainty in these parameters more efficiently using a MCB ensemble approach. A factorial ensemble approach is appropriate for comparing different model structure assumptions and functional forms of relationships and can be used in combination with a MCB ensemble approach. Incorporation of both model and estimation uncertainty in estimates of reference points is important when providing management advice because including only model uncertainty can lead to biased estimates of the precision of reference points. Further work is needed regarding appropriate weighting of ensembles which incorporate different data sources or have different likelihood weightings.

An inverse analysis of the brain cooling process in neonates using the particle filter method

Purpose This study deals with the computational simulation and inverse analysis of the cooling treatment of the hypoxic-ischemic encephalopathy in neonates. A reduced-order model is implemented for real-time monitoring of the internal body temperatures. The purpose of this study is to sequentially estimate the transient temperatures of the brain and other body regions with reduced uncertainties. Design/methodology/approach Pennes’ model was applied in each body element, and Fiala’s blood pool concept was used for the solution of the forward bioheat transfer problem. A state estimation problem was solved with the Sampling Importance Resampling (SIR) algorithm of the particle filter method. Findings The particle filter method was stable and accurate for the estimation of the internal body temperatures, even in situations involving large modeling and measurement uncertainties. Research limitations/implications The proposed reduced-order model was verified with the results of a high-fidelity model available in the literature. Validation of the proposed model and of the solution of the state estimation problem shall be pursued in the future. Practical implications The solution of the state estimation problem with the reduced-order model presented in this paper has great potential to perform as an observer of the brain temperature of neonates, for the analysis and control of the systemic cooling treatment of neonatal hypoxic-ischemic encephalopathy. Social implications The main treatment for hypoxic-ischemic encephalopathy in neonates is the cooling of affected regions. Accurate and fast models might allow the development of individualized protocols, as well as control strategies for the cooling treatment. Originality/value This paper presents the application of the SIR algorithm for the solution of a state problem during the systemic cooling of a neonate for the treatment of the hypoxic-ischemic encephalopathy.

A multiobjective prediction model with incremental learning ability by developing a multi-source filter neural network for the electrolytic aluminium process

Improving current efficiency and reducing energy consumption are two important technical goals of the electrolytic aluminum process (EAP). However, because the process involves complex noise characteristics (i.e., unknown types, redundant distributions and variable forms), it is very difficult to accurately develop a multiobjective prediction model. To overcome this problem, in this paper, a novel framework of multiobjective incremental learning based on a multi-source filter neural network (MSFNN) is presented. The proposed framework first presents a “multi-source filter” (MSF) technique that utilizes the mean and variance in the unscented Kalman filter (UKF) to guide the importance function of the particle filter (PF) based on a density kernel estimation method. Then, the MSF is embedded in the mutated neural network to adjust weights in real time. Third, weights are calculated and normalized by a modified importance function, which is the basis for further optimizing a secondary sampling based on sampling importance resampling (SIR). Finally, the incremental learning model with two objectives (i.e., process power consumption and current efficiency) based on the MSFNN in the EAP is established. The presented framework has been verified by the real-world EAP and some closely related methods. All test results indicate that the MSFNN’s relative prediction errors of the above two objectives are controlled within 0.51% and 0.38%, respectively and prove that MSFNN has significant competitive advantages over other recent filtering network models. Successfully establishment of the proposed framework provides a model foundation for multiobjective optimization problems in the EAP.

Batch sequential adaptive designs for global optimization

Efficient global optimization (EGO) is one of the most popular sequential adaptive design (SAD) methods for expensive black-box optimization problems. A well-recognized weakness of the original EGO in complex computer experiments is that it is serial, and hence the modern parallel computing techniques cannot be utilized to speed up the running of simulator experiments. For those multiple points EGO methods, the heavy computation and points clustering are the obstacles. In this work, a novel batch SAD method, named “Accelerated EGO”, is forwarded by using a refined sampling/importance resampling (SIR) method to search the points with large expected improvement (EI) values. The computation burden of the new method is much lighter, and the points clustering is also avoided. The efficiency of the proposed batch SAD is validated by nine classic test functions with dimension from 2 to 12. The empirical results show that the proposed algorithm indeed can parallelize original EGO, and gain much improvement compared against the other parallel EGO algorithm especially under high-dimensional case. Additionally, the new method is applied to the hyper-parameter tuning of support vector machine (SVM) and XGBoost models in machine learning. Accelerated EGO obtains comparable cross validation accuracy with other methods and the CPU time can be reduced a lot due to the parallel computation and sampling method.

Sequential Estimation of the Radial Temperature Variation in Overhead Power Cables

Cables used in electric power transmission lines are usually composed of layers of stranded metallic wires. Several effects cause a nonuniform distribution of the electric current, which significantly influences heat generation within the cable. The accurate prediction of the cable radial temperature variation is thus of great importance for the design and operation of electric power transmission lines, because of economic and safety reasons. In this work, the Particle Filter method is applied to estimate the transient temperature distribution in the cross section of an Aluminum Conductor Steel Reinforced power cable, by using measurements of the cable surface temperature obtained with an infrared camera. The Sampling Importance Resampling (SIR) algorithm of the Particle Filter method is used for the solution of the state estimation problem, by taking into account uncertainties in the evolution heat conduction model within the cable, as well as in the measured temperatures. The results presented in this work reveal an excellent agreement of the estimated temperatures obtained with the SIR algorithm and temperature measurements from thermocouples inserted into the cable during the manufacturing process, thus validating the proposed approach for the estimation of the radial temperature variation in the power cable.

Modeling nitrous oxide mitigation potential of enhanced efficiency nitrogen fertilizers from agricultural systems

Agriculture soils are responsible for a large proportion of global nitrous oxide (N2O) emissions—a potent greenhouse gas and ozone depleting substance. Enhanced-efficiency nitrogen (N) fertilizers (EENFs) can reduce N2O emission from N-fertilized soils, but their effect varies considerably due to a combination of factors, including climatic conditions, edaphic characteristics and management practices. In this study, we further developed the DayCent ecosystem model to simulate two EENFs: controlled-release N fertilizers (CRNFs) and nitrification inhibitors (NIs) and evaluated their N2O mitigation potentials. We implemented a Bayesian calibration method using the sampling importance resampling (SIR) algorithm to derive a joint posterior distribution of model parameters that was informed by N2O flux measurements from corn production systems a network of experimental sites within the GRACEnet program. The joint posterior distribution can be applied to estimate predictions of N2O reduction factors when EENFs are adopted in place of conventional urea-based N fertilizer. The resulting median reduction factors were − 11.9% for CRNFs (ranging from −51.7% and 0.58%) and − 26.7% for NIs (ranging from −61.8% to 3.1%), which is comparable to the measured reduction factors in the dataset. By incorporating EENFs, the DayCent ecosystem model is able to simulate a broader suite of options to identify best management practices for reducing N2O emissions.

A Repeated Time-to-Positive Symptoms Improvement among Malaysian Patients with Schizophrenia Spectrum Disorders Treated with Clozapine.

Clozapine remains the drug of choice for resistant schizophrenia. However, its dose-response relationship is still controversial. The current investigation aimed to develop a repeated time-to-positive symptoms improvement following the onset of clozapine treatment in Malaysian schizophrenia spectrum disorder patients. Data from patients’ medical records in the Psychiatric Clinic, Penang General Hospital, were retrospectively analyzed. Several parametric survival models were evaluated using nonlinear mixed-effect modeling software (NONMEM 7.3.0). Kaplan–Meier-visual predictive check (KM-VPC) and sampling-importance resampling (SIR) methods were used to validate the final model. A total of 116 patients were included in the study, with a mean follow-up of 306 weeks. Weibull hazard function best fitted the data. The hazard of positive symptoms improvement decreased 4% for every one-year increase in age over the median of 41 years (adjusted hazard ratio (aHR), 0.96; 95% confidence intervals (95% CI), (0.93–0.98)). However, patients receiving a second atypical antipsychotic agent had four-folds higher hazard (aHR, 4.01; 95% CI, (1.97–7.17)). The hazard increased 2% (aHR, 1.02; 95% CI, (1.01–1.03)) for every 1 g increase in the clozapine six months cumulative dose over the median of 34 g. The developed model provides essential information on the hazard of positive symptoms improvement after the first clozapine dose administration, including modifiable predictors of high clinical importance.

State estimation problem for the detection of valve closure in gas pipelines

The undesired and unexpected closure of valves in pipelines is the most frequent failure that causes interruptions in the transport of natural gas. This work aims at the detection of valve closures by solving a state estimation problem with the Particle Filter method. The gas flow problem in the duct is solved with a Weighted Average Flux – Total Variation Diminishing scheme, while state variables are estimated with simulated measurements of pressure, velocity and temperature at different points along the pipeline. Two versions of the particle filter method are implemented in this work for the solution of the state estimation problem, namely, the Sampling Importance Resampling (SIR) and the Auxiliary Sampling Importance Resampling (ASIR) algorithms. Accurate estimations were obtained with both algorithms for configurations involving pipelines with one or three valves. On the other hand, the SIR algorithm required a larger number of particles than the ASIR algorithm for the same solution accuracy.

Sequential estimation of creatinine removal by a haemodialyser

This work is focused on the transient analysis of a haemodialyser. The objective is to sequentially estimate the concentration of creatinine in the blood returning to the patient, by solving a state estimation problem with measurements of the outflow creatinine concentration in the dialysate. Simulated measurements containing Gaussian errors were used in the inverse analysis, which was based on the Sampling Importance Resampling (SIR) algorithm of the Particle Filter method. Accurate results reveal that this technique may possibly be used for online monitoring and control of the haemodialysis therapy.