Sampling Importance Resampling Research Articles

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.

Mathematical Modelling of Glucose-Insulin System and Test of Abnormalities of Type 2 Diabetic Patients

This paper presents a mathematical model of glucose-insulin dynamics which is specific for type 2 diabetic patients. The general modelling is obtained by simplification of a global compartmental model by John Thomas Sorensen. The model parameters are estimated using nonlinear optimization and data collected in Rwanda for type 2 diabetic patients. In order to identify and evaluate possible abnormalities of type 2 diabetic patients, the Sampling Importance Resampling (SIR) particle filtering algorithm is used and implemented through discretization of the developed mathematical model. This process is done by clamping insulin and glucose concentrations at around clinical trial values as proposed by Defronzo. Furthermore, for detecting potential abnormalities in type 2 diabetic patients, we compare our results with results obtained from a simulation of the mathematical model for healthy subjects. The proposed mathematical model allows further investigation of the dynamic behavior of glucose, insulin, glucagon, stored insulin, and labile insulin in different organs for type 2 diabetic patients.

Particle filter-based data assimilation technique for the evaluation of transport of pollutants in small rivers

The discharge of pollutants into water resources has caused many undesirable effects on human health and the environment. In this context, meta-heuristic methods, such as the Simulated Annealing algorithm, allow for only offline estimation of the concentration and dispersion coefficient of pollutant. However, online data assimilation is a very important for decision support in real time. In this regard, the present paper focuses on the use of the so-called Particle Filter as an online observer. Our studies were performed through the algorithms Sampling Importance Resampling (SIR) and Liu and West (LW), using tracer experimental observations from a small river in Brazil. Such approach allowed for tracking satisfactorily the pollutant concentration, longitudinal dispersion coefficient, flow velocity, pollutant load released and distance from the pollution source. The results can be enhanced ever more through the LW filter, which reduces the impoverishment of the samples as well as the computational time due to the use of a smoothing kernel.

Bayesian calibration of the DayCent ecosystem model to simulate soil organic carbon dynamics and reduce model uncertainty

Benefits of carbon sequestration in agricultural soils are well recognized, and process-based models have been developed to better understand sequestration potential. However, most studies ignore the uncertainty arising during model prediction—a critical requirement for scientific understanding, policy implementation and carbon emission trading. Furthermore, the dependencies created in process-based models due to many parameters and a relatively small set of empirical data hinder parameterization. We have implemented a Bayesian approach using the sampling importance resampling (SIR) method to calibrate the DayCent ecosystem model for estimating soil organic carbon (SOC) stocks, and to quantify uncertainty in model predictions. A SOC dataset compiled from 19 long-term field experiments, representing 117 combinations of management treatments, with 491 measurements of SOC, was split into independent datasets for model calibration and evaluation. The most important DayCent model parameters were identified through a global sensitivity analysis (GSA) for parameterization and SIR was used to calibrate the model and produce posterior distributions for the most sensitive parameters. On average, the Bayesian calibration reduced the model uncertainty by a factor of 6.6 relative to the uncertainty associated with the prior. The Bayesian model analysis framework will allow for ongoing updates to the model as new datasets and model structural improvements are made in future research, and overall provide a stronger basis for models to support policy and management decisions associated with GHG mitigation through C sequestration in agricultural soils.

Methods for Model Calibration under High Uncertainty: Modeling Cholera in Bangladesh.

Background. Published data on a disease do not always correspond directly to the parameters needed to simulate natural history. Several calibration methods have been applied to computer-based disease models to extract needed parameters that make a model's output consistent with available data. Objective. To assess 3 calibration methods and evaluate their performance in a real-world application. Methods. We calibrated a model of cholera natural history in Bangladesh, where a lack of active surveillance biases available data. We built a cohort state-transition cholera natural history model that includes case hospitalization to reflect the passive surveillance data-generating process. We applied 3 calibration techniques: incremental mixture importance sampling, sampling importance resampling, and random search with rejection sampling. We adapted these techniques to the context of wide prior uncertainty and many degrees of freedom. We evaluated the resulting posterior parameter distributions using a range of metrics and compared predicted cholera burden estimates. Results. All 3 calibration techniques produced posterior distributions with a higher likelihood and better fit to calibration targets as compared with prior distributions. Incremental mixture importance sampling resulted in the highest likelihood and largest number of unique parameter sets to better inform joint parameter uncertainty. Compared with naïve uncalibrated parameter sets, calibrated models of cholera in Bangladesh project substantially more cases, many of which are not detected by passive surveillance, and fewer deaths. Limitations. Calibration cannot completely overcome poor data quality, which can leave some parameters less well informed than others. Calibration techniques may perform differently under different circumstances. Conclusions. Incremental mixture importance sampling, when adapted to the context of high uncertainty, performs well. By accounting for biases in data, calibration can improve model projections of disease burden.

Characterization of Background Temperature Dynamics of a Multitemporal Satellite Scene through Data Assimilation for Wildfire Detection

Detection of an active fire in an image scene relies on an accurate estimation of the background temperature of the scene, which must be compared to the observed temperature, to decide on the presence of fire. The expected background temperature of a pixel is commonly derived based on spatial-contextual information that can overestimate the background temperature of a fire pixel and therefore results in the omission of a fire event. This paper proposes a method that assimilates brightness temperatures acquired from the Geostationary Earth Orbit (GEO) sensor MSG-SEVIRI into a Diurnal Temperature Cycle (DTC) model. The expected brightness temperatures are observational forecasts derived using the ensemble forecasting approach. The threshold on the difference between the observed and expected temperatures is derived under a Constant False Alarm Rate (CFAR) framework. The detection results are assessed against a reference dataset comprised of MODIS MOD14/MYD14 and EUMETSAT FIR products, and the performance is presented in terms of user’s and producer’s accuracies, and Precision-Recall and Receiver Operating Characteristic (ROC) graphs. The method has a high detection rate when the data assimilation is implemented with an Ensemble Kalman Filter (EnKF) and a Sampling Importance Resampling (SIR) particle filter, while the weak-constraint Four-Dimensional Variational Assimilation (4D-Var) has comparatively lower detection and false alarm rates according to the reference dataset. Consideration of the diurnal variation in the background temperature enables the proposed method to detect even low-power fires.