Discretization Bias Research Articles

An improved unbiased particle filter

Abstract In this paper, we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. We assume that, for numerical reasons, one has to time-discretize the diffusion process, which typically leads to filtering that is subject to discretization bias. The approach in [A. Jasra, K. J. H. Law and F. Yu, Unbiased filtering of a class of partially observed diffusions, Adv. Appl. Probab. 54 (2022), 3, 661–687] establishes that, when only having access to the time discretized diffusion, it is possible to remove the discretization bias with an estimator of finite variance. We improve on this method by introducing a modified estimator based on the recent work [A. Jasra, M. Maama and H. Ombao, Antithetic multilevel particle filters, preprint (2023), https://arxiv.org/abs/2301.12371]. We show that this new estimator is unbiased and has finite variance. Moreover, we conjecture and verify in numerical simulations that substantial gains are obtained. That is, for a given mean square error (MSE) and a particular class of multi-dimensional diffusion, the cost to achieve the said MSE falls.

Bias-Based Soft Label Learning for Facial Expression Recognition

Facial Expression Recognition (FER) suffers from misrecognition due to the similarities between expressions. To address this issue, popular works replace original annotations with soft labels to reflect expression similarities. However, existing soft label learning (SLL) modules are independent of FER modules. In this paper, inspired by automatic control theory, we propose a bias-based soft label learning network for FER named EC-Net. For optimizing FER and SLL modules jointly, EC-Net constitutes the closed-loop feedback between the two modules by designing a module measuring and transmitting the bias between FER module predictions and target labels. Specifically, EC-Net contains three modules: E-subNet, C-subNet, and L-Transmitter. Firstly, E-subNet, i.e., the FER module, attempts to converge to target labels under the supervision of soft labels, acting as the executor. Then, L-Transmitter measures the bias between E-subNet predictions and target labels. It converts multiple discrete biases to the bias-based label through spectral clustering and transmits it to C-subNet. Finally, C-SubNet, i.e., the SLL module, generates soft labels from the bias-based label with a cascaded learner and progressively distinguishes similar expressions. It updates the learned soft labels for E-subNet, performing like the controller. Supervised by the bias-based soft label, E-subNet effectively reduces the dominant bias caused by similar expressions. We conduct extensive experiments on four popular benchmarks, demonstrating the effectiveness of applying closed-loop feedback in the FER task.

Obstacle avoidance in aerial pursuit

Pursuing prey through clutter is a complex and risky activity requiring integration of guidance subsystems for obstacle avoidance and target pursuit. The unobstructed pursuit trajectories of Harris' hawks Parabuteo unicinctus are well modeled by a mixed guidance law feeding back target deviation angle and line-of-sight rate. Here we ask how their pursuit behavior is modified in response to obstacles, using high-speed motion capture to reconstruct flight trajectories recorded during obstructed pursuit of maneuvering targets.We find that Harris' hawks use the same mixed guidance law during obstructed pursuit but appear to superpose a discrete bias command that resets their flight direction to aim at a clearance of approximately one wing length from an upcoming obstacle as they reach some threshold distance from it. Combining a feedback command in response to target motion with a feedforward command in response to upcoming obstacles provides an effective means of prioritizing obstacle avoidance while remaining locked-on to a target. We therefore anticipate that a similar mechanism may be used in terrestrial and aquatic pursuit. The same biased guidance law could also be used for obstacle avoidance in dronesdesigned to intercept other drones in clutter, or to navigate between fixed waypoints in urban environments.

A randomized multi-index sequential Monte Carlo method

We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. Under such an assumption, this work builds upon a recently introduced multi-index sequential Monte Carlo (SMC) ratio estimator, which provably enjoys the complexity improvements of multi-index Monte Carlo (MIMC) and the efficiency of SMC for inference. The present work leverages a randomization strategy to remove bias entirely, which simplifies estimation substantially, particularly in the MIMC context, where the choice of index set is otherwise important. Under reasonable assumptions, the proposed method provably achieves the same canonical complexity of MSE^{-1} as the original method (where MSE is mean squared error), but without discretization bias. It is illustrated on examples of Bayesian inverse and spatial statistics problems.

Association between ambient air pollutants and upper respiratory tract infection and pneumonia disease burden in Thailand from 2000 to 2022: a high frequency ecological analysis

BackgroundA pertinent risk factor of upper respiratory tract infections (URTIs) and pneumonia is the exposure to major ambient air pollutants, with short term exposures to different air pollutants being shown to exacerbate several respiratory conditions.MethodsHere, using disease surveillance data comprising of reported disease case counts at the province level, high frequency ambient air pollutant and climate data in Thailand, we delineated the association between ambient air pollution and URTI/Pneumonia burden in Thailand from 2000 – 2022. We developed mixed-data sampling methods and estimation strategies to account for the high frequency nature of ambient air pollutant concentration data. This was used to evaluate the effects past concentrations of fine particulate matter (PM2.5), sulphur dioxide (SO2), and carbon monoxide (CO) and the number of disease case count, after controlling for the confounding meteorological and disease factors.ResultsAcross provinces, we found that past increases in CO, SO2, and PM2.5 concentration were associated to changes in URTI and pneumonia case counts, but the direction of their association mixed. The contributive burden of past ambient air pollutants on contemporaneous disease burden was also found to be larger than meteorological factors, and comparable to that of disease related factors.ConclusionsBy developing a novel statistical methodology, we prevented subjective variable selection and discretization bias to detect associations, and provided a robust estimate on the effect of ambient air pollutants on URTI and pneumonia burden over a large spatial scale.

Gauging Gerrymandering in Pennsylvania

There is currently no widely accepted standard method to determine whether gerrymandering has occurred. To determine a cutoff for unreasonable gerrymandering, simulating collections of districting plans in the absence of partisan bias has been proposed. In simulation-based methods, real-world election outcomes are compared to results from simulated districting plans. Here, a simulation method that creates possible districts in continuous space is proposed. Existing methods use preliminary spatial discretization of the state to perform simulations. This spatial discretization can result in biased estimates, which could lead to inaccurate conclusions regarding gerrymandering. We use our continuous-space method to analyze the political districts in Pennsylvania. All of our simulated elections result in fewer than 13 Republican seats, indicating that the districting plan used in Pennsylvania prior to 2018 was likely gerrymandered. This finding agrees with and confirms the results of simulation-based discrete-space gerrymandering studies without the presence of discretization bias.

Unbiased estimation using a class of diffusion processes

We study the problem of unbiased estimation of expectations with respect to (w.r.t.) π a given, general probability measure on (Rd,B(Rd)) that is absolutely continuous with respect to a standard Gaussian measure. We focus on simulation associated to a particular class of diffusion processes, sometimes termed the Schrödinger-Föllmer Sampler, which is a simulation technique that approximates the law of a particular diffusion bridge process {Xt}t∈[0,1] on Rd, d∈N0. This latter process is constructed such that, starting at X0=0, one has X1∼π. Typically, the drift of the diffusion is intractable and, even if it were not, exact sampling of the associated diffusion is not possible. As a result, [10,16] consider a stochastic Euler-Maruyama scheme that allows the development of biased estimators for expectations w.r.t. π. We show that for this methodology to achieve a mean square error of O(ϵ2), for arbitrary ϵ>0, the associated cost is O(ϵ−5). We then introduce an alternative approach that provides unbiased estimates of expectations w.r.t. π, that is, it does not suffer from the time discretization bias or the bias related with the approximation of the drift function. We prove that to achieve a mean square error of O(ϵ2), the associated cost (which is random) is, with high probability, O(ϵ−2|log⁡(ϵ)|2+δ), for any δ>0. We implement our method on several examples including Bayesian inverse problems.

Unbiased Estimation Using a Class of Diffusion Processes

We study the problem of unbiased estimation of expectations with respect to (w.r.t.) $\pi$ a given, general probability measure on $(\mathbb{R}^d,\mathcal{B}(\mathbb{R}^d))$ that is absolutely continuous with respect to a standard Gaussian measure. We focus on simulation associated to a particular class of diffusion processes, sometimes termed the Schr\"odinger-F\"ollmer Sampler, which is a simulation technique that approximates the law of a particular diffusion bridge process $\{X_t\}_{t\in [0,1]}$ on $\mathbb{R}^d$, $d\in \mathbb{N}_0$. This latter process is constructed such that, starting at $X_0=0$, one has $X_1\sim \pi$. Typically, the drift of the diffusion is intractable and, even if it were not, exact sampling of the associated diffusion is not possible. As a result, \cite{sf_orig,jiao} consider a stochastic Euler-Maruyama scheme that allows the development of biased estimators for expectations w.r.t.~$\pi$. We show that for this methodology to achieve a mean square error of $\mathcal{O}(\epsilon^2)$, for arbitrary $\epsilon>0$, the associated cost is $\mathcal{O}(\epsilon^{-5})$. We then introduce an alternative approach that provides unbiased estimates of expectations w.r.t.~$\pi$, that is, it does not suffer from the time discretization bias or the bias related with the approximation of the drift function. We prove that to achieve a mean square error of $\mathcal{O}(\epsilon^2)$, the associated cost is, with high probability, $\mathcal{O}(\epsilon^{-2}|\log(\epsilon)|^{2+\delta})$, for any $\delta>0$. We implement our method on several examples including Bayesian inverse problems.

Time-resolved ion energy measurements using a retarding potential analyzer.

A retarding potential energy analyzer was used to obtain temporally resolved ion energy distribution functions (IEDFs) of a flowing laboratory plasma. The plasma of time varying ion energy was generated at 1 and 20 kHz using a commercial gridded ion source and modulated using a wideband power amplifier. Three plasma energy modulation setpoints were tested, and their IEDFs were reconstructed. This method leverages high-speed, low-noise instrumentation to obtain fast collector current measurements at discrete retarding bias levels, recombining them in the time domain using two data fusion techniques. The first method is an empirical transfer function, which determines the linear ratio of complex coefficients in Fourier space. The second method, shadow manifold interpolation, reconstructs the IEDFs point-by-point by comparing input and output datasets in a multi-dimensional phase space. Reconstructed IEDFs from the two methods are presented and compared. The two analysis methods show very good agreement.

Parametric Estimation of Diffusion Processes: A Review and Comparative Study

This paper provides an in-depth review about parametric estimation methods for stationary stochastic differential equations (SDEs) driven by Wiener noise with discrete time observations. The short-term interest rate dynamics are commonly described by continuous-time diffusion processes, whose parameters are subject to estimation bias, as data are highly persistent, and discretization bias, as data are discretely sampled despite the continuous-time nature of the model. To assess the role of persistence and the impact of sampling frequency on the estimation, we conducted a simulation study under different settings to compare the performance of the procedures and illustrate the finite sample behavior. To complete the survey, an application of the procedures to real data is provided.

Unbiased estimation of the gradient of the log-likelihood in inverse problems

We consider the problem of estimating a parameter theta in Theta subseteq {mathbb {R}}^{d_{theta }} associated with a Bayesian inverse problem. Typically one must resort to a numerical approximation of gradient of the log-likelihood and also adopt a discretization of the problem in space and/or time. We develop a new methodology to unbiasedly estimate the gradient of the log-likelihood with respect to the unknown parameter, i.e. the expectation of the estimate has no discretization bias. Such a property is not only useful for estimation in terms of the original stochastic model of interest, but can be used in stochastic gradient algorithms which benefit from unbiased estimates. Under appropriate assumptions, we prove that our estimator is not only unbiased but of finite variance. In addition, when implemented on a single processor, we show that the cost to achieve a given level of error is comparable to multilevel Monte Carlo methods, both practically and theoretically. However, the new algorithm is highly amenable to parallel computation.

To inquire the effects of different geometric electrodes on current characteristics of C24 fullerene molecular junction.

Two different types of geometric electrode configurations were utilized to form C24 fullerene based molecular junction. The C24 molecule was intercalated in-between gold electrodes with two different shapes viz. knife edge and flat edge and the resultant molecular junctions (MJs) were simulated using nonequilibrium Green's function combined with semiempirical extended Huckel theory (EHT). Different transport parameters, namely projected device density of states, current-voltage curve, differential conductance curve, molecular orbitals, and transmission spectra were investigated at discrete bias voltages to gain insight about the various transport phenomena occurring in these molecular junctions. The results show that when the C24 fullerene is placed in between the flat-edged electrodes, current and conductance are higher in magnitude in comparison to the knife-edged configuration. These deductions give us a new perspective to design advanced molecular devices for electronics applications in the future.

Experimental demonstration of a time-domain digital-coding metasurface for a Doppler cloak.

By generating an artificial Doppler shift, a Doppler cloak can compensate for the Doppler shift from a moving object. An object covered by a Doppler cloak will be detected as a static object, even if it is actually moving. Herein, we experimentally demonstrate the Doppler cloak in a radar system using a time-domain digital-coding metasurface. We theoretically illustrate an active metasurface with a modulated reflection phase that can imitate the motion of moving, thereby generating an artificial Doppler shift for a Doppler cloak. Moreover, a reflective metasurface composed of voltage-controlled varactor diodes with a 3-bit reflection phase was designed and fabricated. Finally, we experimentally demonstrate that an artificial Doppler shift for a Doppler cloak is obtained from the proposed metasurface using a discrete time-varying bias voltage. Simulation and measurement results show that the proposed time-domain digital-coding metasurface can cancel the Doppler shift and serve as a Doppler cloak. The proposed metasurface may have potential applications in a Doppler radar illusion, Doppler cancellation in vehicle-to-vehicle communications, and wireless communications.

Unbiased Inference for Discretely Observed Hidden Markov Model Diffusions

We develop a Bayesian inference method for diffusions observed discretely and with noise, which is free of discretization bias. Unlike existing unbiased inference methods, our method does not rely ...

Towards an Optimization of Sample Plot Size and Scanner Position Layout for Terrestrial Laser Scanning in Multi-Scan Mode

A novel approach is presented to model the tree detection probability of terrestrial laser scanning (TLS) in forest inventory applications using a multi-scan mode. The traditional distance sampling framework is further extended to account for multiple scan positions at a single sample plot and to allow for an imperfect detection probability at distance r = 0. The novel methodology is tested with real world data, as well as in simulations. It is shown that the underlying detection model can be parameterized using only data from single scans. Hereby, it is possible to predict the detection probability also for different sample plot sizes and scanner position layouts in a multi-scan setting. Simulations showed that a minor discretization bias can occur if the sample size is small. The methodology enables a generalized optimization of the scanning layout in a multi-scan setting with respect to the detection probability and the sample plot area. This will increase the efficiency of multi-scan TLS-based forest inventories in the future.

Unpaid Work? Emotional Labor Assessments and Episodic Recall Bias in Public Engagement

We test individual-level job-related assessments as a function of a public employee’s induced recall of discrete citizen engagement and one’s intrinsic prosocial motivation. We are interested in whether tangible retentions of public service influence the relationship between stated, but abstract, self-concepts—such as reported prosociality. Little is known as to the impact of citizen consultation on local government employees or the outcomes that engagement might induce. We find that the relationship between self-reports of prosociality and pay satisfaction are contingent upon those concepts being decontextualized, whereas discrete recall bias appears not to affect emotional burnout. Meanwhile, when induced recall is positively valanced, it has a positive direct effect on subjects’ willingness toward future citizen engagement. In other words, subjects seem to accept the emotional labor of engagement as part of their jobs. However, contextualizing engagement may make them more cognizant of its unremunerated dimensions; and, positive reinforcement of engagement provides encouragement to further engagement.

Emotional labor assessments and episodic recall bias in public engagement

In a survey of local officials in Los Angeles County we test individual-level job-related assessments as a function of a public employee’s induced recall of discrete citizen engagement and one’s intrinsic prosocial motivation through a randomized survey experiment. We explore whether tangible retentions of public service influence the relationship between self-concepts—such as reported prosociality—and job-related assessments. We find that the relationship between self-reports of prosociality and pay satisfaction are contingent upon those concepts being decontextualized, whereas discrete recall bias appears not to affect emotional burnout. In other words, subjects seem to accept the emotional labor of engagement as part of their jobs. However, contextualizing engagement may make them more cognizant of its unremunerated dimensions; and, positive reinforcement of engagement provides encouragement to further engagement. Our findings make the case that emotional labor involves a skill set that employees implicitly recognize merits remuneration and that reinforcing positive engagement outcomes inspires employee motivation.

Neural Connectivity Subtypes Predict Discrete Attentional Bias Profiles Among Heterogeneous Anxiety Patients.

On average, anxious patients show altered attention to threat-including early vigilance towards threat and later avoidance of threat-accompanied by altered functional connectivity across brain regions. However, substantial heterogeneity within clinical, neural, and attentional features of anxiety is overlooked in typical group-level comparisons. We used a well-validated method for data-driven parsing of neural connectivity to reveal connectivity-based subgroups among 60 adults with transdiagnostic anxiety. Subgroups were externally compared on attentional patterns derived from independent behavioral measures. Two subgroups emerged. Subgroup A (68% of patients) showed stronger executive network influences on sensory processing regions and a paradigmatic "vigilance-avoidance" pattern on external behavioral measures. Subgroup B was defined by a larger number of limbic influences on sensory regions and exhibited a more atypical and inconsistent attentional profile. Neural connectivity-based categorization revealed an atypical, limbic-driven pattern of connectivity in a subset of anxious patients that generalized to atypical patterns of selective attention.

Unbiased estimation of the solution to Zakai’s equation

Abstract In the following article, we consider the non-linear filtering problem in continuous time and in particular the solution to Zakai’s equation or the normalizing constant. We develop a methodology to produce finite variance, almost surely unbiased estimators of the solution to Zakai’s equation. That is, given access to only a first-order discretization of solution to the Zakai equation, we present a method which can remove this discretization bias. The approach, under assumptions, is proved to have finite variance and is numerically compared to using a particular multilevel Monte Carlo method.

Spatial DIC Errors due to Pattern-Induced Bias and Grey Level Discretization

Digital image correlation (DIC) is an optical metrology method widely used in experimental mechanics for full-field shape, displacement and strain measurements. The required strain resolution for engineering applications of interest mandates DIC to have a high image displacement matching accuracy, on the order of 1/100th of a pixel, which necessitates an understanding of DIC errors. In this paper, we examine two spatial bias terms that have been almost completely overlooked. They cause a persistent offset in the matching of image intensities and thus corrupt DIC results. We name them pattern-induced bias (PIB), and intensity discretization bias (IDB). We show that the PIB error occurs in the presence of an undermatched shape function and is primarily dictated by the underlying intensity pattern for a fixed displacement field and DIC settings. The IDB error is due to the quantization of the gray level intensity values in the digital camera. In this paper we demonstrate these errors and quantify their magnitudes both experimentally and with synthetic images.