Presence Of Observation Errors Research Articles

Bayesian Approach to Estimate Distribution of Relaxation Times for Lithium-Ion Batteries

Electrochemical impedance spectroscopy (EIS) has emerged as a powerful tool for analyzing the state of lithium-ion batteries due to its ability to provide rich electrochemical information. Traditionally, equivalent circuit and physical models have been utilized for interpreting EIS data. However, these methods possess inherent drawbacks: equivalent circuit models are non-unique, while physical models can be challenging to implement. As an alternative, the distribution of relaxation times (DRT) has garnered increasing attention in recent years. The DRT method enables the analysis of EIS data without predefining a model's shape, allowing for the decomposition of internal characteristics in complex systems, such as lithium-ion batteries. Despite its advantages, DRT estimation is an ill-posed inverse problem that often requires regularization or fine-tuning based on empirical choices, which can lead to the misinterpretation of EIS data.To address these challenges, we propose a Bayesian approach that enables the estimation of DRT while considering uncertainties, even in the presence of observational errors in EIS data. Moreover, the proposed method can assist in estimating the state of health (SOH) of the battery, which provides valuable insights into the battery's overall performance, longevity, and safety. To validate the efficacy of our proposed method, we apply it to synthetic EIS data and compare its performance with existing DRT estimation methods. The results show that the proposed Bayesian approach offers a more robust and accurate estimation of DRT. We also demonstrate the practical applicability of the proposed method by applying it to real lithium-ion battery EIS experimental data, where it successfully extracts meaningful information about the battery's internal state and SOH. In summary, the proposed DRT-based Bayesian method has the potential to enable a robust diagnosis of the internal state and SOH of lithium-ion batteries through EIS measurements. By incorporating this approach, researchers and industry practitioners can gain a deeper understanding of battery performance, facilitating the development of improved diagnostic techniques and battery management strategies to enhance the performance and reliability of lithium-ion batteries. This, in turn, could contribute to the broader adoption of sustainable energy solutions, such as electric vehicles and renewable energy storage systems.This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grants funded by the Ministry of Trade, Industry & Energy, Republic of Korea (No. 20214910100070). Figure 1

Model order estimation based on the correntropy of observation eigenvalues

This paper presents a novel approach for estimating the model order in the presence of observation errors. The proposed method is based on the correntropy estimation of eigenvalues in the observation space. By utilizing the bootstrap method to resample the observations, more precise estimations can be obtained. The next step in the algorithm involves partitioning the observation space, generated by the covariance matrix of mixtures, into two subspaces: the signal subspace and the noise subspace. The order of the model, corresponding to the dimension of the signal subspace, is determined using a correntropy estimator based on kernel functions. Theoretical analysis demonstrates the consistency of the proposed algorithm. Comparative evaluations against existing methods in the literature highlight the superior performance of this information-theoretic approach.

A Modified Regression Estimator for Single Phase Sampling in the Presence of Observational Errors

In this paper, a regression method of estimation has been used to derive the mean estimate of the survey variable using simple random sampling without replacement in the presence of observational errors. Two covariates were used and a case where the observational errors were in both the survey variable and the covariates was considered. The inclusion of observational errors was due to the fact that data collected through surveys are often not free from errors that occur during observation. These errors can occur due to over-reporting, under-reporting, memory failure by the respondents or use of imprecise tools of data collection. The expression of mean squared error (MSE) based on the obtained estimator has been derived to the first degree of approximation. The results of a simulation study show that the derived modified regression mean estimator under observational errors is more efficient than the mean per unit estimator and some other existing estimators. The proposed estimator can therefore be used in estimating a finite population mean, while considering observational errors that may occur during a study.

UAV Autonomous Aerial Combat Maneuver Strategy Generation with Observation Error Based on State-Adversarial Deep Deterministic Policy Gradient and Inverse Reinforcement Learning

With the development of unmanned aerial vehicle (UAV) and artificial intelligence (AI) technology, Intelligent UAV will be widely used in future autonomous aerial combat. Previous researches on autonomous aerial combat within visual range (WVR) have limitations due to simplifying assumptions, limited robustness, and ignoring sensor errors. In this paper, in order to consider the error of the aircraft sensors, we model the aerial combat WVR as a state-adversarial Markov decision process (SA-MDP), which introduce the small adversarial perturbations on state observations and these perturbations do not alter the environment directly, but can mislead the agent into making suboptimal decisions. Meanwhile, we propose a novel autonomous aerial combat maneuver strategy generation algorithm with high-performance and high-robustness based on state-adversarial deep deterministic policy gradient algorithm (SA-DDPG), which add a robustness regularizers related to an upper bound on performance loss at the actor-network. At the same time, a reward shaping method based on maximum entropy (MaxEnt) inverse reinforcement learning algorithm (IRL) is proposed to improve the aerial combat strategy generation algorithm’s efficiency. Finally, the efficiency of the aerial combat strategy generation algorithm and the performance and robustness of the resulting aerial combat strategy is verified by simulation experiments. Our main contributions are three-fold. First, to introduce the observation errors of UAV, we are modeling air combat as SA-MDP. Second, to make the strategy network of air combat maneuver more robust in the presence of observation errors, we introduce regularizers into the policy gradient. Third, to solve the problem that air combat’s reward function is too sparse, we use MaxEnt IRL to design a shaping reward to accelerate the convergence of SA-DDPG.

Estimating recruitment from capture–recapture data by modelling spatio‐temporal variation in birth and age‐specific survival rates

Abstract Understanding the factors influencing recruitment in animal populations is an important objective of many research and conservation programmes. However, evaluating hypotheses is challenging because recruitment is the outcome of birth and survival processes that are difficult to directly observe. Capture–recapture is the most general framework for estimating recruitment in the presence of observation error, but existing methods ignore the underlying birth and survival processes, as well as age effects and spatial variation in vital rates. We present an individual‐based, spatio‐temporal model that can be fit to capture–recapture data to draw inferences on the birth and survival processes governing recruitment dynamics. The number, dates, and spatial distribution of births are modelled as outcomes of a point process, and survival is modelled using a failure time approach. Survival parameters can be modelled as functions of individuals traits and time‐varying, spatial covariates. Continuous‐ and discrete‐time formulations are possible. We demonstrate the model using 7 months of camera data collected on white‐tailed deer Odocoileus virginianus fawns in Big Cypress National Preserve. Spot patterns were used to individually identify 28 fawns, detected 1,454 times between December 1, 2015 and July 1, 2016. A total of 37 (95% CI: 30–49) fawns were born, of which 16 (95% CI: 10–23) survived 180 days to the recruitment age. Mean parturition date was February 14 (95% CI: February 6–February 22), much earlier than in more temperate parts of the species’ range, but coinciding with the dry season in southern Florida. We found little evidence that mortality rates decreased with age, but the estimate of the age effect was imprecise. In contrast, we found strong evidence that encounter rates were age‐specific and increased rapidly over the first month of life as fawns became more mobile. Our case study demonstrates the potential of this new model for advancing knowledge of spatial population dynamics by providing insights into the birth and juvenile survival processes that influence recruitment. Because the model can be applied to data from noninvasive survey methods such as camera trapping, it is possible to apply it at broad spatial scales to understand how environmental variables and predator communities influence recruitment.

Bounding reproductive rates in state‐space models for animal population dynamics

AbstractTime‐series models applied in the study of animal population dynamics commonly assume linearity on the log‐scale, leading to log‐normally distributed rates of increase. While this is often computationally convenient, in particular when performing statistical inference in the presence of observation error, it may lead to unrealistic predictions for animals with a limited reproduction. We introduce a model that includes an explicit bound on the reproductive rate of an individual, and apply this to a population time series of ungulates in Kruger National Park, South Africa. Due to observational error, the year‐to‐year increases in animal counts occasionally exceeded the maximal reproductive rate of the animals. In such cases, the traditional unbounded model showed a tendency of overfitting data, leading to unrealistic predictions of the underlying population increase. An observed increase above the maximal reproductive rate also provides empirical confirmation that observation error exists. The model with an explicit bound was able to utilize this in order to separate observational error from population process noise, which the traditional unbounded model was unable to do. We conclude that enforcing a strict upper bound on the reproductive rate of an animal population model may lead to more realistic statistical inference than commonly applied log‐linear models when an explicit bound on reproductive rate is known. We further conclude that introducing a bound on reproduction can greatly assist in separating observational error and population process noise for slow life histories, or more generally, when the rate of sampling is high compared to reproductive rates.

Verification in the presence of observation errors: Bayesian point of view

Verification in the presence of observation errors is approached from the Bayesian point of view. Like data assimilation (DA), Bayesian verification is shown to have a robust foundation established by Bayesian inference. Together, DA and Bayesian verification form two difference levels of Bayesian inference. Evaluation of a model is equivalent to inference on the plausibility of this model given observations. Relative performances between different models are measured by ratios of posterior plausibilities, which becomes ratios of likelihoods in the case of no prior information. These ratios are called the Bayes factors and are the standard verification method in Bayesian model comparison. Since verification scores are used intensively in numerical weather prediction, the verification scores derived from likelihoods are proposed to replace the Bayes factors in Bayesian verification. With two requirements that the verification scores are both strictly proper and local, the logarithm score, i.e. log‐likelihood, and its linear transformation are shown to be the unique class.Log‐likelihoods in Bayesian verification are determined by the form of forecast probability distributions from models. The empirical form is preferable because of its flexibility in incorporating not only observation errors but also other uncertainties in observation biases or observation error variances into calculation to obtain closed forms for log‐likelihoods. When applied to observations with Gaussian errors, the logarithm score induces the weighted mean‐squared error which is non‐dimensional and can be used for both univariate and multivariate observations. The most interesting application of Bayesian verification is to offer a new explanation for rank histograms and quantify flatness of rank histograms by a metric which turns out to be the Kullback–Leibler divergence between the rank distribution observed in reality and a uniform rank distribution. It is worthy of note that the two very different metrics come from the logarithm score.

Measuring forecast performance in the presence of observation error

A new framework is introduced for measuring the performance of probability forecasts when the true value of the predictand is observed with error. In these circumstances, proper scoring rules favour good forecasts of observations rather than of truth and yield scores that vary with the quality of the observations. Proper scoring rules thus can favour forecasters who issue worse forecasts of the truth and can mask real changes in forecast performance if observation quality varies over time. Existing approaches to accounting for observation error provide unsatisfactory solutions to these two problems. A new class of ‘error‐corrected’ proper scoring rules is defined that solves both problems by producing unbiased estimates of the scores that would be obtained if the forecasts could be verified against the truth. A general method for constructing error‐corrected proper scoring rules is given for the case of categorical predictands, and error‐corrected versions of the Dawid–Sebastiani scoring rule are proposed for numerical predictands. The benefits of accounting for observation error in ensemble post‐processing and in forecast verification are illustrated in three data examples that include forecasts for the occurrence of tornadoes and of aircraft icing.

Long time horizon for adaptive management to reveal predation effects in a salmon fishery.

Predator-prey interactions shape ecosystem structure and function, potentially limiting the productivity of valuable species. Simultaneously, stochastic environmental forcing affects species productivity, often through unknown mechanisms. The interacting effects of trophic and environmental conditions complicate management of exploited ecosystems and have motivated calls for more holistic management via ecosystem-based approaches, yet the limitations to these approaches are not widely appreciated. The Chignik salmon fishery in Alaska is managed to achieve maximum sustainable yield for sockeye salmon, though research suggests that predation by less economically valuable, and thus not targeted, coho salmon during juvenile rearing limits the productivity of sockeye salmon. We examined the relationship between historical sockeye salmon recruitment and coho salmon abundance observed in the Chignik system and could not detect a clear effect of coho salmon abundance on sockeye salmon productivity, given existing data. Using simulation models, we examined the probability of detecting a known predation effect on sockeye salmon recruitment in the presence of observation error in coho salmon abundance and stochasticity in sockeye salmon recruitment. Increased recruitment stochasticity reduced the ability to detect predator effects in recruitment, an effect further strengthened when low frequency environmental variation was added to the system. Further, increased observation error biased estimates of predator effects towards zero. Thus, in systems with high observation error on predator abundances, estimates of predation effects will be substantially weaker than true effects. We examined the effects of stochasticity on the ability of an adaptive management program to learn about ecosystem structure and detect an effect of management actions intended to release a prey species from its predators. Simulation models revealed that even under scenarios of large predation effects on sockeye salmon, stochastic recruitment masked detection of an effect of increased coho salmon harvest for nearly a decade. These results highlight the challenges inherent in ecosystem-based management of predator-prey systems due to mismatched timescales of ecosystem dynamics and the willingness of stakeholders to risk losses in order to test uncertain hypotheses. It is critical for stakeholders considering EBFM (ecosystem-based fisheries management) and adaptive management strategies to be aware of the potential timelines of perceiving ecosystem change.

A noisy principal component analysis for forward rate curves

Principal Component Analysis (PCA) is the most common nonparametric method for estimating the volatility structure of Gaussian interest rate models. One major difficulty in the estimation of these models is the fact that forward rate curves are not directly observable from the market so that non-trivial observational errors arise in any statistical analysis. In this work, we point out that the classical PCA analysis is not suitable for estimating factors of forward rate curves due to the presence of measurement errors induced by market microstructure effects and numerical interpolation. Our analysis indicates that the PCA based on the long-run covariance matrix is capable to extract the true covariance structure of the forward rate curves in the presence of observational errors. Moreover, it provides a significant reduction in the pricing errors due to noisy data typically found in forward rate curves.

Estimating the strength of density dependence in the presence of observation errors using integrated population models

Assessing the strength of density dependence is crucial for understanding population dynamics, but its estimation is difficult. Because estimates of population size and demographic parameters usually include errors due to imperfect detection, estimations of the strength of density dependence will be biased if obtained with conventional methods and lack statistical power to detect density dependence. We propose a Bayesian integrated population model to study density dependence. The model allows assessing the effect of density both on the population growth rate as well as the demographic parameters while accounting for imperfect detection. We studied the performance of this model using simulation and illustrate its use with data on red-backed shrikes Lanius collurio. Our simulation results showed that the strength of density dependence is identifiable and it was estimated with higher precision using the integrated population model than the conventional regression model. As expected, the conventional regression model tended to overestimate density dependence at the population level whereas underestimates at the demographic level, but the bias was small. The analysis of the red-backed shrike data revealed negative density dependence at the population level most likely mediated by a density-dependent decline in adult survival. This work highlights the potential of integrated population models in assessing density dependence and its practical application in population studies.

On parameter estimation in population models III: Time-inhomogeneous processes and observation error

Essential to applying a mathematical model to a real-world application is calibrating the model to data. Methods for calibrating population models often become computationally infeasible when the population size (more generally the size of the state space) becomes large, or other complexities such as time-dependent transition rates, or sampling error, are present. Continuing previous work in this series on the use of diffusion approximations for efficient calibration of continuous-time Markov chains, I present efficient techniques for time-inhomogeneous chains and accounting for observation error. Observation error (partial observability) is accounted for by joint estimation using a scaled unscented Kalman filter for state-space models. The methodology will be illustrated with respect to models of disease dynamics incorporating seasonal transmission rate and in the presence of observation error, including application to two influenza outbreaks and measles in London in the pre-vaccination era.

Likelihood based population viability analysis in the presence of observation error

Population viability analysis (PVA) entails calculation of extinction risk, as defined by various extinction metrics, for a study population. These calculations strongly depend on the form of the population growth model and inclusion of demographic and/or environmental stochasticity. Form of the model and its parameters are determined based on observed population time series data. A typical population time series, consisting of estimated population sizes, inevitably has some observation error and likely has missing observations. In this paper, we present a likelihood based PVA in the presence of observation error and missing data. We illustrate the importance of incorporation of observation error in PVA by reanalyzing the population time series of song sparrow Melospiza melodia on Mandarte Island, British Columbia, Canada from 1975–1998. Using Akaike information criterion we show that model with observation error fits the data better than the one without observation error. The extinction risks predicted by with and without observation error models are quite different. Further analysis of possible causes for observation error revealed that some component of the observation error might be due to unreported dispersal. A complete analysis of such data, thus, would require explicit spatial models and data on dispersal along with observation error. Our conclusions are, therefore, two‐fold: 1) observation errors in PVA matter and 2) integrating these errors in PVA is not always enough and can still lead to important biases in parameter estimates if other processes such as dispersal are ignored.

Detection of satellite remnants in the Galactic Halo with Gaia - II. A modified great circle cell method

We propose an extension of the GC3 streamer finding method of Johnston et al. 1996 that can be applied to the future Gaia database. The original method looks for streamers along great circles in the sky, our extension adds the kinematical restriction that velocity vectors should also be constrained to lie along these great circles, as seen by a Galactocentric observer. We show how to use these combined criteria starting from heliocentric observables. We test it by using the mock Gaia catalogue of Brown et al. 2005, which includes a realistic Galactic background and observational errors, but with the addition of detailed star formation histories for the simulated satellites. We investigate its success rate as a function of initial satellite luminosity, star formation history and orbit. We find that the inclusion of the kinematical restriction vastly enhances the contrast between a streamer and the background, even in the presence of observational errors, provided we use only data with good astrometric quality (fractional errors of 30 per cent or better). The global nature of the method diminishes the erasing effect of phase mixing and permits the recovery of merger events of reasonable dynamical age. Satellites with a star formation history different to that of the Galactic background are also better isolated. We find that satellites in the range of 10^8-10^9 Lsun can be recovered even for events as old as ~10 Gyr. Even satellites with 4-5x10^7 Lsun can be recovered for certain combinations of dynamical ages and orbits.

Knowledge acquisition by networks of interacting agents in the presence of observation errors

In this work we investigate knowledge acquisition as performed by multiple agents interacting as they infer, under the presence of observation errors, respective models of a complex system. We focus the specific case in which, at each time step, each agent takes into account its current observation as well as the average of the models of its neighbors. The agents are connected by a network of interaction of Erdos-Rényi or Barabási-Albert type. First, we investigate situations in which one of the agents has a different probability of observation error (higher or lower). It is shown that the influence of this special agent over the quality of the models inferred by the rest of the network can be substantial, varying linearly with the respective degree of the agent with different estimation error. In case the degree of this agent is taken as a respective fitness parameter, the effect of the different estimation error is even more pronounced, becoming superlinear. To complement our analysis, we provide the analytical solution of the overall performance of the system. We also investigate the knowledge acquisition dynamic when the agents are grouped into communities. We verify that the inclusion of edges between agents (within a community) having higher probability of observation error promotes the loss of quality in the estimation of the agents in the other communities.

Estimating environmental effects on population dynamics: consequences of observation error

Within the paradigm of population dynamics a central task is to identify environmental factors affecting population change and to estimate the strength of these effects. We here investigate the impact of observation errors in measurements of population densities on estimates of environmental effects. Adding observation errors may change the autocorrelation of a population time series with potential consequences for estimates of effects of autocorrelated environmental covariates. Using Monte Carlo simulations, we compare the performance of maximum likelihood estimates from three stochastic versions of the Gompertz model (log–linear first order autoregressive model), assuming 1) process error only, 2) observation error only, and 3) both process and observation error (the linear state–space model on log‐scale). We also simulated population dynamics using the Ricker model, and evaluated the corresponding maximum likelihood estimates for process error models. When there is observation error in the data and the considered environmental variable is strongly autocorrelated, its estimated effect is likely to be biased when using process error models. The environmental effect is overestimated when the sign of the autocorrelations of the intrinsic dynamics and the environment are the same and underestimated when the signs differ. With non‐autocorrelated environmental covariates, process error models produce fairly exact point estimates as well as reliable confidence intervals for environmental effects. In all scenarios, observation error models produce unbiased estimates with reasonable precision, but confidence intervals derived from the likelihood profiles are far too optimistic if there is process error present. The safest approach is to use state–space models in presence of observation error. These are factors worthwhile to consider when interpreting earlier empirical results on population time series, and in future studies, we recommend choosing carefully the modelling approach with respect to intrinsic population dynamics and covariate autocorrelation.

ESTIMABILITY OF DENSITY DEPENDENCE IN MODELS OF TIME SERIES DATA.

Estimation of density dependence from time series data on population abundance is hampered in the presence of observation or measurement errors. Fitting state-space models has been proposed as a solution that reduces the bias in estimates of density dependence caused by ignoring observation errors. While this is often true, I show that, for specific parameter values, there are identifiability issues in the linear state-space model when the strength of density dependence and the observation and process error variances are all unknown. Using simulation to explore properties of the estimators, I illustrate that, unless assumptions are imposed on the process or observation error variances, the variance of the estimator of density dependence varies critically with the strength of the density dependence. Under compensatory dynamics, the stronger the density dependence the more difficult it is to estimate in the presence of observation errors. The identifiability issues disappear when density dependence is estimated from the state-space model with the observation error variance known to the correct value. Direct estimates of observation variance in abundance censuses could therefore prove helpful in estimating density dependence but care needs to be taken to assess the uncertainty in variance estimates.

Design of experiments for response diversity

A design method is proposed that sequentially generates observation sites for the construction of a kriging predictive model. The objective of the construction is to allow a precise inversion of the system in the following sense: with any reachable target point T in the output space one wishes to be able to associate an input vector xt such that the system response at xt will be close to T (which requires that the model ensures a precise prediction of the response at xt). Intuitively, the observation sites should not be spread over the admissible input space, but should rather concentrate in areas such that, when mapped by the system, they cover the reachable output space. Two approaches are proposed that are shown on examples (one with five input and two outputs, derived from a problem in oil industry) to give satisfactory results. They are based on the maximization of a measure of dispersion of the observations in the output space and can cope with the presence of observation errors, a rather typical situation for experimentation with real physical systems.

Detection of satellite remnants in the Galactic Halo withGaia- I. The effect of the Galactic background, observational errors and sampling

We address the problem of identifying remnants of satellite galaxies in the halo of our galaxy with Gaia data. The Gaia astrometric mission offers a unique opportunity to search for and study these remnants using full phase-space information for the halo of our Galaxy. However, the remnants have to be extracted from a very large data set (of the order of 109 stars) in the presence of observational errors and against a background population of Galactic stars. We address this issue through numerical simulations with a view towards timely preparations for the scientific exploitation of the Gaia data. We present a Monte Carlo simulation of the Gaia catalogue with a realistic number of entries. We use a model of the galaxy that includes separate light distributions and kinematics for the bulge, disc and stellar halo components. For practical reasons we exclude the region within Galactic coordinates: −90°≤l≤ 90° and −5°≤b≤ 5°, close to the Galactic plane and centre. Nevertheless, our catalogue contains 3.5 × 108 stars. No interstellar absorption has been modelled, as we limit our study to high Galactic latitudes. We perform tree code 106–body simulations of satellite dwarf galaxies in orbit around a rigid mass model of the Galaxy. We follow the simulations for 1010 yr. The resulting shrinking satellite cores and tidal tails are then added to the Monte Carlo simulation of the Gaia catalogue. To assign photometric properties to the particles we use a Hess diagram for the Solar neighbourhood for Galactic particles, while for the dwarf galaxy particles we use isochrones from the Padova group. When combining the Milky Way and dwarf galaxy models we include the complication that the luminosity function of the satellite is probed at various depths as a function of position along the tidal tails. The combined Galaxy and satellites model is converted to a synthetic Gaia catalogue using a detailed model for the expected astrometric and radial velocity errors, depending on magnitude, colour and sky position of the stars. We explore the feasibility of detecting tidal streams in the halo using the energy versus angular momentum plane. We find that a straightforward search in this plane will be very challenging. The combination of the background population and the observational errors will make it difficult to detect tidal streams as discrete structures in the E–Lz plane. In addition the propagation of observational errors leads to apparent caustic structures in the integrals of motion space that may be mistaken for physical entities. Any practical search strategy will have to use a combination of pre-selection of high-quality data and complementary searches using the photometric data that will be provided by Gaia.

Estimating the endpoint of a distribution in the presence of additive observation errors

We consider the problem of estimating the endpoint of a probability distribution in the presence of observation errors, when the available sample is drawn from the convolution with some error density. We study the cases of Gaussian errors and errors with bounded support, and propose estimators that are optimal in a minimax sense.