True Parameters Research Articles

Three new corrections for standardized person-fit statistics for tests with polytomous items.

Recent years have seen a growing interest in the development of person-fit statistics for tests with polytomous items. Some of the most popular person-fit statistics for such tests belong to the class of standardized person-fit statistics, , that is assumed to have a standard normal null distribution. However, this distribution only holds when (a) the true ability parameter is known and (b) an infinite number of items are available. In practice, both conditions are violated, and the quality of person-fit results is expected to deteriorate. In this paper, we propose three new corrections for that simultaneously account for the use of an estimated ability parameter and the use of a finite number of items. The three new corrections are direct extensions of those that were developed by Gorney etal. (Psychometrika, 2024, https://doi.org/10.1007/s11336-024-09960-x) for tests with only dichotomous items. Our simulation study reveals that the three new corrections tend to outperform not only the original statistic but also an existing correction for proposed by Sinharay (Psychometrika, 2016, 81, 992). Therefore, the new corrections appear to be promising tools for assessing person fit in tests with polytomous items.

Prediction of unobserved bifurcation by unsupervised extraction of slowly time-varying system parameter dynamics from time series using reservoir computing

IntroductionNonlinear and non-stationary processes are prevalent in various natural and physical phenomena, where system dynamics can change qualitatively due to bifurcation phenomena. Machine learning methods have advanced our ability to learn and predict such systems from observed time series data. However, predicting the behavior of systems with temporal parameter variations without knowledge of true parameter values remains a significant challenge.MethodsThis study uses reservoir computing framework to address this problem by unsupervised extraction of slowly varying system parameters from time series data. We propose a model architecture consisting of a slow reservoir with long timescale internal dynamics and a fast reservoir with short timescale dynamics. The slow reservoir extracts the temporal variation of system parameters, which are then used to predict unknown bifurcations in the fast dynamics.ResultsThrough experiments on chaotic dynamical systems, our proposed model successfully extracted slowly varying system parameters and predicted bifurcations that were not included in the training data. The model demonstrated robust predictive performance, showing that the reservoir computing framework can handle nonlinear, non-stationary systems without prior knowledge of the system's true parameters.DiscussionOur approach shows potential for applications in fields such as neuroscience, material science, and weather prediction, where slow dynamics influencing qualitative changes are often unobservable.

Neutral atomic and molecular gas dynamics in the nearby spiral galaxies NGC 1512, NGC 4535, and NGC 7496

Neutral atomic gas (H I) effectively traces galactic dynamics across mid to large galactocentric radii. However, its limitations in observing small-scale changes within the central few kiloparsecs, coupled with the often observed H I deficit in galactic centers, necessitates the use of molecular gas emission as a preferred tracer in these regions. Understanding the dynamics of both neutral atomic and molecular gas is crucial for a more complete understanding of how galaxies evolve, funnel gas from the outer disk into their central parts, and eventually form stars. In this work we aim to quantify the dynamics of both, the neutral atomic and molecular gas, in the nearby spiral galaxies NGC 1512, NGC 4535, and NGC 7496 using new MeerKAT H I observations together with ALMA CO (2-1) observations from the PHANGS collaboration. We use the analysis tool 3DBarolo to fit tilted ring models to the H I and CO observations. A combined approach of using the H I to constrain the true disk orientation parameters before applying these to the CO datasets is tested. This paper sets expectations for the results of the upcoming high-resolution H I coverage of many galaxies in the PHANGS-ALMA sample using MeerKAT or VLA, to establish a robust methodology for characterizing galaxy orientations and deriving dynamics from combing new H I with existing CO data.

Self‐Potential Tomography Preconditioned by Particle Swarm Optimization—Application to Monitoring Hyporheic Exchange in a Bedrock River

AbstractA self‐potential (SP) data‐inversion algorithm was developed and tested on an analytical model of electrical‐potential profile data attributed to single and multiple polarized electrical sources. The developed algorithm was then validated by an application to SP‐monitoring field data measured on the floodplain of East Fork Poplar Creek, Oak Ridge, Tennessee, to image electrical sources in areas conducive to preferential flow into the flood plain from the bedrock‐lined riverbed. The algorithm combined stochastic source‐localization by particle‐swarm‐optimization (PSO) of electrical sources characterized by simplified geometries with source tomography by regularized weighted least‐squares minimization of a quadratic objective function. Prior information was incorporated by preconditioning the tomography algorithm by PSO results. Variable percentages of random noise were added to analytical‐model data to evaluate the algorithm performance. Results indicated that true parameters of single‐source models were inverted and approximated with small residual error, whereas inversion of analytical‐model data representing multiple electrical sources accurately approximated the locations of the sources but miscalculated some parameters because of the non‐uniqueness of the inverse‐model solution. Source tomography applied to analytical model data during testing produced a spatially continuous parameter field that identified the locations of point‐scale synthetic dipole sources of electrical current flow with varying degrees of accuracy depending on the prior information incorporated into the tomography. When applied to SP‐monitoring field data, the algorithm imaged electrical sources within a known fault that intersects the bedrock riverbed and flood plain of East Fork Poplar Creek and depicted dynamic electrical conditions attributed to hyporheic exchange.

Inversion of Gravity Anomalies by a Hybrid Metaheuristic Algorithm

In this work, we introduce application of a hybrid algorithm (DE/PSO) to estimate the model parameters from residual gravity anomalies due to some simple geometrical bodies. This algorithm combines differential evolution (DE) and particle swarm optimization (PSO). To investigate the performance of the hybrid algorithm, test studies were carried out using synthetic and field data sets. The synthetic data sets include noise-free and noisy synthetic anomalies. Two published gravity anomalies from Cuba and Canada were used as the field data. In the hybrid algorithm, DE and PSO yield [premature] solutions separately and share their best solutions during an iterative process. An openly accessible metaheuristics package (NMOF) in R programming environment was used to implement the hybrid algorithm. Through simulations using synthetic anomalies, DE/PSO algorithm was successful to provide improved results. In comparison to the solutions from the single algorithms (DE and PSO), the DE/PSO algorithm shows more effectiveness in terms of accuracy and convergence. The true model parameters of noise-free and noisy synthetic gravity anomalies were recovered well by the hybrid algorithm. The results of inversion for the field examples are characterized by low residual values between the observed gravity anomalies and the calculated ones.

A Bhattacharyya-type Conditional Error Bound for Quadratic Discriminant Analysis

We give an upper bound on the conditional error of Quadratic Discriminant Analysis (QDA), conditioned on parameter estimates. In the case of maximum likelihood estimation (MLE), our bound recovers the well-known Chernoff and Bhattacharyya bounds in the infinite sample limit. We perform an empirical assessment of the behaviour of our bound in a finite sample MLE setting, demonstrating good agreement with the out-of-sample error, in contrast with the simpler but uninformative estimated error, which exhibits unnatural behaviour with respect to the sample size. Furthermore, our conditional error bound is applicable whenever the QDA decision function employs parameter estimates that differ from the true parameters, including regularised QDA.

A robust M-estimator for Gaussian ARMA time series based on the Whittle approximation

In the frequency domain, the Whittle approach using the classical periodogram is traditionally used to estimate the parameters of a stationary time series. The M-periodogram has recently become an alternative tool for analyzing the dependence of time series. It is particularly useful for dealing with outliers and heavy-tailed noise. This paper proposes an alternative to the standard Whittle approach, the M-Whittle estimator, built from the M-periodogram. We show that the proposed method is a consistent estimator of the true parameters of an ARMA process. A finite sample investigation is carried out to assess the performance of the estimator in the scenarios of contaminated and uncontaminated time series. As expected, for the uncontaminated data, the M-Whittle estimator performs similarly to the classical Whittle approach. However, the superiority of the first method is clear in terms of root mean squared error when the series has additive outliers. Two applications are considered to illustrate the methodologies in real data contexts. Regardless of whether or not the data are contaminated by additive outliers, the results presented here strongly motivate using the M-Whittle estimator in practical problems.

On learning sparse linear models from cross samples

The sample complexity of a sparse linear model where samples are dependent is studied in this paper. We consider a specific dependency structure of the samples which arises in some experimental designs such as drug sensitivity studies, where two sets of objects (drugs and cells) are sampled independently, and after crossing (making all possible combinations of drugs and cells), the resulting output (efficacy of drugs) is measured. We call these types of samples as “cross samples”. The dependency among such samples is strong, and existing theoretical studies are either inapplicable or fail to provide realistic bounds. We aim at analyzing the performance of the Lasso estimator where the underlying distributions are mixtures of Gaussians and the data dependency arises from the crossing procedure. Our theoretical results show that the performance of the Lasso estimator in case of cross samples follows that of the i.i.d. samples with differences in constant factors. Through numerical results, we observe a phase transition: When datasets are too small, the error for cross samples is much larger than for i.i.d. samples, but once the size is large enough, cross samples are nearly as useful as i.i.d. samples. Our theoretical analysis suggests that the transition threshold is governed by the level of sparsity of the true parameter vector being estimated.

Estimation of spatial demographic maps from polymorphism data using a neural network.

A fundamental goal in population genetics is to understand how variation is arrayed over natural landscapes. From first principles we know that common features such as heterogeneous population densities and barriers to dispersal should shape genetic variation over space, however there are few tools currently available that can deal with these ubiquitous complexities. Geographically referenced single nucleotide polymorphism (SNP) data are increasingly accessible, presenting an opportunity to study genetic variation across geographic space in myriad species. We present a new inference method that uses geo-referenced SNPs and a deep neural network to estimate spatially heterogeneous maps of population density and dispersal rate. Our neural network trains on simulated input and output pairings, where the input consists of genotypes and sampling locations generated from a continuous space population genetic simulator, and the output is a map of the true demographic parameters. We benchmark our tool against existing methods and discuss qualitative differences between the different approaches; in particular, our program is unique because it infers the magnitude of both dispersal and density as well as their variation over the landscape, and it does so using SNP data. Similar methods are constrained to estimating relative migration rates, or require identity-by-descent blocks as input. We applied our tool to empirical data from North American grey wolves, for which it estimated mostly reasonable demographic parameters, but was affected by incomplete spatial sampling. Genetic based methods like ours complement other, direct methods for estimating past and present demography, and we believe will serve as valuable tools for applications in conservation, ecology and evolutionary biology. An open source software package implementing our method is available from https://github.com/kr-colab/mapNN.

STATISTICAL INFERENCE ON SINE-EXPONENTIAL DISTRIBUTION PARAMETER

The Sine-Exponential (Sine-E) distribution is a probability distribution that combines the periodic behavior of the sine function with the decay characteristic of the exponential function. This study addresses the problem of identifying the most accurate and reliable estimation method for the parameter of the Sine-E distribution. The objective is to evaluate various parameter estimation techniques, including Maximum Likelihood Estimation (MLE), Least Squares Estimation (LSE), Weighted Least Squares Estimation (WLSE), Maximum Product of Spacing Estimation (MPSE), Cramer-von-Mises Estimation (CVME), and Anderson-Darling Estimation (ADE), using Mean Square Error (MSE) as the criterion for determining the technique with the minimum error. The study’s findings reveal that as sample size increases, the parameter estimates for all techniques converge to the true parameter value, with decreases in bias, MSE, and mean relative estimates. Among the techniques evaluated, the MPSE method consistently provides estimates closest to the true parameter value and exhibits the least bias and lowest MSE across small, moderate, and large sample sizes, making it the best estimator for the Sine-E distribution.

Estimating Parameters of Physics-Based Battery Models – What Machine Learning Can and Cannot Do

With the widespread use of Lithium-ion (Li-ion) batteries in multiple industries, the design space for the electrochemical cells has increased drastically. Li-ion batteries’ design parameters and material properties, such as porosity, electrode thickness, active material loading, and solid phase diffusivities, typically vary substantially due to different design goals and variation in the manufacturing process. Due to the difficulty in obtaining these and other battery cell parameters, many battery management systems used to control and monitor Li-ion batteries opt for the simplified resistor-capacitor circuit-based battery cell representation over using physics-based battery models. However, if these parameters become obtainable, scientists could implement advanced battery management systems using physics-based battery models to capture precisely how the battery performs and degrades in a wide variety of applications. Multiple methods, such as genetic algorithms, statistics, and machine learning, have been attempted for the parametrization and characterization of battery cells to enable accurate battery simulations using physics-based models [1, 2]. However, there are inherent limitations to the type and number of parameters that can be estimated using these methods if only the standard battery cell cycling data is utilized for this purpose. The present work elucidates and quantifies these limitations specifically in the case of machine learning based approach and provides deeper insights into these limitations that may help develop more robust cell characterization protocols. In the present work, model parameters are varied in a continuum-level physics-based model and simulations are performed for: (1) constant current-constant voltage (CC-CV) charging and constant current discharge at different C-rates, and (2) electrochemical impedance spectroscopy (EIS) in the relevant frequency range at multiple states of charge (SOCs). The Single Particle Model (SPM) is used for performing these simulations due to its relative simplicity and small number of parameters. At first, the charge and discharge data are input as training data in a long short-term memory neural network (LSTM NN), and EIS data is input as training data in a convolutional neural network (CNN). Once trained, the machine learning (ML) model uses charge, discharge, and EIS data withheld from the original training data set to predict SPM parameters. The estimated parameters are compared with the true parameters used for SPM charge, discharge, and EIS simulations, and the error in parameter estimation is quantified. A rigorous grid convergence analysis is performed to highlight the importance of ensuring that the spatial discretization error of the model does not influence the parameter estimation accuracy. For the first error quantification, all parameters are varied concurrently to obtain the parameter estimation error that arises from a large, undetermined parameter set. Parameters are then analyzed individually and in clusters related to diffusion, kinetics, and stoichiometric limitations. Further analysis is performed on parameters that could not be estimated with sufficient accuracy, including theoretical explanations for the incurred error and the effect of this error on the internal state predictions.

Hamiltonian Identification via Quantum Ensemble Classification.

Identifying the Hamiltonian of an unknown quantum system is a critical task in the area of quantum information. In this article, we propose a systematic Hamiltonian identification approach via quantum ensemble multiclass classification (HI-QEMC). This approach is implemented by a three-step iterative refining process, i.e., parameter interval guess, verification, and judgment. In the parameter interval guess step, the parameter interval is divided into several sub-intervals and the true Hamiltonian parameter is guessed in one of them. In the parameter interval verification step, cross verification is applied to verify the accuracy of the guess. In the parameter interval judgment step, an adaptive interval judgment (AIJ) algorithm is designed to determine the sub-interval containing the true Hamiltonian parameter. Numerical results on two typical quantum systems, i.e., two-level quantum systems and three-level quantum systems, demonstrate the effectiveness and superior performance of the proposed approach for quantum Hamiltonian identification.

Blouch: Bayesian Linear Ornstein-Uhlenbeck Models for Comparative Hypotheses.

Relationships among species in the tree of life can complicate comparative methods and testing adaptive hypotheses. Models based on the Ornstein-Uhlenbeck process permit hypotheses about adaptation to be tested by allowing traits to either evolve towards fixed adaptive optima (e.g., regimes or niches) or track continuously changing optima that can be influenced by other traits. These models allow estimation of the effects of both adaptation and phylogenetic inertia - resistance to adaptation due to any source - on trait evolution, an approach known as the "adaptation-inertia" framework. However, previous applications of this framework, and most approaches suggested to deal with the issue of species non-independence, are based on a maximum likelihood approach and thus it is difficult to include information based on prior biological knowledge in the analysis, which can affect resulting inferences. Here I present Blouch, (Bayesian Linear Ornstein-Uhlenbeck Models for Comparative Hypotheses), which fits allometric and adaptive models of continuous trait evolution in a Bayesian framework based on fixed or continuous predictors and incorporates measurement error. I first briefly discuss the models implemented in Blouch, and then the new applications for these models provided by a Bayesian framework. This includes the advantages of assigning biologically meaningful priors when compared to non-Bayesian approaches, allowing for varying effects (intercepts and slopes), and multilevel modeling. Validations on simulated data show good performance in recovering the true evolutionary parameters for all models. To demonstrate the workflow of Blouch on an empirical dataset, I test the hypothesis that the relatively larger antlers of larger bodied deer are the result of more intense sexual selection that comes along with their tendency to live in larger breeding groups. While results show that larger bodied deer that live in larger breeding groups have relatively larger antlers, deer living in the smallest groups appear to have a different and steeper scaling pattern of antler size to body size than other groups. These results are contrary to previous findings and may argue that a different type of sexual selection or other selective pressures govern optimum antler size in the smallest breeding groups.

Estimation of spatial demographic maps from polymorphism data using a neural network.

A fundamental goal in population genetics is to understand how variation is arrayed over natural landscapes. From first principles we know that common features such as heterogeneous population densities and barriers to dispersal should shape genetic variation over space, however there are few tools currently available that can deal with these ubiquitous complexities. Geographically referenced single nucleotide polymorphism (SNP) data are increasingly accessible, presenting an opportunity to study genetic variation across geographic space in myriad species. We present a new inference method that uses geo-referenced SNPs and a deep neural network to estimate spatially heterogeneous maps of population density and dispersal rate. Our neural network trains on simulated input and output pairings, where the input consists of genotypes and sampling locations generated from a continuous space population genetic simulator, and the output is a map of the true demographic parameters. We benchmark our tool against existing methods and discuss qualitative differences between the different approaches; in particular, our program is unique because it infers the magnitude of both dispersal and density as well as their variation over the landscape, and it does so using SNP data. Similar methods are constrained to estimating relative migration rates, or require identity by descent blocks as input. We applied our tool to empirical data from North American grey wolves, for which it estimated mostly reasonable demographic parameters, but was affected by incomplete spatial sampling. Genetic based methods like ours complement other, direct methods for estimating past and present demography, and we believe will serve as valuable tools for applications in conservation, ecology, and evolutionary biology. An open source software package implementing our method is available from https://github.com/kr-colab/mapNN .

Leveraging independence in high-dimensional mixed linear regression.

We address the challenge of estimating regression coefficients and selecting relevant predictors in the context of mixed linear regression in high dimensions, where the number of predictors greatly exceeds the sample size. Recent advancements in this field have centered on incorporating sparsity-inducing penalties into the expectation-maximization (EM) algorithm, which seeks to maximize the conditional likelihood of the response given the predictors. However, existing procedures often treat predictors as fixed or overlook their inherent variability. In this paper, we leverage the independence between the predictor and the latent indicator variable of mixtures to facilitate efficient computation and also achieve synergistic variable selection across all mixture components. We establish the non-asymptotic convergence rate of the proposed fast group-penalized EM estimator to the true regression parameters. The effectiveness of our method is demonstrated through extensive simulations and an application to the Cancer Cell Line Encyclopedia dataset for the prediction of anticancer drug sensitivity.

Bootstrap test procedure for variance components in nonlinear mixed effects models in the presence of nuisance parameters and a singular Fisher information matrix

Summary We examine the problem of variance component testing in general mixed effects models using the likelihood ratio test. We account for the presence of nuisance parameters, ie, the fact that some untested variances might also be equal to zero. Two main issues arise in this context, leading to a nonregular setting. First, under the null hypothesis, the true parameter value lies on the boundary of the parameter space. Moreover, due to the presence of nuisance parameters, the exact locations of these boundary points are not known, which prevents the use of classical asymptotic theory of maximum likelihood estimation. Then, in the specific context of nonlinear mixed effects models, the Fisher information matrix is singular at the true parameter value. We address these two points by proposing a shrunk parametric bootstrap procedure, which is straightforward to apply even for nonlinear models. We show that the procedure is consistent, solving both the boundary and the singularity issues, and we provide a verifiable criterion for the applicability of our theoretical results. We show through a simulation study that, compared to the asymptotic approach, our procedure has a better small sample performance and is more robust to the presence of nuisance parameters. A real data application on bird growth rates is also provided.

Using Object-Oriented Simulation to Assess the Impact of the Frequency and Accuracy of Mobility Scoring on the Estimation of Epidemiological Parameters for Lameness in Dairy Herds.

Mobility scoring data can be used to estimate the prevalence, incidence, and duration of lameness in dairy herds. Mobility scoring is often performed infrequently with variable sensitivity, but how this impacts the estimation of lameness parameters is largely unknown. We developed a simulation model to investigate the impact of the frequency and accuracy of mobility scoring on the estimation of lameness parameters for different herd scenarios. Herds with a varying prevalence (10, 30, or 50%) and duration (distributed around median days 18, 36, 54, 72, or 108) of lameness were simulated at daily time steps for five years. The lameness parameters investigated were prevalence, duration, new case rate, time to first lameness, and probability of remaining sound in the first year. True parameters were calculated from daily data and compared to those calculated when replicating different frequencies (weekly, two-weekly, monthly, quarterly), sensitivities (60-100%), and specificities (95-100%) of mobility scoring. Our results showed that over-estimation of incidence and under-estimation of duration can occur when the sensitivity and specificity of mobility scoring are <100%. This effect increases with more frequent scoring. Lameness prevalence was the only parameter that could be estimated with reasonable accuracy when simulating quarterly mobility scoring. These findings can help inform mobility scoring practices and the interpretation of mobility scoring data.

Optimal estimation of pure states with displaced-null measurements

We revisit the problem of estimating an unknown parameter of a pure quantum state, and investigate ‘null-measurement’ strategies in which the experimenter aims to measure in a basis that contains a vector close to the true system state. Such strategies are known to approach the quantum Fisher information for models where the quantum Cramér-Rao bound (QCRB) is achievable but a detailed adaptive strategy for achieving the bound in the multi-copy setting has been lacking. We first show that the following naive null-measurement implementation fails to attain even the standard estimation scaling: estimate the parameter on a small sub-sample, and apply the null-measurement corresponding to the estimated value on the rest of the systems. This is due to non-identifiability issues specific to null-measurements, which arise when the true and reference parameters are close to each other. To avoid this, we propose the alternative displaced-null measurement strategy in which the reference parameter is altered by a small amount which is sufficient to ensure parameter identifiability. We use this strategy to devise asymptotically optimal measurements for models where the QCRB is achievable. More generally, we extend the method to arbitrary multi-parameter models and prove the asymptotic achievability of the the Holevo bound. An important tool in our analysis is the theory of quantum local asymptotic normality which provides a clear intuition about the design of the proposed estimators, and shows that they have asymptotically normal distributions.

Does the reliability of computational models truly improve with hierarchical modeling? Some recommendations and considerations for the assessment of model parameter reliability : Reliability of computational model parameters.

Computational modeling of behavior is increasingly being adopted as a standard methodology in psychology, cognitive neuroscience, and computational psychiatry. This approach involves estimating parameters in a computational (or cognitive) model that represents the computational processes of the underlying behavior. In this approach, the reliability of the parameter estimates is an important issue. The use of hierarchical (Bayesian) approaches, which place a prior on each model parameter of the individual participants, is thought to improve the reliability of the parameters. However, the characteristics of reliability in parameter estimates, especially when individual-level priors are assumed, as in hierarchical models, have not yet been fully discussed. Furthermore, the suitability of different reliability measures for assessing parameter reliability is not thoroughly understood. In this study, we conduct a systematic examination of these issues through theoretical analysis and numerical simulations, focusing specifically on reinforcement learning models. We note that the heterogeneity in the estimation precision of individual parameters, particularly with priors, can skew reliability measures toward individuals with higher precision. We further note that there are two factors that reduce reliability, namely estimation error and intersession variation in the true parameters, and we discuss how to evaluate these factors separately. Based on the considerations of this study, we present several recommendations and cautions for assessing the reliability of the model parameters.

Scenario based optimisation over uncertain system identification models

Models of dynamical systems are often built from observed data using system identification techniques, and the uncertainty in the model parameters is commonly described using confidence regions to which the true model parameters belong with a certain probability. In this paper we propose methods which use the scenario approach to solve robust optimisation problems for model based design where there is uncertainty in the model parameters. The methods draw samples (scenarios) of the uncertain model parameters and solve an optimisation problem only involving the drawn scenarios. Both a Bayesian system identification setting where the model parameters are stochastic, and a non-Bayesian system identification setting where the model parameters are treated as being deterministic are considered. The Bayesian and non-Bayesian settings require different treatment, and whereas standard scenario optimisation theory can be directly utilised in the Bayesian setting, this is not the case in the non-Bayesian setting. For that reason the model class is restricted to linear regression models with deterministic regressors in the non-Bayesian case. Algorithms are proposed for drawing samples of the parameters such that the uncertainties in the system identification models are reflected in the samples. Theoretical results are given bounding the probability that the found solution to the scenario optimisation problem will give a worse performance when applied to the true system than seen on the drawn scenarios. The methods are illustrated in simulation examples showing good performance.