True Parameter Values Research Articles

Behavioral event detection and rate estimation for autonomous vehicle evaluation

AbstractAutonomous vehicles are continually increasing their presence on public roads. However, before any new autonomous driving software can be approved, it must first undergo a rigorous assessment of driving quality. These quality evaluations typically focus on estimating the frequency of (undesirable) behavioral events. While rate estimation would be straight‐forward with complete data, in the autonomous driving setting this estimation is greatly complicated by the fact that detecting these events within large driving logs is a non‐trivial task that often involves human reviewers. In this article, we outline a streaming partial tiered event review configuration that ensures both high recall and high precision on the events of interest. In addition, the framework allows for valid streaming estimates at any phase of the data collection process, even when labels are incomplete, for which we develop the maximum likelihood estimate and show it is unbiased. Constructing honest and effective confidence intervals (CI) for these rate estimates, particularly for rare safety‐critical events, is a novel and challenging statistical problem due to the complexity of the data likelihood. We develop and compare several CI approximations, including a novel gamma CI method that approximates the exact but intractable distribution with a weighted sum of independent Poisson random variables. There is a clear trade‐off between statistical coverage and interval width across the different CI methods, and the extent of this trade‐off varies depending on the specific application settings (e.g., rare vs. common events). In particular, we argue that our proposed CI method is the best‐suited when estimating the rate of safety‐critical events where guaranteed coverage of the true parameter value is a prerequisite to safely launching a new ADS on public roads.

Structural geologic modeling and restoration using ensemble Kalman inversion

We demonstrate the use of Ensemble Kalman Inversion (EKI) for building three-dimensional, multi-fault, kinematically restorable structural geologic models, by means of a workflow in which fault geometry, the distribution of slip on a fault, and the geometry of folded horizons are all modeled. The models are constrained by observations of faults and horizons in the present deformed state together with the expectation that horizons should restore flat. Two modeling approaches are tested: restoration from the deformed state, and forward modeling from the restored state. We first test these methods on a synthetic model involving a single fault, and then apply them to a real-field example involving five faults. Models are prone to ensemble collapse, which results in underestimation of uncertainty at small ensemble sizes, but localization and covariance inflation can mitigate this issue. With these methods, EKI can recover the true parameter values in the synthetic case and produce a solution consistent with the data in the real case, as well as quantify uncertainty in both cases. EKI, therefore, shows promise as a tool for building complex, restorable structural geologic models, and it holds the potential for integration of fault kinematics with other ensemble-based subsurface modelling workflows.

A Bayesian approach for analyzing crop yield response data with limited treatments

AbstractThis paper proposes a Bayesian multilevel modeling approach to incorporate response parameters from published studies into crop yield response estimation procedures when nonlimiting or limiting treatment levels are omitted or limited in agronomic experiments. Such circumstances may be encountered when data are from farmer‐led research, which may use nonstandardized experimental designs. The paper's focus is on maize yield response to nitrogen fertilizer, but the procedure is flexible enough to accommodate other factors that could affect crop yield response. A proof‐of‐concept Monte Carlo (MC) exercise supplements an empirical application. The MC simulation investigates the small sample properties of the proposed procedure. The empirical example uses field trial data for a maize planter experiment under different nitrogen (N) fertilizer rates. The planter trial compared mechanical planting methods to methods used in developing countries with limited access to mechanized planter technology. Some experiments had no check plots and all experiments lacked nonlimiting fertilizer rates. Linear and quadratic response functions with plateaus are used in the MC simulation and empirical application. MC results suggest that estimates were closest to true parameter values when priors for optimal N rates from published sources were used.

Consistency of mixture models with a prior on the number of components

Abstract This article establishes general conditions for posterior consistency of Bayesian finite mixture models with a prior on the number of components. That is, we provide sufficient conditions under which the posterior concentrates on neighborhoods of the true parameter values when the data are generated from a finite mixture over the assumed family of component distributions. Specifically, we establish almost sure consistency for the number of components, the mixture weights, and the component parameters, up to a permutation of the component labels. The approach taken here is based on Doob’s theorem, which has the advantage of holding under extraordinarily general conditions, and the disadvantage of only guaranteeing consistency at a set of parameter values that has probability one under the prior. However, we show that in fact, for commonly used choices of prior, this yields consistency at Lebesgue-almost all parameter values, which is satisfactory for most practical purposes. We aim to formulate the results in a way that maximizes clarity, generality, and ease of use.

A new LDA formulation with covariates

The Latent Dirichlet Location (LDA) model is a popular method for creating mixed-membership clusters. Despite having been originally developed for text analysis, LDA has been used for a wide range of other applications. We propose a new formulation for the LDA model which incorporates covariates. In this model, a negative binomial regression is embedded within LDA, enabling straight-forward interpretation of the regression coefficients and the analysis of the quantity of cluster-specific elements in each sampling units (instead of the analysis being focused on modeling the proportion of each cluster, as in Structural Topic Models). We use slice sampling within a Gibbs sampling algorithm to estimate model parameters. We rely on simulations to show how our algorithm is able to successfully retrieve the true parameter values and the ability to make predictions for the abundance matrix using the information given by the covariates. The model is illustrated using real data sets from three different areas: text-mining of Coronavirus articles, analysis of grocery shopping baskets, and ecology of tree species on Barro Colorado Island (Panama). This model allows the identification of mixed-membership clusters in discrete data and provides inference on the relationship between covariates and the abundance of these clusters.

Capturing positive network attributes during the estimation of recursive logit models: A prism-based approach

Although the recursive logit (RL) model has been recently popular and has led to many applications and extensions, an important numerical issue with respect to the computation of value functions remains unsolved. This issue is particularly significant for model estimation, during which the parameters are updated every iteration and may violate the feasibility condition of the value function. To solve this numerical issue of the value function in the model estimation, this study performs an extensive analysis of a prism-constrained RL (Prism-RL) model proposed by Oyama and Hato (2019), which has a path set constrained by the prism defined based upon a state-extended network representation. The numerical experiments have shown two important properties of the Prism-RL model for parameter estimation. First, the prism-based approach enables estimation regardless of the initial and true parameter values, even in cases where the original RL model cannot be estimated due to the numerical problem. We also successfully captured a positive effect of the presence of street green on pedestrian route choice in a real application. Second, the Prism-RL model achieved better fit and prediction performance than the RL model, by implicitly restricting paths with large detour or many loops. Defining the prism-based path set in a data-oriented manner, we demonstrated the possibility of the Prism-RL model describing more realistic route choice behavior. The capture of positive network attributes while retaining the diversity of path alternatives is important in many applications such as pedestrian route choice and sequential destination choice behavior, and thus the prism-based approach significantly extends the practical applicability of the RL model.

Distributed Parameter Estimation under Gaussian Observation Noises

In this paper, we consider the problem of distributed parameter estimation in sensor networks. Each sensor makes successive observations of an unknown d-dimensional parameter, which might be subject to Gaussian random noises. They aim to infer true value of the unknown parameter by cooperating with each other. To this end, we first generalize the so-called dynamic regressor extension and mixing (DREM) algorithm to stochastic systems, with which the problem of estimating a d-dimensional vector parameter is transformed to that of d scalar ones: one for each of the unknown parameters. For each of the scalar problem, an estimation scheme is given, where each sensor fuses the regressors and measurements in its in-neighborhood and updates its local estimate by using least-mean squares. Particularly, a counter is also introduced for each sensor, which prevents any (noisy) measurement from being repeatedly used such that the estimation performance will not be greatly affected by certain extreme values. A novel excitation condition termed as local persistent excitation (Local-PE) condition is also proposed, which relaxes the traditional persistent excitation (PE) condition and only requires that the collective signals in each sensor's in-neighborhood are sufficiently excited. With the Local-PE condition and proper step sizes, we show that the proposed estimator guarantee that each sensor infers the true parameter in mean square, even if any individual of them cannot. Numerical examples are finally provided to illustrate the established results.

Estimation of large-scale deformations in VLBI radio source catalogs with mitigation of impact of outliers: A comparison between different L1- and L2-norm-based methods

Aims. In this study, we compare several methods of modeling large-scale systematic differences between catalogs of positions of extragalactic radio sources provided by very long baseline interferometry with an emphasis on mitigating the impact of outliers. Methods. The coordinate difference between catalogs was parameterized by first and second order coefficients of vector spherical harmonics. We solved for these coefficients by using the least-squares method (L2-norm) and, alternatively, by L1-norm minimization. The problem of outliers was addressed either by rejecting them on the basis of their difference to the mean or by using the cell median (CM) method, consisting of reducing the difference field to median values in cells of equal area. The methods were applied to simulated catalogs exhibiting systematics of within 100 microarcseconds - for which we knew the expected results - and to real catalogs. Results. In simulations, the L1 minimization appears practically insensitive to outliers and is within a few microarcseconds of the expected results. Least-squared fitting preceded by L1-norm-based outlier detection performed similarly. The CM method gets close to the true parameter values, within one microarcsecond. When applied to real catalogs, all methods provide close results within a few microarcseconds. Conclusions. The study shows that all tested methods are consistent with each other within a few microarcseconds. Hybrid L2/L1 and iterative L2 methods proved to be very effective in eliminating outliers and showed the best accuracy of the estimated parameters of the mutual orientation of celestial reference frames.

Exploring the Exponentiated Transmuted Inverse Rayleigh Distribution (ETIRD) in Classical and Bayesian Paradigms

We derived, a new three parameters continuous probability distribution called Exponentiated Transmuted Inverse Rayleigh Distribution (ETIRD). Various mathematical properties of the new distribution including mean, rth moments, moment generating function, quantile function etc. are derived. In the Classical paradigm, the estimators of the distribution are obtained using the maximum likelihood method. The Bayes estimators are derived under square error loss function (SELF) using non-informative and informative priors via the Lindley approximation technique. Bayes Estimators are compared with their corresponding maximum likelihood Estimators (MLEs) using a Monte Carlo Simulation Study under different sample sizes, different values of true parameters, using informative and non-informative priors. Performance of Bayes estimators and classical estimates is judged for the four real life data sets. The results of simulation study and real-life example show that the Bayes estimators provided better results than MLEs.

Calibration of a bumble bee foraging model using Approximate Bayesian Computation

1. Challenging calibration of complex models can be approached by using prior knowledge on the parameters. However, the natural choice of Bayesian inference can be computationally heavy when relying on Markov Chain Monte Carlo (MCMC) sampling. When the likelihood of the data is intractable, alternative Bayesian methods have been proposed. Approximate Bayesian Computation (ABC) only requires sampling from the data generative model, but may be problematic when the dimension of the data is high.2. We studied alternative strategies to handle high dimensional data in ABC applied to the calibration of a spatially explicit foraging model for Bombus terrestris. The first step consisted in building a set of summary statistics carrying enough biological meaning, i.e. as much as the original data, and then applying ABC on this set. Two ABC strategies, the use of regression adjustment leading to the production of ABC posterior samples, and the use of machine learning approaches to approximate ABC posterior quantiles, were compared with respect to coverage of model estimates and true parameter values. The comparison was made on simulated data as well as on data from two field studies.3. Results from simulated data showed that some model parameters were easier to calibrate than others. Approaches based on random forests in general performed better on simulated data. They also performed well on field data, even though the posterior predictive distribution exhibited a higher variance. Nonlinear regression adjustment performed better than linear ones, and the classical ABC rejection algorithm performed badly.4. ABC is an interesting and appealing approach for the calibration of complex models in biology, such as spatially explicit foraging models. However, while ABC methods are easy to implement, they often require considerable tuning.

Confidence sequences with composite likelihoods

AbstractIn dominated parametric statistical models, confidence sequences provide conservatively valid frequentist inference directly from a likelihood ratio. They ensure a specific mode of replicability when inference is performed on accumulating data: inferential conclusions that are compatible with a guaranteed probability when the sample is enlarged, in the form of overlapping confidence regions. Here we consider both Robbins' mixture confidence sequences and running maximum likelihood confidence sequences recently considered by Wasserman, Ramdas, and Balakrishnan. We compare through simulation the replicability properties of the two kinds of confidence sequences, evaluating, along a prospected enlargement of the sample, the frequency of incompatible estimation intervals and the frequency of failure of simultaneous coverage of the true parameter value. Moreover, we propose a shortcut to extend the application of mixture confidence sequences to pseudo‐likelihoods, in particular to composite likelihood. The main assumption required is that normal asymptotic theory offers a good approximation to the density of the maximizer of the pseudo‐likelihood. When inference is about a scalar parameter of interest, the computation of the proposed sequence of confidence intervals is straightforward. The method is illustrated by an example with replicability properties evaluated through simulation.

Low-Variance Parameter Estimation Approach for Real-Time Optimization of Noisy Process Systems

Uncertainty is inherent to the measurement and modeling of process systems, where it can have significant impacts on the efficacy of optimization techniques. This work proposes a scheme to address uncertainty as it pertains to real-time optimization (RTO), where noisy measurements are used to estimate model parameters and account for model uncertainty. The parameter estimation (PE) step that accompanies RTO requires plant measurements that are often noisy; this can cause the propagation of noise to the parameter estimates, which may result in poor RTO performance. An information content (IC) metric for choosing the most information-rich measurements and an algorithm to select a favorable subset of measurements, as well as filtering for erroneous parameters, are proposed in this work to improve the PE problem performance. The resulting low-variance PE (lv-PE) algorithm yields parameter estimates that are closer to the true parameter values over many RTO periods. The proposed scheme is tested against a regular RTO/PE on a forced circulation evaporator and the Williams–Otto CSTR. The former case displays the effect of the proposed scheme in avoiding constraint violations, while the latter case shows the economic improvements that the proposed scheme can yield. Both case studies show a reduction in estimate variability with respect to the traditional PE approach; thus, the proposed framework is attractive for the optimization of noisy process systems.

Modifying the linear two-step Windmeijer correction for the presence of spatial error dependence

The aim in the paper is to show how the presence of spatial dependence affects the often-adopted Windmeijer (J Econom 126:25–51, 2005) finite sample correction (For example it is an option facilitating robust estimation in the software package Stata, which is used by many applied econometricians and data analysts.), which corrects the downward bias in estimated parameter standard errors. Windmeijer (2005) explains why, with numerous instruments, the estimated asymptotic standard errors of the efficient, two-step, GMM estimator are downward biased in small samples. GMM estimation is based on an estimated optimal weight matrix, which is the inverse of the covariance of the sample moments, and the bias results from the weight matrix being evaluated at estimated, rather than the true values of parameters. Hwang et al. (J Econom 229(2):276–298, 2022) provide a correction to the Windmeijer (2005) finite sample correction to allow for over-identification bias. The novel contribution of the current paper is to show how the Windmeijer (2005) correction can be modified given spatial dependence in the error term of a model with moments conditions that are linear in parameters estimated by GMM, leading to corrected standard errors and therefore more accurate inference. Monte Carlo simulations are used to demonstrate the effect of the modification and two examples using real data shows how inference may be affected by ignoring the effect of spatial error dependence.

Learning both a value and uncertainty label for seabed parameters from ship noise data

Because the seabed impacts sound propagation in the ocean, machine learning is being used for both seabed classification and to obtain estimates of individual seabed properties. This paper proposes a method to simultaneously estimate these properties and an associated uncertainty label. A residual neural network is trained and validated using synthetic ship noise spectrograms generated with a range-independent normal mode sound propagation model and a ship noise source spectrum. The data set includes 140 seabeds: In each, the top sediment layer has a random thickness and properties randomly chosen from five sets of bounds, which roughly correspond to clay, mud, sand, silt, and gravel. For each of the 140 sediments, a random selection of 405 combinations of ship speed, closest-point-of-approach range, and source depth are used resulting in 22k data samples. Each data sample is labeled with the true values of the sediment parameters as well as a label for the uncertainty level of each. The uncertainty levels are obtained from the Fisher information and qualify of the information content in the ship spectrogram about each parameter. Examples of how the residual neural network learns to perform regression for the parameter value and the uncertainty level will be presented.

On outliers detection and prior distribution sensitivity in standard skew-probit regression models

Regression models with probit and logit link functions are the most frequently used for binary response variables. However, traditional approaches may not be adequate when data are unbalanced. This paper deals with standard skew-probit regression models. Parameters were estimated through a new Bayesian approach which consists of the use of Hamiltonian Monte Carlo (HMC) and the original likelihood function. Simulation studies assessed the efficiency of the estimation method and the sensitivity of prior distributions for parameters related to asymmetry calculating the RMSE (root mean square error). The proposed estimation method was compared when used for detecting outliers. The results show that the proposed method is more efficient than INLA and is successful in the recovery of true parameter values. The sensitivity study enabled the proposal of a new prior distribution configuration for the asymmetry parameter, and the randomized quantile residual proved to be more suitable for detecting outliers. The methodology was applied to a diabetes dataset towards illustrating the results.

EquiDistribution Grid Evolution Method for Line Spectrum Estimation

The grid for traditional estimation methods is usually uniform. This is a conservative strategy to form a grid without using any prior information. Estimation results may become better if the true values of parameters are near the artificial grid points. Therefore, a dense grid is usually used to reach expected accuracy, resulting in heavy computation workload. Notice that the performance of estimation is related to the distribution of its grid. Aiming to achieve higher accuracy while use less grid points, a strategy called equidistribution is proposed in this paper. Estimation problem is reformulated by adding the constraint of equidistribution and is solved by a modified grid evolution method, named as EquiDistribution Grid Evolution (EDGE) method. In EDGE, a nonuniform distribution of grid points is evolved according to the distribution of information, and the distribution of information is progressively updated based on the nonuniform grid. The two procedures iterate alternatively. Finally a spectrum based on the adaptively evolved grid is obtained. Compared with previous methods, the proposed method shows advantages on both accuracy and time consumption. The controlling parameter is significantly simplified compared with previous grid evolution method. Furthermore, the resolution and accuracy in parameters’ domain are adaptive and nonuniform. The effectiveness of the EDGE method is demonstrated by numerical simulations.

Endogeneity and Measurement Bias of the Indicator Variables in Hybrid Choice Models: A Monte Carlo Investigation

We investigate the problem of endogeneity and measurement bias arising from incorporating indicator variables (e.g., measures of attitudes) into discrete choice models. We demonstrate that although a hybrid choice framework can resolve both endogeneity and measurement problems, the former requires explicit accounting for in the model, which has not typically been done in applied studies to date. By conducting a Monte Carlo experiment, we demonstrate the extent of the bias resulting from measurement and endogeneity problems. We propose two novel solutions to address the endogeneity problem: explicitly accounting for correlation between structural and discrete choice component error terms (or with random parameters in a utility function), or introducing additional latent variables. Using simulated data, we demonstrate that these approaches work as expected, i.e. they successfully recover the true values of all model parameters.

Confidence Intervals for Seroprevalence

This paper concerns the construction of confidence intervals in standard seroprevalence surveys. In particular, we discuss methods for constructing confidence intervals for the proportion of individuals in a population infected with a disease using a sample of antibody test results and measurements of the test’s false positive and false negative rates. We begin by documenting erratic behavior in the coverage probabilities of standard Wald and percentile bootstrap intervals when applied to this problem. We then consider two alternative sets of intervals constructed with test inversion. The first set of intervals are approximate, using either asymptotic or bootstrap approximation to the finite-sample distribution of a chosen test statistic. We consider several choices of test statistic, including maximum likelihood estimators and generalized likelihood ratio statistics. We show with simulation that, at empirically relevant parameter values and sample sizes, the coverage probabilities for these intervals are close to their nominal level and are approximately equi-tailed. The second set of intervals are shown to contain the true parameter value with probability at least equal to the nominal level, but can be conservative in finite samples.

Inconsistency for the Gaussian QMLE in GARCH-type models with infinite variance

We are occupied with the issue of consistency of the Gaussian QMLE in GARCH-type models with very heavy tailed squared innovations. We show that the appropriately scaled likelihood function weakly epi-converges to a stochastic process that is a.s. lower semi-continuous and proper. When moreover the volatility filter is increasing w.r.t. the parameter, inconsistency follows due to that the true parameter value misses the set of minimizers of the limit. This holds for models like the AGARCH, the Augmented GARCH, and the GQARCH.

The application of the orthogonal decomposition method for the algebraic solver separator

The method which is valid for improving the transmission of information and a clean separation of signal and noise is suggested in [1]. The basis of the proposed new way of developing the theory and methods of communication is the rejection of the probabilistic method for evaluating noisy signals according to the maximum likelihood rule. This method contains the mathematical procedure for absolutely accurate separation, as well as proving the absence of any fundamental theoretical limits [2,3] on the effectiveness of communications, including the absence of channel capacity limitations [4]. This approach includes the fundamentally new concept and the technical aspects of implementing telecommunication systems and uses systems of linear algebra equations (SLAE) to filter signals from noise. The SLAE matrix is the linear algebraic matrix (LSM) that separates and extracts the true values of informative signal parameters. Such a SLAE always has the solution, but obtaining this solution sometimes requires a particular method to be used, because its matrix is not always square, but can be rectangular as well. Therefore, the method of the orthogonal decomposition is proposed in this paper. For obtaining the matrices of orthogonal decomposition the Gram–Schmidt process, which is suitable for matrices of any size and composition, can be used. The method of solving a SLAE includes full description of solution and acceptable for matrices of any size. The example of solving the SLAE with a small matrix is presented in the paper. The MathCad Prime has been implemented for a bigger matrix. The implementation includes the functions that can be used in any other programming language. The solution has minimal norm and acceptable for linear algebraic matrices that separate signal and noise.