Sequential Estimation Procedure Research Articles

Parameter estimation in optional semimartingale regression models

The paper is devoted to the problem of parameter estimation in a multivariate optional semimartingale regression model. The family of optional semimartingales is a rich class of stochastic processes that contains càdlàg semimartingales. In general, such processes do not admit càdlàg modifications, i.e. right-continuous with finite left-limits. The weighted least squares estimator is derived, and its strong consistency is proved under general conditions on regressors. Furthermore, sequential least squares estimates are systematically studied. It is shown that such estimates have a nice statistical property called fixed accuracy. Sequential estimation procedure developed in the paper works without restrictions on dimensions of unknown parameter and of observation process. The paper contains several examples of multivariate regressions to demonstrate our results and proposed techniques.

Learning and Predicting Shape Deviations of Smooth and Non-Smooth 3D Geometries Through Mathematical Decomposition of Additive Manufacturing

In additive manufacturing (AM), final product geometries are often deformed or distorted. The deviations of three-dimensional (3D) shapes from their intended designs can be represented as 2D surfaces in a R³ space, which constitutes a complicated set of data for learning and predicting geometric quality. Patterns of deviation surfaces vary with shape geometries, sizes/volumes, materials, and AM processes. Our previous work has established an engineering-informed convolution framework to learn shape deviation from a small set of training products built with the same material and process. It incorporates the characteristics of the layer-wise shape forming process through a convolution formulation and the size factor for a category of smooth 3D shapes such as domes or cylinders. This study extends this fabrication-aware learning framework to a larger class of products including both smooth and non-smooth surfaces (polyhedral shapes). The key idea of learning heterogeneous deviation surface data under a unified model is to establish the association between the deviation profiles of smooth base shapes and those of non-smooth polyhedral shapes. The association, which is characterized by a novel 3D cookie-cutter function, views polyhedral shapes as being carved out from smooth base shapes. In essence, the AM process of building non-smooth shapes is mathematically decomposed into two steps: additively fabricate smooth base shapes using a convolution learning framework, and then subtract extra materials using a cookie-cutter function. The proposed joint learning framework of shape deviation data reflects this decomposition by adopting a sequential model estimation procedure. The model learning procedure first establishes the convolution model to capture the effects of layer-wise fabrication and sizes, and then estimates the 3D cookie-cutter function to realize geometric differences between smooth and non-smooth shapes. A new Gaussian process model is proposed to consider the spatial correlation among neighboring regions within a 3D shape and across different shapes. The case study demonstrates the feasibility and prospects of prescriptive learning of complex 3D shape deviations in AM and extension to broader engineering surface data.

Multiresolution functional characterization and correction of biofouling for improved biosensing efficacy

Multielectrode electrochemical biosensors promise on-the-spot inspection of target compounds in biofluids, reducing costs in personalized healthcare. However, sensor sensitivity may decrease after each use due to biofouling, where chemical attachments on sensor electrodes curtail sensing signals. Current biofouling characterization techniques rely on time-consuming offline tests and analysis, making them impractical for on-the-spot signal correction. Alternatively, we propose to statistically model and correct the biofouling-induced signal changes. However, in addition to biofouling, the signals are influenced by multiple sources of variation, each with different levels of impact. To effectively characterize and separate biofouling effects from the major sources of variability, we establish a multiresolution functional mixed-effect model based on domain knowledge. A biosensing signal is first decomposed into a smooth trend and local peaks. The smooth trend models the effects of population-level biofluid composition, as well as patient and electrode effects to isolate variability sources. Changes in local peak location and amplitude indicate biofouling. These local peaks are modeled using a sparse subset of high-order functional terms. By modeling the changes of those high-order terms, we can characterize and predict the biofouling between consecutive measurements. We propose a sequential parameter estimation procedure that ensures model identifiability. A nonparametric regression model is developed for biofouling prediction. The proposed strategy is validated through simulation and real case studies, effectively correcting biofouling-affected signals from new patients.

Distributed sequential estimation procedures

AbstractData collected from distributed sources or sites commonly have different distributions or contaminated observations. Active learning procedures allow us to assess data when recruiting new data into model building. Thus, combining several active learning procedures together is a promising idea, even when the collected data set is contaminated. Here, we study how to conduct and integrate several adaptive sequential procedures at a time to produce a valid result via several machines or a parallel‐computing framework. To avoid distraction by complicated modelling processes, we use confidence set estimation for linear models to illustrate the proposed method and discuss the approach's statistical properties. We then evaluate its performance using both synthetic and real data. We have implemented our method using Python and made it available through Github at https://github.com/zhuojianc/dsep.

Maximum precision estimation for a step-stress model using two-stage methodologies

In this paper, we consider a two-stage sequential estimation procedure to estimate the parameters of a cumulative exposure model under an accelerated testing scenario. In particular, we focus on a step-stress model where the stress level changes after a pre-specified number of failures occur, which is also random. This is termed as a ‘random stress change time’ in the literature. We further aim to estimate these parameters using maximum precision and hence use a certain variance optimality criteria. Our proposed two-stage estimation procedures follow interesting efficiency properties and their applicability is seen through extensive simulation analyses and a pseudo-real data example from reliability studies.

Sequential estimation of quantiles from delayed observations

The problem of sequentially estimating quantiles is considered in the case when the observations become available at random times. Certain class of sequential estimation procedures which are composed of optimal stopping time and sequential minimum risk invariant estimator of a median is obtained under a invariant loss function and with the observation cost determined by a convex function of the moment of stopping and the number of observations up to this moment.

Simultaneous estimation procedure reveals the object-based, but not space-based, dependence of visual working memory representations

Visual working memory (VWM) allows us to actively represent a limited amount of visual information in mind. Although its severe capacity limit is widely accepted, researchers disagree on the nature of its representational unit. Object-based theories argue that VWM organizes feature representations into integrated representations, whereas feature-based theories argue that VWM represents visual features independently. Supporting a feature-based account of VWM, recent studies have demonstrated that features comprising an object can be forgotten independently. Although evidence of feature-based forgetting invalidates a pure object-based account of VWM that assumes perfect integration of feature representations, it is possible that feature representations may be organized in a dependent manner on the basis of objects when they exist in memory. Furthermore, many previous studies prompted participants to recall object features independently by sequentially displaying a response probe for each feature (i.e., sequential estimation procedure), and this task demand might have promoted the independence of feature representations in VWM. To test these possibilities, we created a novel task to simultaneously capture the representational quality of two features of the same object (i.e., simultaneous estimation procedure) and tested their dependence across the entire spectrum of representational quality. Here, we found that the quality of feature representations within the same object covaried reliably in both sequential and simultaneous estimation procedures, but this representational dependence was statistically stronger in the simultaneous estimation procedure than in the sequential estimation procedure. Furthermore, we confirmed that neither the shared spatial location nor simultaneous estimation of two features was sufficient to induce representational dependence in VWM. Thus, our results demonstrate that feature representations in VWM are organized in a dependent manner on the basis of objects, but the degree of dependence can vary based on the current task demand.

Generalized co-sparse factor regression

Multivariate regression techniques are commonly applied to explore the associations between large numbers of outcomes and predictors. In real-world applications, the outcomes are often of mixed types, including continuous measurements, binary indicators, and counts, and the observations may also be incomplete. Building upon the recent advances in mixed-outcome modeling and sparse matrix factorization, generalized co-sparse factor regression (GOFAR) is proposed, which utilizes the flexible vector generalized linear model framework and encodes the outcome dependency through a sparse singular value decomposition (SSVD) of the integrated natural parameter matrix. To avoid the estimation of the notoriously difficult joint SSVD, GOFAR proposes both sequential and parallel unit-rank estimation procedures. By combining the ideas of alternating convex search and majorization–minimization, an efficient algorithm is developed to solve the sparse unit-rank problem and implemented in the R package gofar. Extensive simulation studies and two real-world applications demonstrate the effectiveness of the proposed approach.

Estimation of mean value of a normal distribution with constraints on the relative error and d-risk

ABSTRACTWe consider a problem of mean value estimation for a normal distribution with prior knowledge of its randomness and extreme smallness. We continue our investigation presented in article [Volodin et al. Estimation of the mean value for the normal distribution with constrains on d-risk. Lobachevskii J Math. 2018;39:377–387], where the constraints have been made on the absolute estimation error. It is more appropriate to control its relative estimation error, not the absolute. In this article, we consider not only estimates based on a fixed number of observations, but also the sequential procedure of estimation. Both estimators guarantee the given constraints on their d-risks (the so-called d-guarantee procedure). We present a simple method for calculating the minimal sample size that guarantees the given constraints on the d-risk of the relative error when the estimators with uniformly minimal d-risk and Bayesian are applied. A sequential guarantee estimation procedure is also proposed, and the distribution of the corresponding stopping time is illustrated by the results of statistical simulations. As a practical application of the proposed statistical procedures, the problem of estimating the concentration of arsenic in drinking water is considered.

Sequential fixed-accuracy confidence intervals for the stress–strength reliability parameter for the exponential distribution: two-stage sampling procedure

In this paper, a two-stage sequential estimation procedure is considered to construct fixed-accuracy confidence intervals of the reliability parameter R under the stress–strength model when the stress and strength are independent exponential random variables with different scale parameters. The exact distribution of the total sample size, explicit formulas for the expected value, and mean squared error of the maximum likelihood estimator of the reliability parameter under the stress–strength model are provided under the two-stage sequential procedure. Performances of the proposed methodology are investigated with the help of simulations. Finally, using three pairs of real datasets, the procedure is clearly illustrated. We used MATLAB in order to implement computations, simulation studies, and real data analysis.

Sequential accuracy in parameter estimation for population correlation coefficients.

Correlation coefficients are effect size measures that are widely used in psychology and related disciplines for quantifying the degree of relationship of two variables, where different correlation coefficients are used to describe different types of relationships for different types of data. We develop methods for constructing a sufficiently narrow confidence interval for 3 different population correlation coefficients with a specified upper bound on the confidence interval width (e.g., .10 units) at a specified level of confidence (e.g., 95%). In particular, we develop methods for Pearson's r, Kendall's tau, and Spearman's rho. Our methods solve an important problem because existing methods of study design for correlation coefficients generally require the use of supposed but typically unknowable population values as input parameters. We develop sequential estimation procedures and prove their desirable properties in order to obtain sufficiently narrow confidence interval for population correlation coefficients without using supposed values of population parameters, doing so in a distribution-free environment. In sequential estimation procedures, supposed values of population parameters for purposes of sample size planning are not needed, but instead stopping rules are developed and once satisfied, they provide a rule-based stop to the sampling of additional units. In particular, data in sequential estimation procedures are collected in stages, whereby at each stage the estimated population values are updated and the stopping rule evaluated. Correspondingly, the final sample size required to obtain a sufficiently narrow confidence interval is not known a priori, but is based on the outcome of the study. Additionally, we extend our methods to the squared multiple correlation coefficient under the assumption of multivariate normality. We demonstrate the effectiveness of our sequential procedure using a Monte Carlo simulation study. We provide freely available R code to implement the methods in the MBESS package. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

COMBINATORIAL OPTIMIZATION UNDER UNCERTAINTY AND FORMAL MODELS OF EXPERT ESTIMATION

Previously, the author formalized the concepts of uncertainty, compromise solution, compromise criteria and conditions for a quite general class of combinatorial optimization problems. The functional of the class’ problems contains linear convolution of weights and arbitrary numerical characteris­tics of a feasible solution. It was shown that the efficiency of the presented algorithms for the uncertainty resolution is largely determined by the effi­ciency of solving the combinatorial optimization problem in a deterministic formulation. A part of the formulated compromise criteria and conditions uses expert weights. Previously, the author and his disciples also formulated combinatorial optimization models, optimality criteria, criteria for deci­sions’ consistency. The models allow to evaluate and justify the degree of stability and reliability of the estimated values of empirical coefficients using a formally ill-conditioned empirical pairwise comparison matrix of arbitrary dimension. The matrix may contain zero elements. The theoretical research and statistical experiments allowed to choose the most efficient of these optimization models. In this article, on the base of earlier results by the author and his disciples, we formalize and substantiate the efficiency of the proposed sequential procedure for expert estimation of weights that determine compromise criteria and conditions. The procedure is an integral part of the algorithm introduced by the author to solve combinatorial optimization problems under uncertainty of the mentioned class. We give unified algorithm for efficient uncertainty resolution that includes original and efficient formal procedure for expert coefficients’ estimation using empirical matrices of pairwise comparisons.

A k-stage procedure for estimating the mean vector of a multivariate normal population

In this article, we have estimated the mean vector of a multivariate normal population by using a k-stage sequential estimation procedure. Point estimation as well as confidence region estimation is done. Second-order approximations are obtained in both the cases. In case of minimum risk point estimation of , negative regret is achieved.

Estimating Multiscale Direct Causality Graphs in Neural Spike-Field Networks

Neural representations span various spatiotemporal scales of brain activity, from the spiking activity of single neurons to field activity measuring large-scale networks. The simultaneous analyses of spikes and fields to uncover causal interactions in multiscale networks could help understand neural mechanisms. However, assessing causality within spike-field networks is challenging as spikes are binary-valued with a fast time-scale while fields are continuous-valued with slower time-scales. Current causality measures are largely not applicable to mixed discrete-continuous network activity. Here, in this paper, we develop a novel multiscale causality estimation algorithm for spike-field networks. We construct a likelihood function comprised of point process models for spikes and linear Gaussian models for fields. For spikes, firing rates are modeled as a function of the history of both field signals and binary spike events within the network. For fields, to make their linear models consistent with biophysical findings, we use the history of field signals and the history of the latent log-firing rates of neurons as predictors. To resolve the challenge of estimating the network model parameters in the presence of latent firing rates, we develop a sequential maximum-likelihood parameter estimation procedure that extends to large networks. Once models are estimated, we compute directed information as our measure of multiscale causality and devise two statistical tests to assess its significance. Using extensive simulations, we show that the algorithm can accurately reconstruct the true causality graphs of random spike-field networks. Moreover, the algorithm is robust to the number of connections, connection strengths, or exact topology of the network. This multiscale causality estimation algorithm has important implications for studying neural mechanisms and for future neurotechnology design.

Accuracy in parameter estimation for a general class of effect sizes: A sequential approach.

Sequential estimation is a well recognized approach to inference in statistical theory. In sequential estimation the sample size to use is not specified at the start of the study, and instead study outcomes are used to evaluate a predefined stopping rule, if sampling should continue or stop. In this article we develop a general theory for sequential estimation procedure for constructing a narrow confidence interval for a general class of effect sizes with a specified level of confidence (e.g., 95%) and a specified upper bound on the confidence interval width. Our method does not require prespecified, yet usually unknowable, population values of certain parameters for certain types of distributions, thus offering advantages compared to commonly used approaches to sample size planning. Importantly, we make our developments in a distribution-free environment and thus do not make untenable assumptions about the population from which observations are sampled. Our work is thus very general, timely due to the interest in effect sizes, and has wide applicability in the context of estimation of a general class of effect sizes. (PsycINFO Database Record

Sequential prevalence estimation with pooling and continuous test outcomes.

Prevalence estimation is crucial for controlling the spread of infections and diseases and for planning of health care services. Prevalence estimation is typically conducted via pooled, or group, testing due to limited testing budgets. We study a sequential estimation procedure that uses continuous pool readings and considers the dilution effect of pooling so as to efficiently estimate an unknown prevalence rate. Embedded into the sequential estimation procedure is an optimization model that determines the optimal pooling design (number of pools and pool sizes) under a limited testing budget, considering the trade-off between testing cost and estimation accuracy. Our numerical study indicates that the proposed sequential estimation procedure outperforms single-stage procedures, or procedures that use binary test outcomes. Further, the sequential procedure provides robust prevalence estimates in cases where the initial estimate of the unknown prevalence rate is poor, or the assumed distribution of the biomarker load in infected subjects is inaccurate. Thus, when limited and unreliable information is available about the current status of, or biomarker dynamics related to, an infection, the sequential procedure becomes an attractive estimation strategy, due to its ability to mitigate the initial bias.

Evidence-Based Design of Fixed-Dose Combinations: Principles and Application to Pediatric Anti-Tuberculosis Therapy.

Background and ObjectivesFixed-dose combination formulations where several drugs are included in one tablet are important for the implementation of many long-term multidrug therapies. The selection of optimal dose ratios and tablet content of a fixed-dose combination and the design of individualized dosing regimens is a complex task, requiring multiple simultaneous considerations.MethodsIn this work, a methodology for the rational design of a fixed-dose combination was developed and applied to the case of a three-drug pediatric anti-tuberculosis formulation individualized on body weight. The optimization methodology synthesizes information about the intended use population, the pharmacokinetic properties of the drugs, therapeutic targets, and practical constraints. A utility function is included to penalize deviations from the targets; a sequential estimation procedure was developed for stable estimation of break-points for individualized dosing. The suggested optimized pediatric anti-tuberculosis fixed-dose combination was compared with the recently launched World Health Organization-endorsed formulation.ResultsThe optimized fixed-dose combination included 15, 36, and 16% higher amounts of rifampicin, isoniazid, and pyrazinamide, respectively. The optimized fixed-dose combination is expected to result in overall less deviation from the therapeutic targets based on adult exposure and substantially fewer children with underexposure (below half the target).ConclusionThe development of this design tool can aid the implementation of evidence-based formulations, integrating available knowledge and practical considerations, to optimize drug exposures and thereby treatment outcomes.Electronic supplementary materialThe online version of this article (doi:10.1007/s40262-017-0577-6) contains supplementary material, which is available to authorized users.

Reliable error estimation for Sobol’ indices

A practical problem concerning the estimation of Sobol' indices is how large to choose the number of evaluations to ensure that estimates are accurate enough. This paper addresses this challenge by proposing a reliable error bound for Sobol' indices based on digital sequences. The error bound is defined in terms of the discrete Walsh coefficients of the integrands involved in the Sobol' indices definition. We propose a sequential estimation procedure of first-order and total effect Sobol' indices using the error bound as stopping criterion. The procedure operates under the assumption that all integrands lie inside a particular cone of functions

Feasibility study on real-time γ-ray spectrum / dose measurement system

Recently, medical applications of radiation have been widely spread. However, exposure of medical staffs is sometimes not focused on because treatment of patients is the first priority. It is thus important to decrease exposure for them as much as possible. The purpose of this study is to develop a system which can measure energy spectrum and dose of gamma-rays at the same time in real time in medical application spots. As a result, the medical staff could be guided to aware the risk of radiation and finally the exposure dose to them could be suppressed substantially. We first decided to use a CsI(Tl) scintillator as the gamma-ray detection device. A Multi-Pixel Photon Counter (MPPC) was attached to the scintillator to detect gamma-ray signals. Pulse height spectra were measured with several standard gamma-ray sources. The detection efficiency and energy resolution were deduced from the measured results and the detection efficiency was compared with the calculation result by MCNP5. After evaluating the response function, the energy spectrum was derived with the spectrum type Bayesian estimation and the sequential Bayesian estimation procedure. From the result, it was confirmed that the sequential Bayesian estimation could be applied to real time measurement of gamma-ray energy spectrum and dose.

Coupled sequential detection and estimation procedure for track‐before‐detect

In this study, the authors consider the coupled sequential detection and estimation of weak targets for track-before-detect algorithm in long range early warning radar. They present a new strategy and develop a coupled cost function consisting of detection, position estimation and tracking estimation loss. In the proposed procedure, the sequential stopping and detection rules are simplified. Moreover, they derive the lower bounds of the detection and estimation probabilities, which can be used to design the suitable related parameter values. Finally, several numerical simulations of the new strategy and the comparisons are presented and discussed.