Point Estimates Of Parameters Research Articles

Application of diffusion-non-monoton distribution to model the radio-electronic equipment operation process

The emergence of reliability as an applied mathematical discipline is associated with the 50-60 years of the last century, when large and complex technical systems began to be created in various branches of technology. In this regard, an acute reliability problem arose, that is, ensuring the functioning and operability of these complex and expensive systems. The whole variety of reliability studies is aimed at solving the following three problems: assessment and prediction of product reliability at the design stages (a priori methods); experimental evaluation of reliability indicators, that is, confirmation of the projected level of reliability according to the results of tests or operation (posterior methods); taking measures to achieve and ensure a given level of reliability by optimizing the maintenance strategy, redundancy, spare parts, etc. (optimization problems) The traditional has developed a certain division in the areas of theory and practice of reliability of machines (mechanical objects, technical systems containing mechanical components) and equipment (electronic products, technical devices containing electronic and radio elements). The main tasks of reliability of machines and equipment - the establishment of patterns of failure and the assessment of quantitative indicators of reliability - can be solved in two different ways. To date, the direction based on the use of only probabilistic concepts (purely probabilistic theory) has received the greatest development in the theory and practice of reliability. The second way to establish quantitative indicators of reliability, in contrast to a purely probabilistic approach, is based on the study of mechano-physico-chemical properties and some physical parameters of products characterizing the technical condition of the latter using probabilistic methods. The methodology for establishing quantitative reliability indicators based on the study of certain physical parameters characterizing the technical condition of products consists in identifying the kinetic laws of degradation processes (building mathematical models of degradation processes) and determining the analytical relationship between these laws and reliability indicators. The article discusses the use of diffusion-nonmonotonic distribution for modeling the process of operation of electronic equipment. Particular attention is paid to the determination of point estimates of distribution parameters based on the results of operational observations.

An Electronic Screening and Brief Intervention for Hazardous and Harmful Drinking Among Swedish University Students: Reanalysis of Findings From a Randomized Controlled Trial Using a Bayesian Framework.

BackgroundDue to a resurgent debate on the misuse of P values, the Journal of Medical Internet Research is hosting a standing theme issue inviting the reanalysis of (primarily digital health) trial data using a Bayesian framework. This first paper in this series focuses on an electronic screening and brief intervention (eSBI), targeting harmful and hazardous alcohol consumption, which student health care centers across Sweden have routinely administerd to all students during the past decade. The second Alcohol Email Assessment and Feedback Study Dismantling Effectiveness for University Students (AMADEUS-2) trial aimed to assess the effect of the eSBI on alcohol consumption among students who were harmful and hazardous drinkers. A two-arm randomized controlled trial design was employed, randomizing eligible participants to either a waiting list or direct access to an eSBI. Follow-up assessments were conducted 2 months after randomization. Subsequent analysis of the trial followed the conventional null hypothesis approach, and no statistical significance was found between groups at follow-up with respect to the number of standard drinks consumed weekly. However, in an unspecified sensitivity analysis, it was discovered that removing three potential outliers made the difference between the groups significant.ObjectiveThe objective of this study is to reperform the primary and sensitivity analysis of the AMADEUS-2 trial using a Bayesian framework and to compare the results with those of the original analysis.MethodsThe same regression models used in the original analysis were employed in this reanalysis (negative binomial regression). Model parameters were given uniform priors. Markov chain Monte Carlo was used for Bayesian inference, and posterior probabilities were calculated for prespecified thresholds of interest.ResultsNull hypothesis tests did not identify a statistically significant difference between the intervention and control groups, potentially due to a few extreme data points. The Bayesian analysis indicated a 93.6% probability that there was a difference in grams of alcohol consumed at follow-up between the intervention and control groups and a 71.5% probability that the incidence rate ratio was <0.96. Posterior probabilities increased when excluding three potential outliers, yet such post hoc analyses were not necessary to show the preference toward offering an eSBI to harmful and hazardous drinkers among university students.ConclusionsThe null hypothesis framework relies on point estimates of parameters. P values can therefore swing heavily, depending on a single or few data points alone, casting doubt on the value of the analysis. Bayesian analysis results in a distribution over parameter values and is therefore less sensitive to outliers and extreme values. Results from analyses of trials of interventions where small-to-modest effect sizes are expected can be more robust in a Bayesian framework, making this a potentially better approach for analyzing digital health research data.Trial RegistrationInternational Standard Randomized Controlled Trial Number (ISRCTN) 02335307; http://www.isrctn.com/ISRCTN02335307

Estimating Parameters of Structural Models Using Neural Networks

Machine learning tools such as neural networks are increasingly applied in marketing and economics to learn complex relations in data. The learned relations allow machines to perform various tasks, such as recognizing objects from images or recognizing emotions from speech. This paper explores using a neural net to learn the relation between data (moments) and the parameter values of a structural economic model, so that it can “recognize,” or estimate, these parameter values from the data (moments). We train the neural net with the datasets generated by the structural model under different parameter values. The neural net can be trained to give not only the point estimates of parameters but also their statistical accuracy. We show this Neural Net Estimator (NNE) converges to meaningful and well-known limits when the number of training datasets is sufficiently large. NNE does not require computing integrals over the unobservables in the structural model. Thus, it is suitable for models where such integrals are costly in MLE/GMM. We benchmark NNE in two Monte Carlo studies. NNE is able to achieve high estimation accuracies under very light estimation costs.

Descriptive Statistics in Medical Research

Related Article, see p 1474KEY POINT: “…the object of statistical methods is the reduction of data. A quantity of data …is to be replaced by relative few quantities which shall adequately represent the whole.” —Sir Ronald Fisher, 1922In this issue of Anesthesia & Analgesia, Meersch et al1 report results of an observational study on the role of vascular adhesion protein (VAP)-1 in the development of acute kidney injury (AKI) after cardiac surgery. The authors are commended for applying a range of descriptive statistics to characterize the patients and appropriately using and clearly reporting these statistics (Figure).Figure.: Excerpt of Table 1 from Meersch et al.1 Nominal (sex) and ordinal (ASA physical status score) data are reported as counts (absolute frequencies) and percentages (relative frequencies). Note that the numerators (counts per category per group: inside red squares) and denominators (total number of patients per group: inside blue squares) are appropriately presented. Quantitative data are reported as the mean (SD)—which is generally preferred to mean ± SD—or as the median with the Q1, Q3 values. ASA indicates American Society of Anesthesiologists; SD, standard deviation.The choice of the most appropriate summary statistic depends on the type and distribution of data. The following data types are distinguished:2 Nominal data have 2 (eg, sex) or more (eg, blood type) nonordered categories. Ordinal data have categories with a logical order (eg, American Society of Anesthesiologists [ASA] physical status score). Interval data are numeric and have an arbitrary zero point (eg, temperature in Celsius), while ratio data have an absolute zero point (eg, weight). Nominal and ordinal data are correctly summarized with the counts (absolute frequencies) and proportions or percentages (relative frequencies) of observations within the categories. When reporting relative frequencies, the numerator and denominator should both be presented. Interval and ratio data can also be summarized by frequencies within specific strata of the quantitative data (eg, number of patients with age 0–10 years, 11–20 years, etc). These frequencies are commonly reported as a histogram, providing a useful visual display of the data distribution. Two key characteristics of an interval or ratio dataset are (a) its central tendency characteristic—the “average” location of the data and (b) its variability—the extent to which individual values vary around the center. Both should be reported. For approximately normally distributed data, the arithmetic mean appropriately describes the center of the data.3 It is the sum of all observed values, divided by the number of observations. The mean is commonly accompanied by the standard deviation (SD), which describes how far the data points are dispersed around the mean. For normally distributed data, 68% are within 1 SD, 95% are within 2 SDs, and >99% are within 3 SDs on both sides of the mean.3 The median is the value that divides a dataset into 2 equal-sized parts, with the same number of datapoints above and below it.3 It is relatively robust to asymmetric (skewed) distributions, and extreme values (outliers). Therefore, the median is preferred to the mean for non-normally distributed data, and it can also be used for ordinal data.3 The median is commonly reported with the first and third quartiles (Q1, Q3), often loosely referred to as interquartile range. Quartiles divide the dataset into4 equally sized parts, and the interval between Q1 and Q3 contains the middle 50% of the data points. Descriptive statistics are also sometimes used as point estimates of population parameters (eg, using a sample to estimate a proportion or a mean in the population). In this case, they should be accompanied by a confidence interval as a measure of the estimate precision.4

Bayesian inference for parameter estimation in lactoferrin-mediated iron transport across blood-brain barrier

BackgroundIn neurodegenerative diseases such as Alzheimer's and Parkinson's, excessive irons as well as lactoferrin (Lf), but not transferrin (Tf), have been found in and around the affected regions of the brain. These evidences suggest that lactoferrin plays a critical role during neurodegenerative diseases, although Lf-mediated iron transport across blood-brain barrier (BBB) is negligible compared to that of transferrin in normal condition. However, the kinetics of lactoferrins and lactoferrin-mediated iron transport are still unknown. MethodTo determine the kinetic rate constants of lactoferrin-mediated iron transport through BBB, a mass-action based ordinary differential equation model has been presented. A Bayesian framework is developed to estimate the kinetic rate parameters from posterior probability density functions. The iron transport across BBB is studied by considering both Lf- and Tf-mediated pathways for both normal and pathologic conditions. ResultsUsing the point estimates of kinetic parameters, our model can effectively reproduce the experimental data of iron transport through BBB endothelial cells. The robustness of the model and parameter estimation process are further verified by perturbation of kinetic parameters. Our results show that surge in high-affinity receptor density increases lactoferrin as well as iron in the brain. ConclusionsDue to the lack of a feedback loop such as iron regulatory proteins (IRPs) for lactoferrin, iron can transport to the brain continuously, which might increase brain iron to pathological levels and can contribute to neurodegeneration. General significanceThis study provides an improved understanding of presence of lactoferrin and iron in the brain during neurodegenerative diseases.

Mobile Health Coaching on Nutrition and Lifestyle Behaviors for Subfertile Couples Using the Smarter Pregnancy Program: Model-Based Cost-Effectiveness Analysis.

BackgroundThe health care costs for reproductive care have substantially increased with the use of in vitro fertilization (IVF) treatment. The mobile health (mHealth) coaching program Smarter Pregnancy is an effective intervention to improve nutrition and lifestyle behaviors and pregnancy rates in (sub)fertile couples, including those who undergo IVF treatment. Therefore, we hypothesize that this mHealth program can also reduce health care costs associated with IVF treatment.ObjectiveThis study aimed to evaluate the cost-effectiveness of the mHealth coaching program Smarter Pregnancy and compare it to usual care in women of subfertile couples who start their first IVF cycle.MethodsThis model-based cost-effectiveness analysis was performed on data from couples undergoing IVF treatment at the Erasmus MC, University Medical Center Rotterdam. A decision tree model was used to assess the incremental cost-effectiveness ratio (ICER) of ongoing pregnancies and costs of use of the mHealth program as compared to usual care. A probabilistic sensitivity analysis was performed to consider the uncertainty surrounding the point estimates of the input parameters.ResultsBased on our model including 793 subfertile women undergoing IVF treatment, use of the mHealth program resulted in 86 additional pregnancies and saved €270,000 compared to usual care after two IVF cycles, with an ICER of –€3050 (95% CI –3960 to –540) per additional pregnancy. The largest cost saving was caused by the avoided IVF treatment costs. Sensitivity analyses showed that the mHealth program needs to increase the ongoing pregnancy rate by at least 51% after two IVF cycles for cost saving.ConclusionsThe mHealth coaching program Smarter Pregnancy is potentially cost saving for subfertile couples preceding their first IVF treatment. Implementation of this mHealth program in routine preconception care for subfertile couples should be seriously considered, given the relatively low costs and promising cost-effectiveness estimates.

Statistical Modeling of Multivariate Destructive Degradation Tests With Blocking

In degradation tests, the test units are usually divided into several groups, with each group tested simultaneously in a test rig. Each rig constitutes a rig-layer block from the perspective of design of experiments. Within each rig, the test units measured at the same time further form a gauge-layer block. Due to the uncontrollable factors among test rigs and the common errors incurred for each measurement, the degradation measurements of the test units may differ among various blocks. On the other hand, the degradation should be more homogeneous within a block. Motivated by an application of emerging contaminants (ECs), this study proposes a multivariate statistical model to account for the two-layer block effects in destructive degradation tests. A multivariate Wiener process is first used to model the correlation among different dimensions of degradation. The rig-layer block effect is modeled by a one-dimensional frailty motivated by the degradation physics, while the gauge-layer block effect at each measurement epoch is captured by a common additive measurement error. We develop an expectation-maximization algorithm to obtain the point estimates of the model parameters and construct confidence intervals for the parameters. A procedure is proposed to test significance of the block effects in the degradation data. Through a case study on an EC degradation dataset, we show the existence of the two-layer block effects from the test. By making use of the proposed model, decision makers can readily make risk assessment of each contaminant and determine the minimal water treatment time for removal of the contaminants. Supplementary materials for this article are available online.

Different Estimation Methods and Joint Condence Region for the Inverse Burr Distribution Based on Progressively First-Failure Censored Sample with Application to the Nanodroplet Data

In this article, the point and interval estimation of parameters for an in-verse Burr distribution based on progressively rst-failure censored sampleis studied. In point estimation, the maximum likelihood and Bayesian meth-ods are developed for estimating the unknown parameters. An expectation-maximization algorithm is applied for computing the maximum likelihoodestimators. The Bayes estimates relative to both the symmetric and asym-metric loss functions are provided using the Lindley's approximation andthe Metropolis-Hastings algorithm. In interval estimation, approximate andexact condence intervals with the exact condence region for the two parameters have been introduced. Moreover, the proposed methods are carriedout to a real data set contains the spreading of nanodroplet impingementonto a solid surface in order to demonstrate the applicabilities.

Macroeconomic Shocks on Model Parameters: Stress Testing Mortgage Loan Default Rate

We simulate default rate distributions based on models built on crisis and tranquil periods to explore the impact changes in model parameters between different scenarios have on stress testing results. We apply the parameter posterior distribution obtained in a Bayesian approach to stress testing to reduce the estimation risk that results from using parameter point estimates. We compute the VaRs and required capital with both the effect of macroeconomic shocks on model parameters and the estimation risk considered. We find that the required capital is underestimated by over 170% when neither parameter instability nor estimation risk is addressed.

Instrumental Variables Estimation of Systems of Simultaneous Equations: Interrelation of Methods

The article is devoted to the interrelation between methods of estimating parameters of simultaneous equations. Simultaneous equations model (SEM) is commonly used to model complex socio-economic phenomena. SEM is a set of linear simultaneous equations in which response variables are among explanatory variables in each equation of regression. This causes the problem of endogeneity and leads to biased and inconsistent estimation of parameters. There is a number of special methods to solve the problem of endogeneity of regressors: method of instrumental variables (IV), indirect least squares method (ILS), two-stage least squares method (2SLS), and three-stage least squares method (3SLS). In this article, the relationship between 2SLS and IV, ILS and 2SLS, ILS and OLS with restrictions on structural parameters, as well as the equivalence of point estimates of parameters and autocovariance matrices, is shown using empirical example.

Scaling Recurrent Models via Orthogonal Approximations in Tensor Trains.

Modern deep networks have proven to be very effective for analyzing real world images. However, their application in medical imaging is still in its early stages, primarily due to the large size of three-dimensional images, requiring enormous convolutional or fully connected layers - if we treat an image (and not image patches) as a sample. These issues only compound when the focus moves towards longitudinal analysis of 3D image volumes through recurrent structures, and when a point estimate of model parameters is insufficient in scientific applications where a reliability measure is necessary. Using insights from differential geometry, we adapt the tensor train decomposition to construct networks with significantly fewer parameters, allowing us to train powerful recurrent networks on whole brain image volume sequences. We describe the "orthogonal" tensor train, and demonstrate its ability to express a standard network layer both theoretically and empirically. We show its ability to effectively reconstruct whole brain volumes with faster convergence and stronger confidence intervals compared to the standard tensor train decomposition. We provide code and show experiments on the ADNI dataset using image sequences to regress on a cognition related outcome.

Reliability Assessment for Very Few Failure Data and Weibull Distribution

Only very few failure data can be obtained for the time censored test of high-reliability and long-life products. For very few failure data, the current methods fail to obtain both the point estimation and confidence interval of reliability parameters. If the point estimation and confidence interval of reliability parameters are obtained based on different methods, the results tend to be unreliable. In this study, based on the existing research, a Bayesian reliability evaluation method for very few failure data under the Weibull distribution was proposed. First, the range of failure probability was limited based on the convexity and self-features of the Weibull distribution function. Second, based on the background of the sample with very few failure data, the pretest distribution function and parameters were set and solved. The point estimation and confidence interval model of failure probability based on the Bayesian formula was established. The improved match distribution curve method was used to compute both the point estimation and confidence interval of reliability parameters. Furthermore, by comparing the results of numerical examples, the calculation results obtained by the proposed method were verified as being very reasonable. Finally, taking wet friction plates as an example, the results showed the effectiveness of this method in engineering practice.

Bayesian pharmacokinetic modeling of dynamic contrast-enhanced magnetic resonance imaging: validation and application

Tracer-kinetic analysis of dynamic contrast-enhanced magnetic resonance imaging data is commonly performed with the well-known Tofts model and nonlinear least squares (NLLS) regression. This approach yields point estimates of model parameters, uncertainty of these estimates can be assessed e.g. by an additional bootstrapping analysis. Here, we present a Bayesian probabilistic modeling approach for tracer-kinetic analysis with a Tofts model, which yields posterior probability distributions of perfusion parameters and therefore promises a robust and information-enriched alternative based on a framework of probability distributions. In this manuscript, we use the quantitative imaging biomarkers alliance (QIBA) Tofts phantom to evaluate the Bayesian tofts model (BTM) against a bootstrapped NLLS approach. Furthermore, we demonstrate how Bayesian posterior probability distributions can be employed to assess treatment response in a breast cancer DCE-MRI dataset using Cohen’s d. Accuracy and precision of the BTM posterior distributions were validated and found to be in good agreement with the NLLS approaches, and assessment of therapy response with respect to uncertainty in parameter estimates was found to be excellent. In conclusion, the Bayesian modeling approach provides an elegant means to determine uncertainty via posterior distributions within a single step and provides honest information about changes in parameter estimates.

Gaussian process modelling with Gaussian mixture likelihood

Gaussian Process (GP), as a probabilistic non-linear multi-variable regression model, has been widely used in nonparametric Bayesian framework for the data based modelling of complex processes. The noise dynamics in standard GP regression is assumed to follow a Gaussian distribution. In this setting, the point estimation of the model parameters can be obtained analytically using the maximum likelihood (ML) approach in a straight forward fashion. However, in practical scenarios, processes may have been corrupted by the outliers and other disturbances or have multiple modes of operation, resulting a non-Gaussian data likelihood. In this work, to model such scenarios, we propose to employ a mixture of two Gaussian distributions as the noise model to capture both regular noise and irregular noise, thereby enhancing the robustness of the regression model. Further, we present an Expectation Maximization (EM) algorithm-based approach to obtain the optimal parameters set of the proposed GP regression model. The predictive distribution can then be found according to the estimated hyperparameters from the EM algorithm. The efficacy and practicality of the proposed method are illustrated with two sets of synthetic data, a simulated example, as well as an industrial dataset.

Estimation procedures for Kumaraswamy distribution parameters under adaptive type-II hybrid progressive censoring

This paper describes the point and interval estimation of the unknown parameters of Kumaraswamy (Ku) distribution under the adaptive Type-II hybrid progressive censored samples. First, we obtain the maximum likelihood estimation (MLE) of the parameters using Newton-Raphson (NR) method, expectation maximization (EM) and stochastic EM (SEM) algorithms. In addition, we derive the asymptotic distribution of the parameters and the asymptotic confidence intervals. Moreover, two bootstrap confidence intervals are achieved. Second, the Bayesian estimation of the parameters is approximated by using the Markov Chain Monte Carlo (MCMC) algorithm and Lindley’s method due to the lack of explicit forms. Furthermore, the highest posterior density (HPD) credible intervals of the parameters are derived. Finally, the different proposed estimations have been compared by the simulation studies and a practical data set is analyzed to illustrative aims.

Bayesian approach for cure models with a change-point based on covariate threshold: application to breast cancer data

ABSTRACT In this study, a Bayesian approach was suggested to estimate a change-point according to a covariate threshold when some patients never experienced the event of interest. Gibbs sampler algorithm with latent binary cure indicators was used to simplify the implementation of Markov chain Monte Carlo method. Then, the accuracy of new model was demonstrated by simulation studies to compute the point and interval estimates of parameters. Finally, an effective threshold was suggested in age at surgery time to experience the metastasis when the model was applied for a data set of breast cancer patients.

Minimum risk sequential point estimation of the stress-strength reliability parameter for exponential distribution

In this article, using purely and two-stage sequential procedures, the problem of minimum risk point estimation of the reliability parameter (R) under the stress–strength model, in case the loss function is squared error plus sampling cost, is considered when the random stress (X) and the random strength (Y) are independent and both have exponential distributions with different scale parameters. The exact distribution of the total sample size and 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. Using the law of large numbers and Monte Carlo integration, the exact distribution of the stopping rule under the purely sequential procedure is approximated. Moreover, it is shown that both proposed sequential procedures are finite and for special cases the exact distribution of stopping times has a degenerate distribution at the initial sample size. The performances of the proposed methodologies are investigated with the help of simulations. Finally, using a real data set, the procedures are clearly illustrated.

Second-order analysis of regret for sequential estimation of the autoregressive parameter in a first-order autoregressive model

This article revisits the problem of sequential point estimation of the autogressive parameter in an autoregressive model of order 1, where the errors are independent and identically distributed with mean 0 and unknown variance . This problem was originally considered in Sriram (1988), where first-order efficiency properties and a second-order expansion for the expected value of a stopping rule were established. Here, we obtain an asymptotic expression for the so-called regret due to not knowing σ, as the cost of estimation error tends to infinity. Under suitable assumptions, our extensive analysis shows that all but one term in the regret are asymptotically bounded. If the errors have a bounded support, however, then the regret remains asymptotically bounded. Finally, we illustrate the performance of our sequential procedure and the associated regret for well-known blowfly data (Nicholson, 1950) and Internet traffic data using the residual bootstrap method for autoregressive models.

On second-order improved estimation of a gamma scale parameter

ABSTRACTThis paper concludes our comprehensive study on point estimation of model parameters of a gamma distribution from a second-order decision theoretic point of view. It should be noted that efficient estimation of gamma model parameters for samples ‘not large’ is a challenging task since the exact sampling distributions of the maximum likelihood estimators and its variants are not known. Estimation of a gamma scale parameter has received less attention from the earlier researchers compared to shape parameter estimation. What we have observed here is that improved estimation of the shape parameter does not necessarily lead to improved scale estimation if a natural moment condition (which is also the maximum likelihood restriction) is satisfied. Therefore, this work deals with the gamma scale parameter estimation as a separate new problem, not as a by-product of the shape parameter estimation, and studies several estimators in terms of second-order risk.

Exponential Dispersion Process for Degradation Analysis

The methods for analyzing degradation data are usually based on a specific degradation model. However, this may result in a large bias to estimate the reliability of the product when the assumed model is wrong. In this paper, a new stochastic process, called exponential dispersion process, is developed to describe the degradation path of the product's physical or chemical characteristics. Exponential dispersion process includes the most used degradation models (Wiener process, gamma process, inverse Gaussian process, and compound Poisson process) as special cases. Thus, it is useful for suggesting an appropriate degradation model for a specific dataset. We investigate the exponential dispersion model with nonlinear degradation path, and use approximated maximum likelihood method and bootstrap approach to obtain the point and confidence interval estimates of the unknown model parameters. Furthermore, exponential dispersion process models with acceleration factors and random effects are also explored. The developed methodologies are then applied to real data analysis.