Point Estimates Of Parameters Research Articles

Implementation of Miettinen-Nurminen score method with or without stratification in R

Analysis of a 2 × 2 table for clinical data involves computing the point estimate and confidence interval for risk difference, relative risk, or odds ratio. While point estimates of these comparative parameters are uniquely defined, several statistical methods have been proposed to estimate the confidence interval for each parameter. The Miettinen-Nurminen (MN) score method is expected to be used increasingly over traditional interval estimation methods. The MN score method has not been previously implemented in R software for data with stratification. There is a need for a comprehensive software implementation of the MN score method. This article describes the implementation of the MN score method in the sasLM R software package. To demonstrate the usage of the sasLM functions introduced, recently published clinical data are provided as examples.

Robust Passivity-Based Control of Underactuated Systems via Neural Approximators and Bayesian Inference

Inspired by passivity-based control (PBC) techniques, we propose a data-driven approach in order to learn a neural net parameterized storage function of underactuated mechanical systems. First, the PBC problem is cast as an optimization problem that searches for point estimates of the neural net parameters. Then, we improve the robustness properties of this deterministic framework against system parameter uncertainties and measurement error by injecting techniques from Bayesian inference. In the Bayesian framework, the neural net parameters are samples drawn from a posterior distribution learned via Variational Inference. We demonstrate the performance of the deterministic and Bayesian trainings on the swing-up task of an inertia wheel pendulum in simulation and realworld experiments.

Some comparisons of point estimates of parameters by Bayesian analysis with respect to RMSE and bias: A report from the point of view of experimental psychology

Some comparisons of point estimates of parameters by Bayesian analysis with respect to RMSE and bias: A report from the point of view of experimental psychology

Cosmological parameter estimation and inference using deep summaries

The ability to obtain reliable point estimates of model parameters is of crucial importance in many fields of physics. This is often a difficult task given that the observed data can have a very high number of dimensions. In order to address this problem, we propose a novel approach to construct parameter estimators with a quantifiable bias using an order expansion of highly compressed deep summary statistics of the observed data. These summary statistics are learned automatically using an information maximising loss. Given an observation, we further show how one can use the constructed estimators to obtain approximate Bayes computation (ABC) posterior estimates and their corresponding uncertainties that can be used for parameter inference using Gaussian process regression even if the likelihood is not tractable. We validate our method with an application to the problem of cosmological parameter inference of weak lensing mass maps. We show in that case that the constructed estimators are unbiased and have an almost optimal variance, while the posterior distribution obtained with the Gaussian process regression is close to the true posterior and performs better or equally well than comparable methods.

A new class of mechanism-equivalence-based Wiener process models for reliability analysis

It is quite common to see that a unit of a product with a higher degradation rate also presents a more prominent dispersion. This phenomenon has motivated studies on developing new degradation models. In particular, a variety of Wiener process models have been developed by correlating the drift parameter and the diffusion parameter based on the statistical features of data. However, no insightful explanations are provided for such interesting correlations. In this article, degradation mechanism equivalence is first introduced based on the acceleration factor invariant principle, and the correlation between degradation rate and variation is explained using basic principles. Then, mechanism-equivalence-based Wiener process models, including a basic model and a random-effects model, are proposed to characterize such degradation behavior of a product. Analytical solutions for both point estimation and interval estimation of unknown model parameters are obtained using the maximum likelihood estimation method and an expectation–maximization algorithm. An extension of the proposed model that is able to handle accelerated degradation tests is developed. A simulation study and two real-world applications are provided to illustrate the effectiveness of the proposed models in product reliability estimation based on degradation data.

Partially constant-stress accelerated life tests model for parameters estimation of Kumaraswamy distribution under adaptive Type-II progressive censoring

In a life testing experiments, accelerated life tests (ALTs) model has provided a significant decrease for the cost and time. The problem of statistical inference of constant-stress ALTs based on censored data is discussed in this paper. So, we implement partially constant-stress ALTs model to test units have two parameter Kumaraswamy lifetime population under adaptive Type-II progressive censoring scheme. The population parameters as well as acceleration factor are estimated by using maximum likelihood method for point and interval estimation. Two different confidence intervals are obtained under bootstrap technique. Also, Bayesian approach under different loss functions is used to contract the point and interval estimates of the model parameters with the help of Markov chain Monte Carlo method (MCMC). For illustrative purpose a simulate data set are analyzed. Different developed results discussed in this paper are compared through Monte Carlo simulation study.

Bayesian inference for modified Weibull distribution under simple step‐stress model based on type‐I censoring

AbstractIn this paper, we consider a simple step‐stress accelerated life test (SSALT) model under the tampered random variable (TRV) model for the modified Weibull distribution (MWD) with type‐I censoring. We consider the classical and Bayesian estimation methods for the estimation of unknown parameters of the MWD model. In the classical scenario, we derive the maximum likelihood estimates (MLEs) and approximate confidence intervals (ACIs) for model parameters. Also, a parametric bootstrap resampling technique is used to derive the bootstrap confidence intervals. Under the Bayesian paradigm, the point estimates of the unknown parameters for different symmetric, asymmetric, and balanced loss functions and highest posterior density (HPD) credible intervals (CIs) are derived via Gibbs within metropolis‐hasting sampling procedure. A simulation study is conducted to compare the performance of Bayesian estimates with MLEs. Moreover, we also compare the precision of considered CIs. Finally, a real application is considered for illustration purpose.

Modelling and estimation of system reliability under dynamic operating environments and lifetime ordering constraints

Modern systems are operating under dynamic environments and the components therein often exhibit positively correlated lifetimes. Moreover, due to various practical reasons such as the load sharing mechanism, it is not uncommon that lifetimes of some components dominate the others within the same system. In this study, we first propose a statistical model for system reliability evaluation by jointly considering the correlated component lifetimes and the lifetime ordering constraints. In specific, the effects of the dynamic environments are incorporated by modelling the cumulative hazard function as an exponential dispersion process and the lifetime ordering constraints are modelled by truncating the support of the joint lifetime distribution. We then discuss the statistical inference based on the proposed model. The point estimates of the model parameters as well as the lifetime quantiles are obtained by the maximum likelihood method, and the confidence intervals are constructed by using the generalized pivots. Extensive simulation show that the proposed interval estimation procedures can achieve accurate coverage even under small sample sizes. Two real examples are used to illustrate the proposed modelling and estimation framework.

The Latent Class Multinomial Logit Model for Modeling Front-Seat Passenger Seatbelt Choice, Considering Seatbelt Status of Driver

The literature review highlighted the impacts of drivers’ behavior on passengers’ attitudes in the choice of seatbelt usage. However, limited studies have been done to determine those impacts. Studying the passengers’ seatbelt use is especially needed to find out why passengers choose not to buckle up, and consequently it helps decision makers to target appropriate groups. So, this study was conducted to find drivers’ characteristics that might impact the passenger’s seatbelt use, in addition to other passengers’ characteristics themselves. While performing any analysis, it is important to use a right statistical model to achieve a less biased point estimate of the model parameters. The latent class multinomial logit model (LC-MNL) can be seen as an alternative to the mixed logit model, replacing the continuous with a discrete distribution, by capturing possible heterogeneity through membership in various clusters. In this study, instead of a response to the survey or crash observations, we employed a real-life observational data for the analysis. Results derived from the analysis reveal a clear indication of heterogeneity across individuals for almost all parameters. Various socio-demographic variables for class allocation and models with different latent numbers were considered and checked in terms of goodness of fit. The results indicated that a class membership with three factors based on vehicle type would result in a best fit. The results also highlighted the significant impacts of driver seatbelt status, time of a day, distance of traveling, vehicle type, and driver gender, instead of passenger gender, as some of the factors impacting the passengers’ choice of seatbelt usage. In addition, it was found that the belting status of passengers is positively associated with the belting condition of drivers, highlighting the psychological behavioral impact of drivers on passengers. Extensive discussion has been made regarding the implications of the findings.

Evaluation of methods for feasible parameter set estimation of Takagi-Sugeno models for nonlinear regression with bounded errors

Abstract In data-driven modeling besides the point estimate of the model parameters, an estimation of the parameter uncertainty is of great interest. For this, bounded error parameter estimation methods can be used. These are particularly interesting for problems where the stochastical properties of the random effects are unknown and cannot be determined. In this paper, different methods for obtaining a feasible parameter set are evaluated for the use with Takagi-Sugeno models. Case studies with simulated data and with measured data from a manufacturing process are presented.

A new statistical inference method for multi-stress accelerated life testing based on random variable transformation

The limited sample size in multi-stress accelerated life testing makes the conventional large-sample-based inference methods inefficient. To overcome this problem, this paper develops a new statistical inference method based on random variable transformation for multi-stress accelerated life testing with Weibull distribution and progressive Type-II censoring. Firstly, a χ2 statistic is constructed using the random variable transformation method, and the exact point estimates of model parameters are derived based on the χ2 statistic. Subsequently, based on the χ2 statistic, the exact confidence interval of shape parameter is provided, while the generalized confidence intervals of the accelerated model parameters are calculated by constructing the new multivariate generalized pivotal quantities. Furthermore, the generalized confidence intervals of some commonly used reliability indexes are provided for better reliability management and decision making. Finally, a simulation study and a real case study are conducted to illustrate the implementation and effectiveness of the proposed method.

Beta regression model nonlinear in the parameters with additive measurement errors in variables.

We propose in this paper a general class of nonlinear beta regression models with measurement errors. The motivation for proposing this model arose from a real problem we shall discuss here. The application concerns a usual oil refinery process where the main covariate is the concentration of a typically measured in error reagent and the response is a catalyst’s percentage of crystallinity involved in the process. Such data have been modeled by nonlinear beta and simplex regression models. Here we propose a nonlinear beta model with the possibility of the chemical reagent concentration being measured with error. The model parameters are estimated by different methods. We perform Monte Carlo simulations aiming to evaluate the performance of point and interval estimators of the model parameters. Both results of simulations and the application favors the method of estimation by maximum pseudo-likelihood approximation.

A scenario-based interval-input output model to analyze the risk of COVID-19 pandemic in port logistics

PurposePresently, Indian sectors are manifesting a higher level of interdependency and making the economy more vulnerable to human-caused and natural disasters. COVID-19 pandemic creates a devastating effect on the world economy. The Indian economy was expected to lose around ₹ 32,000 crores every day during the first 21 days of complete lockdown. This motivates to conduct the research on how the COVID-19 pandemic affects the port logistics sector and how the effects of COVID-19 on port logistics propagate to other sectors owing to its interconnectedness and affect the economy of the country.Design/methodology/approachThe purpose of the study is analyze how perturbation in one sector can affect the system of interdependent sectors and it is done with interdependency analysis. It uses Wassily Leontief’s inoperability input-output model (IIM) and interval programming (IP) to develop a framework. IP is used to address situations where assumptions are not valid because of uncertainties associated with disruptive events.FindingsThe model helps in describing how the effect of the COVID-19 pandemic in port logistics can propagate owing to the interconnectedness across other sectors. The model uses the latest five-year data available on the Organisation for Economic Co-operation and Development database. It uses metrics like inoperability and economic loss to study the consequences of COVID-19 pandemic on various sectors. This study also presents the ranking of the affected sectors based on their inoperability and economic lossResearch limitations/implicationsIn the future study, other techniques like dynamic evolution, multiplex network analysis, analytical hierarchy process, pinch analysis, stochastic evolution and pinch graph could be integrated with input-output (I-O) modelling. Integrated stochastic evolution with an I-O model allows capturing the likelihood of the events; it includes probability distributions instead of point estimates for scenario parameters. Methods like dynamic evolution and multiplex network analysis can be introduced in future work to shed lights on interdependency among the sector, which could potentially provide additional insights for transport policy formulations.Originality/valueThis study discusses the theory, methodology and application of the IIM-IP model in the domain of port logistics. The developed IIM-IP model helps decision-makers to manage risk in port logistics. Firstly, it studies how different sectors are interconnected with each other. Secondly, it helps in identifying the most vulnerable sectors based on economic loss and inoperability. Thirdly, it provides the ranking of the sectors based on their economic losses.

Method G: Uncertainty Quantification for Distributed Data Problems Using Generalized Fiducial Inference

It is not unusual for a data analyst to encounter datasets distributed across several computers. This can happen for reasons such as privacy concerns, efficiency of likelihood evaluations, or just the sheer size of the whole dataset. This presents new challenges to statisticians as even computing simple summary statistics such as the median becomes computationally challenging. Furthermore, if other advanced statistical methods are desired, then novel computational strategies are needed. In this article, we propose a new approach for distributed analysis of massive data that is suitable for generalized fiducial inference and is based on a careful implementation of a “divide-and-conquer” strategy combined with importance sampling. The proposed approach requires only small amount of communication between nodes, and is shown to be asymptotically equivalent to using the whole dataset. Unlike most existing methods, the proposed approach produces uncertainty measures (such as confidence intervals) in addition to point estimates for parameters of interest. The proposed approach is also applied to the analysis of a large set of solar images. Supplementary materials for this article are available online.

Inference over radiative transfer models using variational and expectation maximization methods

Earth observation from satellites offers the possibility to monitor our planet with unprecedented accuracy. Radiative transfer models (RTMs) encode the energy transfer through the atmosphere, and are used to model and understand the Earth system, as well as to estimate the parameters that describe the status of the Earth from satellite observations by inverse modeling. However, performing inference over such simulators is a challenging problem. RTMs are nonlinear, non-differentiable and computationally costly codes, which adds a high level of difficulty in inference. In this paper, we introduce two computational techniques to infer not only point estimates of biophysical parameters but also their joint distribution. One of them is based on a variational autoencoder approach and the second one is based on a Monte Carlo Expectation Maximization (MCEM) scheme. We compare and discuss benefits and drawbacks of each approach. We also provide numerical comparisons in synthetic simulations and the real PROSAIL model, a popular RTM that combines land vegetation leaf and canopy modeling. We analyze the performance of the two approaches for modeling and inferring the distribution of three key biophysical parameters for quantifying the terrestrial biosphere.

Designing, Not Checking, for Policy Robustness: An Example with Optimal Taxation

Economists typically check the robustness of their results by comparing them across plausible ranges of parameter values and model structures. A preferable approach to robustness—for the purposes of policymaking and evaluation—is to design policy that takes these ranges into account. We modify the standard optimal income tax model to include the policymaker’s subjective uncertainty over parameter values, and we characterize robust optimal policy as that which maximizes expected social welfare. After calibrating uncertainty over the elasticity of taxable income from past empirical work and novel survey data on economists’ beliefs, we compare the implied robust optimal marginal tax rates to the alternative benchmark policy based on the best point estimates of relevant parameters. Our results suggest that robust optimal marginal tax rates are typically more progressive than in benchmark analyses, raising top marginal tax rates by between 5 and 7 percentage points, and generating modest expected welfare gains. Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Inference for a constant-stress model under progressive type-I interval censored data from the generalized half-normal distribution

In this paper, we discuss the problem of constant-stress accelerated life test when the failure data are progressive type-I interval censored. Both classical and Bayesian inferential approaches of the distribution parameters and reliability characteristics are discussed. In the classical scenario, the maximum likelihood estimates are approximated using the EM algorithm and the mid-point approximation method. Furthermore, the model's parameters are estimated by method of moments. Next in the Bayesian framework, the point estimates of unknown parameters are obtained using Tierney-Kadane's technique and Markov Chain Monte Carlo (MCMC) method. In addition, both approximate and credible confidence intervals (CIs) of the estimators are constructed. For illustration purpose, a Monte Carlo simulation is conducted to investigate the performance of the proposed estimators and a real data set is analysed.

PET-ABC: fully Bayesian likelihood-free inference for kinetic models

Aims. We describe an intuitive, easy to use method called PET-ABC that enables full Bayesian statistical inference from single subject dynamic PET data. The performance of PET-ABC was compared with weighted non-linear least squares (WNLS) in terms of reliability of kinetic parameter estimation and statistical power for model selection. Methods. Dynamic PET data based on 1-tissue and 2-tissue compartmental models were simulated with 2 noise models and 3 noise levels. PET-ABC was used to evaluate the reliability of parameter estimates under each condition. It was also used to perform model selection for a simulated noisy dataset composed of a mixture of 1- and 2-tissue compartment kinetics. Finally, PET-ABC was used to analyze a non-steady state dynamic [11C] raclopride study performed on a fully conscious rat administered either 2 mg.kg−1 amphetamine or saline 20 min after tracer injection. Results. PET-ABC yielded posterior point estimates for model parameters with smaller variance than WNLS, as well as probability density functions indicating confidence intervals for those estimates. It successfully identified the superiority of a 2-tissue compartment model to fit the simulated mixed model data. For the drug challenge study, the post observation probability of striatal displacement of the PET signal was 0.9 for amphetamine and approximately 0 for saline, indicating a high probability of amphetamine-induced endogenous dopamine release in the striatum. PET-ABC also demonstrated superior statistical power to WNLS (0.87 versus 0.09) for selecting the correct model in a simulated ligand displacement study. Conclusions. PET-ABC is a simple and intuitive method that provides complete Bayesian statistical analysis of single subject dynamic PET data, including the extent to which model parameter estimates and model choice are supported by the data. Software for PET-ABC is freely available as part of the PETabc package https://github.com/cgrazian/PETabc.

Bayesian Estimation of the ETAS Model for Earthquake Occurrences

ABSTRACT The epidemic-type aftershock sequence (ETAS) model is widely used in seismic forecasting. However, most studies of ETAS use point estimates for the model parameters, which ignores the inherent uncertainty that arises from estimating these from historical earthquake catalogs, resulting in misleadingly optimistic forecasts. In contrast, Bayesian statistics allows parameter uncertainty to be explicitly represented and fed into the forecast distribution. Despite its growing popularity in seismology, the application of Bayesian statistics to the ETAS model has been limited by the complex nature of the resulting posterior distribution, which makes it infeasible to apply to catalogs containing more than a few hundred earthquakes. To combat this, we develop a new framework for estimating the ETAS model in a fully Bayesian manner, which can be efficiently scaled up to large catalogs containing thousands of earthquakes. We also provide easy-to-use software that implements our method.

Latent Class Model with Heterogeneous Decision Rule for Identification of Factors to the Choice of Drivers’ Seat Belt Use

The choice of not buckling a seat belt has resulted in a high number of deaths worldwide. Although extensive studies have been done to identify factors of seat belt use, most of those studies have ignored the presence of heterogeneity across vehicle occupants. Not accounting for heterogeneity might result in a bias in model outputs. One of the main approaches to capture random heterogeneity is the employment of the latent class (LC) model by means of a discrete distribution. In a standard LC model, the heterogeneity across observations is considered while assuming the homogeneous utility maximization for decision rules. However, that notion ignores the heterogeneity in the decision rule across individual drivers. In other words, while some drivers make a choice of buckling up with some characteristics, others might ignore those factors while making a choice. Those differences could be accommodated for by allowing class allocation to vary based on various socio-economic characteristics and by constraining some of those rules at zeroes across some of the classes. Thus, in this study, in addition to accounting for heterogeneity across individual drivers, we accounted for heterogeneity in the decision rule by varying the parameters for class allocation. Our results showed that the assignment of various observations to classes is a function of factors such as vehicle type, roadway classification, and vehicle license registration. Additionally, the results showed that a minor consideration of the heterogeneous decision rule resulted in a minor gain in model fits, as well as changes in significance and magnitude of the parameter estimates. All of this was despite the challenges of fully identifying exact attributes for class allocation due to the inclusion of high number of attributes. The findings of this study have important implications for the use of an LC model to account for not only the taste heterogeneity but also heterogeneity across the decision rule to enhance model fit and to expand our understanding about the unbiased point estimates of parameters.