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Combining Theory and Data-Driven Approaches for Epidemic Forecasts
Published in Anuj Karpatne, Ramakrishnan Kannan, Vipin Kumar, Knowledge-Guided Machine Learning, 2023
Lijing Wang, Aniruddha Adiga, Jiangzhuo Chen, Bryan Lewis, Adam Sadilek, Srinivasan Venkatramanan, Madhav Marathe
In statistics, point estimation involves the use of sample data to calculate a single value (known as a point estimate since it identifies a point in some parameter space) which is to serve as a “best guess” or “best estimate” of an unknown parameter. In infectious disease epidemiology, point predictions are often served as the best guess of an unknown target. More often, probabilistic forecast is necessary to properly reflect forecasting uncertainty. It is an estimation of the distribution of an unknown target. For example, in the CDC FluSight Challenge (see Section 3.1.3.1), for peak week forecasting, the point prediction could be the week the peak is most likely to occur during the current flu season, and the probabilistic forecast is the probabilities that the peak will occur on each week during the season (e.g., 50% peak will occur on week 1; 30% chance on week 2; 20% chance on week 3).
Main Statements of Statistical Estimation Theory
Published in Vyacheslav Tuzlukov, Signal Processing in Radar Systems, 2017
In theory, for statistical parameter estimation, two types of estimates are used: the interval estimations based on the definition of confidence interval, and the point estimation, that is, the estimate defined at the point. Employing the interval estimations, we need to indicate the interval, within the limits of which there is the true value of unknown random process parameter with the probability that is not less than the predetermined value. This predetermined probability is called the confidence factor and the indicated interval of possible values of estimated random process parameter is called the confidence interval. The upper and lower bounds of the confidence interval, which are called the confidence limits, and the confidence interval are the functions to be considered during digital signal processing (a discretization) or during analog signal processing (continuous function). of the received realization x (t). In the case of point estimation, we assign one parameter value to the unknown parameter from the interval of possible parameter values; that is, some value is obtained based on the analysis of the received realization x (t) and we use this value as the true value of the evaluated parameters.
Voltage/Var
Published in James A. Momoh, Adaptive Stochastic Optimization Techniques with Applications, 2015
In statistics, point estimation involves the use of sample data to calculate a single value (known as a stochastic) that is to serve as a “best guess” or “best estimate” of an unknown (fixed or random) population parameter. More formally, it is the application of a point estimator to the data. In general, point estimation should be contrasted with interval estimation: such interval estimates are typically either confidence intervals, in the case of frequents inference, or credible intervals in the case of Bayesian inference: MinG=-(CDTPD-CSTPS)
Interval estimation of the two-parameter exponential constant stress accelerated life test model under Type-II censoring
Published in Quality Technology & Quantitative Management, 2022
Wenhui Wu, Bing Xing Wang, Jiayan Chen, Jiuzhou Miao, Qingyuan Guan
The two-parameter exponential distribution is a commonly used life distribution. In addition, due to the randomness of the samples, the point estimator may be biased. Compared to point estimation, interval estimation can quantify the uncertainties in reliability estimation and prediction, and can provide more information than point estimator. Hence, it is meaningful and necessary to study the interval estimation method for the two-parameter exponential distribution based on CSALT data. However, since this model does not satisfy the regularity conditions, it is difficult to derive interval estimation using commonly used classical statistical methods. In this paper, we consider the interval estimation for the two-parameter exponential CSALT model in which both the location and scale parameters are log-linear functions of stress level. The proposed inferential methods can be easily understood and implemented by quality and reliability engineers.
Interval estimation for Wiener processes based on accelerated degradation test data
Published in IISE Transactions, 2018
Lanqing Hong, Zhi-Sheng Ye, Josephine Kartika Sari
Compared with point estimation, interval estimation is usually of more interest, as it is able to quantify uncertainties in the estimators. Confidence intervals for parameters in the Wiener process, as well as reliability characteristics, such as product reliability and lifetime quantiles, are often obtained based on the asymptotic normal approximation or the bootstrap. For example, Whitmore and Schenkelberg (1997), Padgett and Tomlinson (2004), and Paroissin (2015) used the large-sample normal approximation to construct confidence intervals for model parameters, mean-time-to-failure and lifetime quantiles. Wang (2010) used both the bootstrap-percentile and the bootstrap-t methods to construct confidence intervals for parameters of a mixed-effects Wiener process. The interval estimation procedures based on the large sample normal approximation and the bootstrap are panaceas for most statistical problems. Their performance is usually asymptotically efficient. According to our simulation studies and application experiences, however, coverage probabilities of the confidence intervals so constructed are often not satisfactory for the Wiener degradation process, especially when the sizes of data are limited (see Section 4 for evidence). In addition, the bootstrap method is usually time-consuming.
A new method in introducing the uniformly most accurate confidence set
Published in International Journal of Mathematical Education in Science and Technology, 2022
Lin-An Chen, Chu-Lan Michael Kao
Classical statistics considers a random variable with a density with known function but unknown (distributional) parameter a quantitative characteristic of the population. The statistical inferences are used to understand this parameter based on a random sample from this density. Point estimation gives a single value as an estimate of the parameter. A point estimate can be larger or smaller than the true value of the parameter; therefore, it may not provide sufficient information about the unknown parameter.