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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).
Confidence Intervals
Published in Lawrence S. Aft, Fundamentals of Industrial Quality Control, 2018
In addition to stating the point estimate, it is often desirable to establish an interval within which the true population parameter may be expected with a certain degree of confidence to fall. For example, after measuring the tensile strength of steel rods, one might say that the best estimate of the average tensile strength is 732; the true mean is between 725 and 739. (If more confidence were desired for the same data, a wider interval would be specified. A 95 percent confidence interval would be even wider — for example, between 722.49 and 741.51.) A confidence interval is a range of values that has a specified likelihood of including the true value of a population parameter. It is calculated from sample calculations of the parameters.
Sampling and estimation theories
Published in John Bird, Higher Engineering Mathematics, 2017
An estimate of a population parameter, such as mean or standard deviation, based on a single number is called a point estimate. An estimate of a population parameter given by two numbers between which the parameter may be considered to lie is called an interval estimate. Thus if an estimate is made of the length of an object and the result is quoted as 150 cm, this is a point estimate. If the result is quoted as 150 ± 10 cm, this is an interval estimate and indicates that the length lies between 140 and 160 cm. Generally, a point estimate does not indicate how close the value is to the true value of the quantity and should be accompanied by additional information on which its merits may be judged. A statement of the error or the precision of an estimate is often called its reliability. In statistics, when estimates are made of population parameters based on samples, usually interval estimates are used. The word estimate does not suggest that we adopt the approach ‘let’s guess that the mean value is about ...’ but rather that a value is carefully selected and the degree of confidence which can be placed in the estimate is given in addition.
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.
Effectively communicating developmental system reliability growth plans and risk
Published in Australian Journal of Multi-Disciplinary Engineering, 2022
Paul Nation, Martin Wayne, Mohammad Modarres
An estimator of a population reliability parameter is an approximation depending solely on sample information. There are several classes of an estimator, which include point, interval and distribution estimates. A point estimate represents a single reliability estimate, whereas interval and distribution estimates represent a range of potential true reliability values. Interval estimates provide much more information to a decision-maker and are preferred when making inferences. Similarly, distribution estimates are derived from a distribution function and convey the most information about a sample of reliability test observations. Each has its benefits in communicating reliability and risk as well as shortcomings.