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Step detection is the process of finding abrupt changes in the mean level of a time series or signal. It is usually considered as a special kind of statistical method known as change point detection. Often, the step is small and the time series is corrupted by some kind of noise, and this makes the problem challenging because the step may be ...
The two-step estimator discussed above is a limited information maximum likelihood (LIML) estimator. In asymptotic theory and in finite samples as demonstrated by Monte Carlo simulations, the full information (FIML) estimator exhibits better statistical properties. However, the FIML estimator is more computationally difficult to implement. [9]
The step detection problem occurs in multiple scientific and engineering contexts, for example in statistical process control [1] (the control chart being the most directly related method), in exploration geophysics (where the problem is to segment a well-log recording into stratigraphic zones [2]), in genetics (the problem of separating ...
The use of a sequence of experiments, where the design of each may depend on the results of previous experiments, including the possible decision to stop experimenting, is within the scope of sequential analysis, a field that was pioneered [12] by Abraham Wald in the context of sequential tests of statistical hypotheses. [13]
While many scientific investigations make use of data, statistics is generally concerned with the use of data in the context of uncertainty and decision-making in the face of uncertainty. [10] [11] Statistics is indexed at 62, a subclass of probability theory and stochastic processes, in the Mathematics Subject Classification. [12]
Replication in statistics evaluates the consistency of experiment results across different trials to ensure external validity, while repetition measures precision and internal consistency within the same or similar experiments. [5] Replicates Example: Testing a new drug's effect on blood pressure in separate groups on different days.
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The history of scientific method considers changes in the methodology of scientific inquiry, not the history of science itself. The development of rules for scientific reasoning has not been straightforward; scientific method has been the subject of intense and recurring debate throughout the history of science, and eminent natural philosophers and scientists have argued for the primacy of ...