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Select Methods for Measuring Model Performance
Published in Craig Friedman, Sven Sandow, Utility-Based Learning from Data, 2016
Sufficiency principle: Two observations, y1 and y2, that lead to the same value of a sufficient statistic, T, i.e., with T(y1) = T(y2), lead to the same inference on the parameter vector θ. Here, a sufficient statistic is a function of Y such that, if Y has the probability distribution pθ, the probabilities of Y given T(Y) are independent of θ. Intuitively, a sufficient statistic, if it exists, contains all the information about the parameter vector θ that can be extracted from the data.
Spectral Estimation and Modeling
Published in Richard C. Dorf, Circuits, Signals, and Speech and Image Processing, 2018
S. Unnikrishna Pillai, Theodore I. Shim, Stella N. Batalama, Dimitri Kazakos, Ping Xiong, David D. Sworder, John E. Boyd
A sufficient statistic is a set of the observations (or functions of the data) that carries all the information about the unknown parameter. Thus, given a sufficient statistic, the distribution of the data no longer depends on the unknown parameter. A sufficient statistic is said to be minimal if of all sufficient statistics it provides the greatest possible reduction of the data. Furthermore, a sufficient statistic is complete if there is only one function of the statistic that is unbiased.
Probability Distribution Density of the Amplitude and Phase of the Target Return Signal
Published in Vyacheslav P. Tuzlukov, Signal and Image Processing in Navigational Systems, 2018
It is customary to reference the last term on the right side of Equation (11.17) to a threshold independent of the observed input stochastic sample, as in Equation (11.8). Equation (11.17), obtained by the definition of the resulting sufficient statistics, is the logarithm of the likelihood function.
Safety risk assessment for autonomous vehicle road testing
Published in Traffic Injury Prevention, 2023
Huizhao Tu, Min Wang, Hao Li, Lijun Sun
Then: E-Step. Calculate the expected sufficient statistic of missing value based on the existing value, with probability distribution: where: is the probability distribution of when and are known, wile is the probability distribution of when is known.
Worst-case analysis for a leader–follower partially observable stochastic game
Published in IISE Transactions, 2022
Yanling Chang, Chelsea C. White
We remark that this sufficient statistic is more computationally tractable than most of the sufficient statistics presented in the POSG literature. In a multi-agent system, not only do agents have to infer the underlying system state, but also must consider other agents’ beliefs to infer the other agents’ actions. As a result, the existing sufficient statistics are often complex and in high dimensions: they usually include a belief over the other agent’s (finite) information history whereunder the finite-memory assumption (Chang et al., 2015), or a belief over the other agent’s complete model (Gmytrasiewicz and Doshi, 2004). The worst-case modeling requires no such assumptions and the leader examines the follower’s worst-case action based on its own knowledge, resulting in a much simpler sufficient statistic and a more computationally attractive problem.
Statistical inference on traffic intensity in an M / M / 1 queueing system
Published in International Journal of Management Science and Engineering Management, 2018
Now that we have proposed an estimator, it behoves us to examine its properties. . So is an unbiased estimator of .For large n, Hence is a consistent estimator of .The complete sufficient statistic for is m. Also . Thus, by the Lehmann–Scheffe theorem, is the uniformly minimum variance unbiased estimator (UMVUE) of (Rohatgi & Ehsanes Saleh, 2001).