On the Mathematical Foundations of Theoretical Statistics

By Stanislav Grof, M. D. Transpersonal

Centre of Location. That abscissa of a frequency curve for which the sampling errors of optimum location are uncorrelated with those of optimum scaling. (9.)

Subfields: Statistics and Probability

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Citations in the corpus

Training Neural Networks with Fixed Sparse Masks (2021, background): “It can be shown [34, 37] that as δ → 0 , to second order, where F θ ∈ R | θ |×| θ | is the Fisher information matrix [14, 4], deﬁned as Given this relation, it can be seen that the Fisher information matrix is closely connected to how much each parameter affects the model’s predictions.”
The Ideal Continual Learner: An Agent That Never Forgets (2023, background): “ICL† is Sufficient and Minimal In this section, we show that the Ideal Continual Learner† is sufficient (Fisher, 1922) and minimal (Lehmann & Scheffé, 1950), which are two general and fundamental properties in the information-theoretical and statistical sense.”
Phaser crystallographic software (2007, background): “…of statistical inference that asserts that the best model on the evidence of the data is the one that explains what has in fact been observed with the ‡ Present address: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK. highest probability (Fisher, 1922).”
Information and Entropy Econometrics - A Review and Synthesis (2008, methodology): “That philosophy was continued by Fisher (1912, 1922) in his work on the Maximum Likelihood method and continued later with a (seemingly) competing approach known as the Minimum Chi-Square (Neyman and Pearson, 1928a,b), that led to Ferguson’s Method of Moments (Ferguson, 1958).”
Letter of Intent: The Precision IceCube Next Generation Upgrade (PINGU) (2014, methodology): “The Fisher information matrix (the inverse of the covariance matrix), describing the effect of different systematics and of changes in the oscillation parameters, then provides a measure of the confidence with which the correct hierarchy can be determined [45].”
TIES-Merging: Resolving Interference When Merging Models (2023, methodology): “Fisher Merging [45] goes beyond simple averaging to identify the importance of individual parameters using Fisher Information Matrix [18, 3, 34] and uses it to weigh the parameters in each model when merging.”
Bayesian Estimation and Inference (2015, methodology): “Populations are defined by fixed parameters in θ (Fisher, 1922), so that parameters are unknowable but take on singular values with a probability of 1.”
Self-exciting point process models of civilian deaths in Iraq (2011, unknown): “To estimate parameters, we use maximum likelihood estimation (MLE) ( Fisher, 1922 ; Rubin, 1972 ; Ozaki, 1979 ).”
USING A NEW STATISTICAL MODEL FOR TESTLETS TO SCORE TOEFL (2000, methodology): “For a variety of reasons, not the least of which were the cumbersome calculations required to determine the standard error of a composite, Fisher (1922) preferred to use a transformation of standard error he termed “information.”
Learning to Match Anchors for Visual Object Detection (2021, methodology): “To fulfill these purposes, we propose to define an anchor bag for each object and perform object-anchor matching in a maximum likelihood estimation (MLE) framework [11], [12].”
Power-Law Distributions in Empirical Data (2007, methodology): “The first version of a proof of the asymptotic Gaussian distribution of the MLE, and its relation to the Fisher information, may be found in Fisher (1922).”
Inductive Principles for Restricted Boltzmann Machine Learning (2010, background): “The prevalence of maximum likelihood (ML) as an inductive principle for estimating the parameters of statistical models is based on two key properties: asymptotic consistency and asymptotic efficiency (Fisher, 1922, p. 316).”
FreeAnchor: Learning to Match Anchors for Visual Object Detection (2019, methodology): “To fulﬁll these objectives, we formulate object-anchor matching as a maximum likelihood estimation (MLE) procedure [8, 9], which selects the most representative anchor from a “bag" of anchors for each object.”
The MM, ME, ML, EL, EF and GMM approaches to estimation: a synthesis (2002, methodology): “Fisher (1922) performed an extensive analysis of the efficiency of ML and MM estimators for fitting distributions belonging to the Pearson (1895) family.”
Bayesian Adaptive Sampling for Variable Selection and Model Averaging (2011, background): “This is similar in spirit to a desirable finite sample property called Fisher-consistency (Fisher 1922) where the estimator will recover the population quantities when applied to the entire population.”
Measurement Error Models (2000, methodology): “The most celebrated information measure in statistics is the one developed by Fisher (1921) for the purpose of quantifying information in f (zp) about the parameter, given by (9) 8) is a measure of information in the sense that it quantifies “the ease with which a parameter can be estimated” by z…”