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Sampling Theory
Sampling Theory

Asymptotic properties of sample quantiles from a finite population Arindam Chatterjee
Asymptotic properties of sample quantiles from a finite population Arindam Chatterjee

INTRODUCTION AND REVIEW OF PROBABILITY
INTRODUCTION AND REVIEW OF PROBABILITY

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The Laws of Probability

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... During the next few lectures we will be looking at the inference from training data problem as a random process modeled by the joint probability distribution over input (measurements) and output (say class labels) variables. In general, estimating the underlying distribution is a daunting and unwiel ...
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Lecture Notes - Department of Statistics, Purdue University

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Identifiability of the proportion of null hypotheses in skew

... of π0 is guaranteed if the p-value density under the alternative attains the minimum value 0 as the p-values approach 1, since then the weight π0 attached to the uniform can be easily identified from the height of the mixture density for the original p-values at one; see Ghosal et al. (2008). For te ...
Discrete Data
Discrete Data



Functional volumes modeling: Scaling for group size
Functional volumes modeling: Scaling for group size

... The M1-mouth locations (left and right) were determined in each SPI, as follows. The 30-subject SPI was scanned with a local-maximum search algorithm [Mintun et al., 1989], to determine the locations of the M1-mouth areas (left and right) in the image with the highest possible signal to noise (i.e., ...
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Chapter 8 b

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Tree-based credal networks for classification

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... We are told: “The article referenced in Example 2.5 also gave graduation rates for all student athletes at the 63 schools in the 2009 Division I basketball playoffs. The data are listed below. Also listed are the differences between the graduation rate for all student athletes and the graduation rat ...
Probability-Possibility Transformations, Triangular Fuzzy Sets
Probability-Possibility Transformations, Triangular Fuzzy Sets

Chapter 8 Sampling Methods and the Central Limit Theorem
Chapter 8 Sampling Methods and the Central Limit Theorem

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History of statistics

The History of statistics can be said to start around 1749 although, over time, there have been changes to the interpretation of the word statistics. In early times, the meaning was restricted to information about states. This was later extended to include all collections of information of all types, and later still it was extended to include the analysis and interpretation of such data. In modern terms, ""statistics"" means both sets of collected information, as in national accounts and temperature records, and analytical work which requires statistical inference.Statistical activities are often associated with models expressed using probabilities, and require probability theory for them to be put on a firm theoretical basis: see History of probability.A number of statistical concepts have had an important impact on a wide range of sciences. These include the design of experiments and approaches to statistical inference such as Bayesian inference, each of which can be considered to have their own sequence in the development of the ideas underlying modern statistics.
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