"In the laws of probability theory, likelihood distributions are fixed properties of a hypothesis. In the art of rationality, to explain is to anticipate. To anticipate is to explain." (Eliezer S. Yudkowsky, "A Technical Explanation of Technical Explanation", 2005)
"I have always thought that statistical design and sampling from populations should be the first courses taught, but all elementary courses I know of start with statistical methods or probability. To me, this is putting the cart before the horse!" (Walter Federer, "A Conversation with Walter T Federer", Statistical Science Vol 20, 2005)
"For some scientific data the true value cannot be given by a constant or some straightforward mathematical function but by a probability distribution or an expectation value. Such data are called probabilistic. Even so, their true value does not change with time or place, making them distinctly different from most statistical data of everyday life.
"In fact, H [entropy] measures the amount of uncertainty that exists in the phenomenon. If there were only one event, its probability would be equal to 1, and H would be equal to 0 - that is, there is no uncertainty about what will happen in a phenomenon with a single event because we always know what is going to occur. The more events that a phenomenon possesses, the more uncertainty there is about the state of the phenomenon. In other words, the more entropy, the more information." (Diego Rasskin-Gutman, "Chess Metaphors: Artificial Intelligence and the Human Mind", 2009)
"The four questions of data analysis are the questions of description, probability, inference, and homogeneity. [...] Descriptive statistics are built on the assumption that we can use a single value to characterize a single property for a single universe. […] Probability theory is focused on what happens to samples drawn from a known universe. If the data happen to come from different sources, then there are multiple universes with different probability models. [...] Statistical inference assumes that you have a sample that is known to have come from one universe." (Donald J Wheeler," Myths About Data Analysis", International Lean & Six Sigma Conference, 2012)
"When statisticians, trained in math and probability theory, try to assess likely outcomes, they demand a plethora of data points. Even then, they recognize that unless it’s a very simple and controlled action such as flipping a coin, unforeseen variables can exert significant influence." (Zachary Karabell, "The Leading Indicators: A short history of the numbers that rule our world", 2014)
"Entropy is a measure of amount of uncertainty or disorder present in the system within the possible probability distribution. The entropy and amount of unpredictability are directly proportional to each other." (G Suseela & Y Asnath V Phamila, "Security Framework for Smart Visual Sensor Networks", 2019)
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