Edinburgh, United Kingdom

Probability and Stochastic Analysis

Language: English Studies in English
University website: www.ed.ac.uk
Doctor of Philosophy (PhD)
Doctor of Philosophy (PhD)
Analysis
Analysis is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 B.C.), though analysis as a formal concept is a relatively recent development.
Probability
Probability is the measure of the likelihood that an event will occur. See glossary of probability and statistics. Probability is quantified as a number between 0 and 1, where, loosely speaking, 0 indicates impossibility and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).
Stochastic
The word stochastic is an adjective in English that describes something that was randomly determined. The word first appeared in English to describe a mathematical object called a stochastic process, but now in mathematics the terms stochastic process and random process are considered interchangeable. The word, with its current definition meaning random, came from German, but it originally came from Greek στόχος (stokhos), meaning 'aim, guess'.
Probability
As is known, the question of the objectivity or the subjectivity of probability has divided the world of science into two camps. Some maintain that there exist two types of probability, as above, others, that only the subjective exists, because regardless of what is supposed to take place, we cannot have full knowledge of it. Therefore, some lay the uncertainty of future events at the door of our knowledge of them, whereas others place it within the realm of the events themselves.
Stanisław Lem, "De Impossibilitate Vitae and De Impossibilitate Vitae Prognoscendi", in A Perfect Vacuum (1971), tr. Michael Kandel (1978).
Analysis
Government, in the last analysis, is organized opinion. Where there is little or no public opinion, there is likely to be bad government, which sooner or later becomes autocratic government.
William Lyon Mackenzie King, Message of the Carillon (1927)
Probability
No human being can give an eternal resolution to another or take it from him; If someone objects that then one might just as well be silent if there is no probability of winning others, he thereby has merely shown that although his life very likely thrived and prospered in probability and everyone of his undertakings in the service of probability went forward, he has never really ventured and consequently has never had or given himself the opportunity to consider that probability is an illusion, but to venture the truth is what gives human life and the human situation pith and meaning, to venture is the fountainhead of inspiration, whereas probability is the sworn enemy of enthusiasm, the mirage whereby the sensate person drags out time and keeps the eternal away, whereby he cheats God, himself, and his generation: cheats God of the honor, himself of liberating annihilation, and his generation of the equality of conditions.
Søren Kierkegaard, Four Upbuilding Discourses (31 August 1844) in Eighteen Upbuilding Discourses p. 382.
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