Ratios and Rates
... Ratio: A ratio uses division to compare two quantities. Equivalent Two ratios are called equivalent ratios when they have the same value. ratios: Rate: A ratio of two quantities measured in different units. Unit rate: A rate that has a denominator of 1 when expressed in fraction form. ...
... Ratio: A ratio uses division to compare two quantities. Equivalent Two ratios are called equivalent ratios when they have the same value. ratios: Rate: A ratio of two quantities measured in different units. Unit rate: A rate that has a denominator of 1 when expressed in fraction form. ...
aachen_stat_1
... Random variables and probability density functions A random variable is a numerical characteristic assigned to an element of the sample space; can be discrete or continuous. Suppose outcome of experiment is continuous value x → f(x) = probability density function (pdf) ...
... Random variables and probability density functions A random variable is a numerical characteristic assigned to an element of the sample space; can be discrete or continuous. Suppose outcome of experiment is continuous value x → f(x) = probability density function (pdf) ...
Bayesian Statistical Methods 1 Running head
... A number of other axioms of probability can be derived from these three basic axioms. Nevertheless, these three can be used to deal with the relatively easy case of the coin flipping example mentioned above. For example, if we toss a fair coin an infinite number of times, we expect it to land heads ...
... A number of other axioms of probability can be derived from these three basic axioms. Nevertheless, these three can be used to deal with the relatively easy case of the coin flipping example mentioned above. For example, if we toss a fair coin an infinite number of times, we expect it to land heads ...
LNCS 8349 - 4-Round Resettably
... respect to an attacker that gets an arbitrary polynomial number of queries to a signing oracle and thus resettable-soundness follows in exactly the same way as the (non-resetting) soundness property. Formalizing this intuition, however, is subtle. CPS first introduce an “oracleaided” model where both ...
... respect to an attacker that gets an arbitrary polynomial number of queries to a signing oracle and thus resettable-soundness follows in exactly the same way as the (non-resetting) soundness property. Formalizing this intuition, however, is subtle. CPS first introduce an “oracleaided” model where both ...
EM Demystified: An Expectation-Maximization
... how likely it is that the complete data is exactly x, that is, calculate the conditional distribution p(x | y, θ(m) ). Step 3: Throw away your guess θ(m) , but keep Step 2’s guess of the probability of the complete data p(x | y, θ(m) ). Step 4: In Step 5 we will make a new guess of θ that maximizes ...
... how likely it is that the complete data is exactly x, that is, calculate the conditional distribution p(x | y, θ(m) ). Step 3: Throw away your guess θ(m) , but keep Step 2’s guess of the probability of the complete data p(x | y, θ(m) ). Step 4: In Step 5 we will make a new guess of θ that maximizes ...
Exercise Problems: Information Theory and Coding
... to an asymptotic limit. That limit can be evaluated by observing that in the limit of small α, the quantity ln(1 + α) approaches α. In this case, setting α = N0PW and allowing W to become arbitrarily large, C approaches the limit NP0 log2 (e). Thus there are vanishing returns from endless increase i ...
... to an asymptotic limit. That limit can be evaluated by observing that in the limit of small α, the quantity ln(1 + α) approaches α. In this case, setting α = N0PW and allowing W to become arbitrarily large, C approaches the limit NP0 log2 (e). Thus there are vanishing returns from endless increase i ...
1 23 Wisdom of crowds versus groupthink: Conor Mayo-Wilson, Kevin Zollman &
... action that currently appears best may fail to find an optimal action because they do not engage in sufficient experimentation. To address this problem, one can modify a greedy strategy by introducing some probabilistic experimentation. For instance, suppose n n∈N is a sequence of probabilities t ...
... action that currently appears best may fail to find an optimal action because they do not engage in sufficient experimentation. To address this problem, one can modify a greedy strategy by introducing some probabilistic experimentation. For instance, suppose n n∈N is a sequence of probabilities t ...
Fair and Efficient Secure Multiparty Computation with Reputation
... security requires that the result of a secure protocol be like the outcome of an ideal execution where an incorruptible trusted party is used to compute the function for all the parties. We remark that if there is no honest majority, then it is impossible to achieve fairness in general [8]. Under th ...
... security requires that the result of a secure protocol be like the outcome of an ideal execution where an incorruptible trusted party is used to compute the function for all the parties. We remark that if there is no honest majority, then it is impossible to achieve fairness in general [8]. Under th ...
Distinguishing Hidden Markov Chains
... that s0 and s1 output the same observation a in the example). This motivates the term hidden. HMCs are widely employed in fields such as speech recognition (see [21] for a tutorial), gesture recognition [6], musical score following [22], signal processing [9], and climate modeling [1]. HMCs are heav ...
... that s0 and s1 output the same observation a in the example). This motivates the term hidden. HMCs are widely employed in fields such as speech recognition (see [21] for a tutorial), gesture recognition [6], musical score following [22], signal processing [9], and climate modeling [1]. HMCs are heav ...
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[pdf]
... to the topic. This notes also provides to the best of my knowledge, the most generalized statement and proof for Symmetrization lemma. I also provides the less famous but geralized proof for Jensen’s inequality and logarithmic sobolev inequality. Refer [2] for a more detailed review of many of these ...
... to the topic. This notes also provides to the best of my knowledge, the most generalized statement and proof for Symmetrization lemma. I also provides the less famous but geralized proof for Jensen’s inequality and logarithmic sobolev inequality. Refer [2] for a more detailed review of many of these ...
Probability interpretations
The word probability has been used in a variety of ways since it was first applied to the mathematical study of games of chance. Does probability measure the real, physical tendency of something to occur or is it a measure of how strongly one believes it will occur, or does it draw on both these elements? In answering such questions, mathematicians interpret the probability values of probability theory.There are two broad categories of probability interpretations which can be called ""physical"" and ""evidential"" probabilities. Physical probabilities, which are also called objective or frequency probabilities, are associated with random physical systems such as roulette wheels, rolling dice and radioactive atoms. In such systems, a given type of event (such as the dice yielding a six) tends to occur at a persistent rate, or ""relative frequency"", in a long run of trials. Physical probabilities either explain, or are invoked to explain, these stable frequencies. Thus talking about physical probability makes sense only when dealing with well defined random experiments. The two main kinds of theory of physical probability are frequentist accounts (such as those of Venn, Reichenbach and von Mises) and propensity accounts (such as those of Popper, Miller, Giere and Fetzer).Evidential probability, also called Bayesian probability (or subjectivist probability), can be assigned to any statement whatsoever, even when no random process is involved, as a way to represent its subjective plausibility, or the degree to which the statement is supported by the available evidence. On most accounts, evidential probabilities are considered to be degrees of belief, defined in terms of dispositions to gamble at certain odds. The four main evidential interpretations are the classical (e.g. Laplace's) interpretation, the subjective interpretation (de Finetti and Savage), the epistemic or inductive interpretation (Ramsey, Cox) and the logical interpretation (Keynes and Carnap).Some interpretations of probability are associated with approaches to statistical inference, including theories of estimation and hypothesis testing. The physical interpretation, for example, is taken by followers of ""frequentist"" statistical methods, such as R. A. Fisher, Jerzy Neyman and Egon Pearson. Statisticians of the opposing Bayesian school typically accept the existence and importance of physical probabilities, but also consider the calculation of evidential probabilities to be both valid and necessary in statistics. This article, however, focuses on the interpretations of probability rather than theories of statistical inference.The terminology of this topic is rather confusing, in part because probabilities are studied within a variety of academic fields. The word ""frequentist"" is especially tricky. To philosophers it refers to a particular theory of physical probability, one that has more or less been abandoned. To scientists, on the other hand, ""frequentist probability"" is just another name for physical (or objective) probability. Those who promote Bayesian inference view ""frequentist statistics"" as an approach to statistical inference that recognises only physical probabilities. Also the word ""objective"", as applied to probability, sometimes means exactly what ""physical"" means here, but is also used of evidential probabilities that are fixed by rational constraints, such as logical and epistemic probabilities.It is unanimously agreed that statistics depends somehow on probability. But, as to what probability is and how it is connected with statistics, there has seldom been such complete disagreement and breakdown of communication since the Tower of Babel. Doubtless, much of the disagreement is merely terminological and would disappear under sufficiently sharp analysis.