THE INVARIANCE APPROACH TO THE PROBABILISTIC ENCODING OF INFORMATION by
... they are based . Probability theory gives a way of reasoning about one state of information in terms of other states of information . The means by which this reasoning is accomplished is Bayes' Rule, a simple formula that is equivalent to the multiplication law for conditional probabilities . Since ...
... they are based . Probability theory gives a way of reasoning about one state of information in terms of other states of information . The means by which this reasoning is accomplished is Bayes' Rule, a simple formula that is equivalent to the multiplication law for conditional probabilities . Since ...
A Tricentenary history of the Law of Large Numbers
... De Moivre’s (1733) result also gives an answer to estimating precision of the relative frequency X/n as an estimate of an unknown p, for given n; or of determining n for given precision (the inverse problem), in frequentist fashion, using the inequality4 p(1 − p) ≤ 1/4. De Moivre’s results appeared ...
... De Moivre’s (1733) result also gives an answer to estimating precision of the relative frequency X/n as an estimate of an unknown p, for given n; or of determining n for given precision (the inverse problem), in frequentist fashion, using the inequality4 p(1 − p) ≤ 1/4. De Moivre’s results appeared ...
Poisson Processes and Applications in Hockey
... a game that lasts at least 60 minutes could potentially have hundreds of goals scored. If events are memoryless then the probability of the next event occurring does not depends on previous events. If scoring in hockey is not memoryless then goals would occur in bunches similar to baseball. We can s ...
... a game that lasts at least 60 minutes could potentially have hundreds of goals scored. If events are memoryless then the probability of the next event occurring does not depends on previous events. If scoring in hockey is not memoryless then goals would occur in bunches similar to baseball. We can s ...
conditional probability - ANU School of Philosophy
... the set of outcomes that we are prepared to countenance. When our model says that the die may land with an outcome from the set {1, 2, 3, 4, 5, 6}, it has already ruled out its landing on an edge, or on a corner, or flying away, or disintegrating, or . . . , so there is a good sense in which it is t ...
... the set of outcomes that we are prepared to countenance. When our model says that the die may land with an outcome from the set {1, 2, 3, 4, 5, 6}, it has already ruled out its landing on an edge, or on a corner, or flying away, or disintegrating, or . . . , so there is a good sense in which it is t ...
Conditioning using conditional expectations: The Borel
... However, for a general A the conditional expectation cannot be given explicitly, its existence is the corollary of the Radon-Nykodim theorem, which is a non-constructive, pure existence theorem. Note also that (24) is not defined for events Ai that have zero probability. For i) can be replaced by an ...
... However, for a general A the conditional expectation cannot be given explicitly, its existence is the corollary of the Radon-Nykodim theorem, which is a non-constructive, pure existence theorem. Note also that (24) is not defined for events Ai that have zero probability. For i) can be replaced by an ...
LNCS 8349 - 4-Round Resettably
... rounds in this protocol. Barak’s Protocol and the BGGL Transformation. Recall that Barak’s protocol relies on the existence of a family of collision-resistant hash function h : {0, 1}∗ → {0, 1}n; note that any such family of collision-resistant hash functions can be implemented from a family of coll ...
... rounds in this protocol. Barak’s Protocol and the BGGL Transformation. Recall that Barak’s protocol relies on the existence of a family of collision-resistant hash function h : {0, 1}∗ → {0, 1}n; note that any such family of collision-resistant hash functions can be implemented from a family of coll ...
Why Simple Hash Functions Work: Exploiting the Entropy in a Data
... that each (new) data item is sufficiently unpredictable given the previous items. This is formalized by Chor and Goldreich’s notion of a block source [CG],1 where we require that the i’th item Xi has at least some k bits of “entropy” conditioned on the previous items X1 , . . . , Xi−1 . There are va ...
... that each (new) data item is sufficiently unpredictable given the previous items. This is formalized by Chor and Goldreich’s notion of a block source [CG],1 where we require that the i’th item Xi has at least some k bits of “entropy” conditioned on the previous items X1 , . . . , Xi−1 . There are va ...
Survival probabilities of weighted random walks
... Proposition 2.12. Unfortunately, an explicit computation of λβ does not seem to be possible easily. 1.3. Related work. Let us briefly summarize some important known results on survival probabilities. For Brownian motion, the survival exponent is easily seen to be θ = 1/2 by the reflection principle. ...
... Proposition 2.12. Unfortunately, an explicit computation of λβ does not seem to be possible easily. 1.3. Related work. Let us briefly summarize some important known results on survival probabilities. For Brownian motion, the survival exponent is easily seen to be θ = 1/2 by the reflection principle. ...
here
... measure on the events in the space, called the agent’s belief type at the state. In such models it is impossible to formalize the counterfactual probabilistic thinking that is essential for rational choice in extensive form games—for example, a player’s assessment of the relative likelihood of conti ...
... measure on the events in the space, called the agent’s belief type at the state. In such models it is impossible to formalize the counterfactual probabilistic thinking that is essential for rational choice in extensive form games—for example, a player’s assessment of the relative likelihood of conti ...
The spacey random walk: a stochastic process for higher-order data
... picks the next state based on a set of transition probabilities, but those transition probabilities evolve as the process continues. A simple example would be a random walk on a graph where the edge traversals are proportional to the amount of time spent at each vertex so far [Diaconis, 1988]. At th ...
... picks the next state based on a set of transition probabilities, but those transition probabilities evolve as the process continues. A simple example would be a random walk on a graph where the edge traversals are proportional to the amount of time spent at each vertex so far [Diaconis, 1988]. At th ...
twin primes
... international mathematics journal in 2003, approaches the twin primes problem from a few different perspectives. MSC: 11-XX (Number Theory) INTRODUCTION Many believe that the twin primes are infinite. In fact, twin primes pairs could easily be found among the integers. There is evidently no region o ...
... international mathematics journal in 2003, approaches the twin primes problem from a few different perspectives. MSC: 11-XX (Number Theory) INTRODUCTION Many believe that the twin primes are infinite. In fact, twin primes pairs could easily be found among the integers. There is evidently no region o ...
Universal Noiseless Coding
... wish to block encode without error to minimize the average One of the surprising results, which will be shown subcodeword length, where the code is not allowed to depend sequently, is that the probabilities of (3) provide codes as on some unknown parameters of the source message probgood asymptotica ...
... wish to block encode without error to minimize the average One of the surprising results, which will be shown subcodeword length, where the code is not allowed to depend sequently, is that the probabilities of (3) provide codes as on some unknown parameters of the source message probgood asymptotica ...
Benchmarking real-valued acts
... maximize the probability to raise enough money and meet her future needs. Let f and β represent the money raised by an investment and the amount needed by Julia, respectively. At this time, both are uncertain quantities that we can view as acts. The payoff f depends on events such as the business cy ...
... maximize the probability to raise enough money and meet her future needs. Let f and β represent the money raised by an investment and the amount needed by Julia, respectively. At this time, both are uncertain quantities that we can view as acts. The payoff f depends on events such as the business cy ...
PSTAT 120B Probability and Statistics - Week 2
... couple notes about hw1 about #3(6.14): uses transformation method. We can begin with CDF to do the transformation, or set the Jacobian and use the transformation formula. carefully compute integral. this type of problem is very IMPORTANT. Same type of problem came up again in hw2 #1. ...
... couple notes about hw1 about #3(6.14): uses transformation method. We can begin with CDF to do the transformation, or set the Jacobian and use the transformation formula. carefully compute integral. this type of problem is very IMPORTANT. Same type of problem came up again in hw2 #1. ...
Infinite monkey theorem
The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare.In this context, ""almost surely"" is a mathematical term with a precise meaning, and the ""monkey"" is not an actual monkey, but a metaphor for an abstract device that produces an endless random sequence of letters and symbols. One of the earliest instances of the use of the ""monkey metaphor"" is that of French mathematician Émile Borel in 1913, but the first instance may be even earlier. The relevance of the theorem is questionable—the probability of a universe full of monkeys typing a complete work such as Shakespeare's Hamlet is so tiny that the chance of it occurring during a period of time hundreds of thousands of orders of magnitude longer than the age of the universe is extremely low (but technically not zero). It should also be noted that real monkeys don't produce uniformly random output, which means that an actual monkey hitting keys for an infinite amount of time has no statistical certainty of ever producing any given text.Variants of the theorem include multiple and even infinitely many typists, and the target text varies between an entire library and a single sentence. The history of these statements can be traced back to Aristotle's On Generation and Corruption and Cicero's De natura deorum (On the Nature of the Gods), through Blaise Pascal and Jonathan Swift, and finally to modern statements with their iconic simians and typewriters. In the early 20th century, Émile Borel and Arthur Eddington used the theorem to illustrate the timescales implicit in the foundations of statistical mechanics.