Compound Probability March 10, 2014
... 6. In the Seattle Mariners’ historical 2001 season, Edgar Martinez batted 0.306 (meaning 30.6% of the times he was at the plate he got a hit), Ichiro Suzuki batted 0.350, and Bret Boone batted 0.331. If these three players were to each come up to bat one more time, what is the probability that none ...
... 6. In the Seattle Mariners’ historical 2001 season, Edgar Martinez batted 0.306 (meaning 30.6% of the times he was at the plate he got a hit), Ichiro Suzuki batted 0.350, and Bret Boone batted 0.331. If these three players were to each come up to bat one more time, what is the probability that none ...
6 The Basic Rules of Probability
... Now E is logically equivalent to the occurrence of E with something that is sure to happen. Hence, Pr([sure event] & E) Pr(E). Pr([sure event/E]) [Pr(E)] / [Pr(E)] ...
... Now E is logically equivalent to the occurrence of E with something that is sure to happen. Hence, Pr([sure event] & E) Pr(E). Pr([sure event/E]) [Pr(E)] / [Pr(E)] ...
Context-specific approximation in probabilistic inference
... wouldn't expect that the conditional probability of the child would not be affected very much for all values of its other parents. It seems more plausible that in some contexts the value of the parent doesn't make much difference. The general idea is to simplify the network, by ignoring distinctions ...
... wouldn't expect that the conditional probability of the child would not be affected very much for all values of its other parents. It seems more plausible that in some contexts the value of the parent doesn't make much difference. The general idea is to simplify the network, by ignoring distinctions ...
Rational Expectations and Ambiguity: A Comment on Abel
... a decision maker’s belief puts some weight (measured by the degree of optimism λ) on the best consequence as well as some weight (measured by the degree of pessimism γ = 1 − λ) on the worst consequence possible. In the context of Abel’s model, we interpret this additive probability distribution π as ...
... a decision maker’s belief puts some weight (measured by the degree of optimism λ) on the best consequence as well as some weight (measured by the degree of pessimism γ = 1 − λ) on the worst consequence possible. In the context of Abel’s model, we interpret this additive probability distribution π as ...
Targil 10
... 1. Prove that for any 0 < p < 1, and integers m, n > 1, (1 – pn)m + (1 – (1 – p)m)n > 1. Solution. Consider a m n table – it has n rows, m columns. In every cell, we write 1 with probability p, and 0 with probability 1 – p. So, a probability that a given column row doesn't consists of ones is 1 – pn ...
... 1. Prove that for any 0 < p < 1, and integers m, n > 1, (1 – pn)m + (1 – (1 – p)m)n > 1. Solution. Consider a m n table – it has n rows, m columns. In every cell, we write 1 with probability p, and 0 with probability 1 – p. So, a probability that a given column row doesn't consists of ones is 1 – pn ...
Binomial Distribution
... The following example illustrates a problem that is not binomial. It violates the condition of independence. ABC College has a student advisory committee made up of 10 staff members and 6 students. The committee wishes to choose a chairperson and a recorder. What is the probability that the chairper ...
... The following example illustrates a problem that is not binomial. It violates the condition of independence. ABC College has a student advisory committee made up of 10 staff members and 6 students. The committee wishes to choose a chairperson and a recorder. What is the probability that the chairper ...
Five Useful Properties of Probabilistic Knowledge Representations
... in probabilistic models. Each of these methods is fairly well understood theoretically and has been practically implemented. While I would like to direct interested readers to our paper for a comprehensive treatment of the issue of relevance in probabilistic models, I will give a avor of these met ...
... in probabilistic models. Each of these methods is fairly well understood theoretically and has been practically implemented. While I would like to direct interested readers to our paper for a comprehensive treatment of the issue of relevance in probabilistic models, I will give a avor of these met ...
Think-Tac-Toe: Probability
... Overview: These Think-Tac-Toe options allow students to choose their own ways of showing what they have come to know and understand about probability and its applications in the real world. The tasks are structured to address student interest and personal choice. Students may choose any three option ...
... Overview: These Think-Tac-Toe options allow students to choose their own ways of showing what they have come to know and understand about probability and its applications in the real world. The tasks are structured to address student interest and personal choice. Students may choose any three option ...
Chinese-Whispers-Bas.. - Bayes
... The distinction between probability and proportion is an example of a more general distinction Consider a respiratory treatment where response is increase in FEV1 from baseline There is variability in patient responses They form a distribution (not a probability distribution) There is uncertainty ab ...
... The distinction between probability and proportion is an example of a more general distinction Consider a respiratory treatment where response is increase in FEV1 from baseline There is variability in patient responses They form a distribution (not a probability distribution) There is uncertainty ab ...
Powerpoint 9.1 Significance Tests -- The Basics
... a) Explain what it means for the null hypothesis to be true in this setting. In this setting, H0: σ = 15 means that the true standard deviation with the new 7-iron is 15 yards. That is, Mike is equally consistent with the new and old 7-iron. b) Interpret the P-value in context. The P-value is the ...
... a) Explain what it means for the null hypothesis to be true in this setting. In this setting, H0: σ = 15 means that the true standard deviation with the new 7-iron is 15 yards. That is, Mike is equally consistent with the new and old 7-iron. b) Interpret the P-value in context. The P-value is the ...
Analysis of State Transitions
... Now we have our two-state model, we are ready to investigate how this model is used by actuaries in practice. We’ll start from our example of a product that requires policyholders to pay regular premiums when they are alive and then provides a one-off payment when the policyholder dies. ...
... Now we have our two-state model, we are ready to investigate how this model is used by actuaries in practice. We’ll start from our example of a product that requires policyholders to pay regular premiums when they are alive and then provides a one-off payment when the policyholder dies. ...
Chapter 5 Confidence Intervals and Hypothesis Testing
... (*Bstr; Bolinger, 1962; Müller, 1997). For example, pepper and salt violates this constraint against ultimate-syllable stress, but its alternate salt and pepper does not. We can construct a simple probabilistic model of the role of *Bstr in binomial ordering preferences by assuming that every time ...
... (*Bstr; Bolinger, 1962; Müller, 1997). For example, pepper and salt violates this constraint against ultimate-syllable stress, but its alternate salt and pepper does not. We can construct a simple probabilistic model of the role of *Bstr in binomial ordering preferences by assuming that every time ...
here
... The set {1, …, n} could represent a partition of a larger space (the ‘hidden parameters’), but what these integers represent is not relevant to the argument; in our proofs, they function simply as an index set. We can think of the members of R as also indexed by these integers, in a corresponding fa ...
... The set {1, …, n} could represent a partition of a larger space (the ‘hidden parameters’), but what these integers represent is not relevant to the argument; in our proofs, they function simply as an index set. We can think of the members of R as also indexed by these integers, in a corresponding fa ...
Lecture 3
... So what’s the problem? • An obvious conclusion is that induction should be used with a certain measure of common sense. • The problem with common sense is that it is impossible (?) to formalize it. • If that is so, it seems impossible to give an algorithmic description of scientific procedure (usin ...
... So what’s the problem? • An obvious conclusion is that induction should be used with a certain measure of common sense. • The problem with common sense is that it is impossible (?) to formalize it. • If that is so, it seems impossible to give an algorithmic description of scientific procedure (usin ...
A Review on `Probability and Stochastic Processes`
... important concept in theory and application in finance and for stochastic integration and partial differential equations. These are topics the book touches at the end. The study of Brownian motion is rather brief and does not contain the deep and important aspects that it plays in practical applicat ...
... important concept in theory and application in finance and for stochastic integration and partial differential equations. These are topics the book touches at the end. The study of Brownian motion is rather brief and does not contain the deep and important aspects that it plays in practical applicat ...
Slide 14 - Haiku Learning
... know what outcomes could happen, but we don’t know which particular outcome did or will happen. In general, each occasion upon which we observe a random phenomenon is called a trial. At each trial, we note the value of the random phenomenon, and call it an outcome. When we combine outcomes, the resu ...
... know what outcomes could happen, but we don’t know which particular outcome did or will happen. In general, each occasion upon which we observe a random phenomenon is called a trial. At each trial, we note the value of the random phenomenon, and call it an outcome. When we combine outcomes, the resu ...
Sigmund Freud was born in the year:
... GENERAL KNOWLEDGE QUIZ Answer the following general knowledge to the best of your ability. Circle your correct answer as a or b. Indicate your level of confidence that your answer is correct in percentage terms next to the probability line. ...
... GENERAL KNOWLEDGE QUIZ Answer the following general knowledge to the best of your ability. Circle your correct answer as a or b. Indicate your level of confidence that your answer is correct in percentage terms next to the probability line. ...
Bayesian and frequentist approaches
... the probabilities of such half-open intervals uniquely determine the complete probability distribution on the line. In practice, only a few values are ever made, such as choosing prior as a Cauchy density with median and first quartile specified. Clearly, the effect of features of the prior that wer ...
... the probabilities of such half-open intervals uniquely determine the complete probability distribution on the line. In practice, only a few values are ever made, such as choosing prior as a Cauchy density with median and first quartile specified. Clearly, the effect of features of the prior that wer ...
The consequences of understanding expert probability reporting as
... identifying (relative) frequency with belief, precisely because one may run into kinds of complications outlined above. It follows from the above that personal probabilities are at least as informed, in terms of data, as other types of probabilities. This is an important message because one frequent ...
... identifying (relative) frequency with belief, precisely because one may run into kinds of complications outlined above. It follows from the above that personal probabilities are at least as informed, in terms of data, as other types of probabilities. This is an important message because one frequent ...
Bayesian Networks without Tears
... why we want the evidence blocking restricpossible for two variables to be independent tion. This restriction is what says that once of each other given E but dependent given E we know about a middle node, we do not ∪ {f} and vise versa (they may be dependent need to know about anything further away. ...
... why we want the evidence blocking restricpossible for two variables to be independent tion. This restriction is what says that once of each other given E but dependent given E we know about a middle node, we do not ∪ {f} and vise versa (they may be dependent need to know about anything further away. ...
The Metaphysics of Chance
... • The notion of probability, or chance, shows up in almost every science. – According to statistical mechanics, the entropy of any closed system will increase with very high probability. – According to quantum mechanics, there are particles in states such that, if you were to observe their x-spin, t ...
... • The notion of probability, or chance, shows up in almost every science. – According to statistical mechanics, the entropy of any closed system will increase with very high probability. – According to quantum mechanics, there are particles in states such that, if you were to observe their x-spin, t ...
Uniform Laws of Large Numbers
... I am glad you asked! The Laws of Large Numbers, or LLNs for short, come in three basic flavors: Weak, Strong and Uniform. They all state that the observed frequencies of events tend to approach the actual probabilities as the number of observations increases. Saying it in another way, the LLNs show ...
... I am glad you asked! The Laws of Large Numbers, or LLNs for short, come in three basic flavors: Weak, Strong and Uniform. They all state that the observed frequencies of events tend to approach the actual probabilities as the number of observations increases. Saying it in another way, the LLNs show ...
Bayesian Networks without Tears
... why we want the evidence blocking restricpossible for two variables to be independent tion. This restriction is what says that once of each other given E but dependent given E we know about a middle node, we do not ∪ {f} and vise versa (they may be dependent need to know about anything further away. ...
... why we want the evidence blocking restricpossible for two variables to be independent tion. This restriction is what says that once of each other given E but dependent given E we know about a middle node, we do not ∪ {f} and vise versa (they may be dependent need to know about anything further away. ...
Document
... Dubois proved that the only numerical counterparts of comparative possibility are possibility measures. The significance of this is that a comparative relation on 2U describing the location of an unknown variable x induces a complete preordering on U that can be viewed as a preference relation on th ...
... Dubois proved that the only numerical counterparts of comparative possibility are possibility measures. The significance of this is that a comparative relation on 2U describing the location of an unknown variable x induces a complete preordering on U that can be viewed as a preference relation on th ...
Dempster–Shafer theory
The theory of belief functions, also referred to as evidence theory or Dempster–Shafer theory (DST), is a general framework for reasoning with uncertainty, with understood connections to other frameworks such as probability, possibility and imprecise probability theories. First introduced by Arthur P. Dempster in the context of statistical inference, the theory was later developed by Glenn Shafer into a general framework for modeling epistemic uncertainty - a mathematical theory of evidence. The theory allows one to combine evidence from different sources and arrive at a degree of belief (represented by a mathematical object called belief function) that takes into account all the available evidence.In a narrow sense, the term Dempster–Shafer theory refers to the original conception of the theory by Dempster and Shafer. However, it is more common to use the term in the wider sense of the same general approach, as adapted to specific kinds of situations. In particular, many authors have proposed different rules for combining evidence, often with a view to handling conflicts in evidence better. The early contributions have also been the starting points of many important developments, including the Transferable Belief Model and the Theory of Hints.