The Value of Using Imprecise Probabilities in
... precise information about the irreducible uncertainty, shown in Fig. 1共b兲, is defined as imprecision. Other authors use terms such as epistemic uncertainty, ignorance, or reducible uncertainty 关15–17兴 to describe similar aspects of uncertainty. We specifically avoid the terms aleatory and epistemic ...
... precise information about the irreducible uncertainty, shown in Fig. 1共b兲, is defined as imprecision. Other authors use terms such as epistemic uncertainty, ignorance, or reducible uncertainty 关15–17兴 to describe similar aspects of uncertainty. We specifically avoid the terms aleatory and epistemic ...
QUANTITATIVE METHODS IN PSYCHOLOGY On the Probability of
... probability of the obtained outcome but as a conditional probability of the truth of the null hypothesis itself. A common device that promotes this ambiguity is a 2 X 2 table showing the probability of a correct or incorrect decision as a function of (a) the truth or falsehood of the null hypothesis ...
... probability of the obtained outcome but as a conditional probability of the truth of the null hypothesis itself. A common device that promotes this ambiguity is a 2 X 2 table showing the probability of a correct or incorrect decision as a function of (a) the truth or falsehood of the null hypothesis ...
How bad is a 10% chance of losing a toe?
... from 18 to 62 years (median, 34), and only 18% were male. Seven others were removed because they were part of a group that was distinct from other subjects in being both very fast and extremely inconsistent, leaving 109 subjects. The physicians consisted of two subgroups. The 59 members of one subgr ...
... from 18 to 62 years (median, 34), and only 18% were male. Seven others were removed because they were part of a group that was distinct from other subjects in being both very fast and extremely inconsistent, leaving 109 subjects. The physicians consisted of two subgroups. The 59 members of one subgr ...
Subjective multi-prior probability: A representation of a partial
... processes carried out by many organizations. For instance, the US intelligence community produces National Intelligence Estimates, in which the likelihood of various events is assessed. Questions such as, ‘Is it more likely that democracy will prevail in Libya, or that a military regime will be esta ...
... processes carried out by many organizations. For instance, the US intelligence community produces National Intelligence Estimates, in which the likelihood of various events is assessed. Questions such as, ‘Is it more likely that democracy will prevail in Libya, or that a military regime will be esta ...
Abstract The language and constructions of category theory have
... this particular case, we can easily count the probabilities of individual events, but as we will see in the next example, probabilities are most naturally assigned to collections of events rather than individual events. Not all random variables can be fully described by considering the probabilities ...
... this particular case, we can easily count the probabilities of individual events, but as we will see in the next example, probabilities are most naturally assigned to collections of events rather than individual events. Not all random variables can be fully described by considering the probabilities ...
Coherent conditional probabilities and proper scoring rules
... and, as proved in [14, 15] (see also [18]), is equivalent to the notion of coherence for conditional probability assessments studied by other authors; see e.g. [8, 22, 30, 34, 35]. In order to unify the treatment of unconditional and conditional events, the definition of coherence given by de Finett ...
... and, as proved in [14, 15] (see also [18]), is equivalent to the notion of coherence for conditional probability assessments studied by other authors; see e.g. [8, 22, 30, 34, 35]. In order to unify the treatment of unconditional and conditional events, the definition of coherence given by de Finett ...
Descriptive Assessment of Jeffrey’s Rule Jiaying Zhao () Daniel Osherson ()
... (3) is known as “Jeffrey’s rule.” It shows how change in the probability of B is propagated to G, without experience directly affecting G. It is straightforward to generalize (3) to finer partitions, in place of the binary partition B, B. Assuming invariance, it is easy to show that (3) defines a ge ...
... (3) is known as “Jeffrey’s rule.” It shows how change in the probability of B is propagated to G, without experience directly affecting G. It is straightforward to generalize (3) to finer partitions, in place of the binary partition B, B. Assuming invariance, it is easy to show that (3) defines a ge ...
Hypothesis Testing: Methodology and Limitations
... calculate the probability that, if the hypothesis holds, the test statistic will assume a value equal to or larger than the value actually observed. The idea of testing was further codified and elaborated in the first decades of the twentieth century, mainly by R. A. Fisher (e.g., 1925). In his sign ...
... calculate the probability that, if the hypothesis holds, the test statistic will assume a value equal to or larger than the value actually observed. The idea of testing was further codified and elaborated in the first decades of the twentieth century, mainly by R. A. Fisher (e.g., 1925). In his sign ...
Relevant Explanations: Allowing Disjunctive Assignments
... ally, Jack may have used any one of 99 different meth ods (such as walking, taking a bus, etc.), all equally likely given that Jack intended to get to the tracks, for the sake of this example. The method variable is represented by a node with 100 possible values, one for each method, and one for no ...
... ally, Jack may have used any one of 99 different meth ods (such as walking, taking a bus, etc.), all equally likely given that Jack intended to get to the tracks, for the sake of this example. The method variable is represented by a node with 100 possible values, one for each method, and one for no ...
A New Foundation for Support Theory
... In the New Foundation, a description α of a probabilistic event is assumed to give rise to a cognitive representation A. The probabilistic estimate for α is the result of weighing the evidence in favor of A against the evidence against A. It is assumed that the participant measures the evidence in f ...
... In the New Foundation, a description α of a probabilistic event is assumed to give rise to a cognitive representation A. The probabilistic estimate for α is the result of weighing the evidence in favor of A against the evidence against A. It is assumed that the participant measures the evidence in f ...
Bayesian Networks
... What would you do? In other words what are the probabilities P(A|NA,C ) and P(B|NA,C )? ...
... What would you do? In other words what are the probabilities P(A|NA,C ) and P(B|NA,C )? ...
Test Martingales, Bayes Factors and p-Values
... test martingales and emphasized their betting interpretation. As we have explained, a test martingale under P is the capital process for a betting strategy that starts with a unit capital and bets at rates given by P , risking only the capital with which it begins. Such a strategy is an obvious way ...
... test martingales and emphasized their betting interpretation. As we have explained, a test martingale under P is the capital process for a betting strategy that starts with a unit capital and bets at rates given by P , risking only the capital with which it begins. Such a strategy is an obvious way ...
Transcription
... Complete ten trials where you choose two cubes, without replacing the first one, and record the number of times where each combination of colors is chosen using tally marks. Place tally marks under the column labeled “Tallies.” What did we create by recording all of our data in the table? A frequenc ...
... Complete ten trials where you choose two cubes, without replacing the first one, and record the number of times where each combination of colors is chosen using tally marks. Place tally marks under the column labeled “Tallies.” What did we create by recording all of our data in the table? A frequenc ...
Introduction to Probability Theory 1
... to consist of all outcomes that are either in E or in F or in both E and F . That is, the event E ∪ F will occur if either E or F occurs. For example, in (1) if E = {H } and F = {T }, then E ∪ F = {H, T } That is, E ∪ F would be the whole sample space S. In (2) if E = {1, 3, 5} and F = {1, 2, 3}, th ...
... to consist of all outcomes that are either in E or in F or in both E and F . That is, the event E ∪ F will occur if either E or F occurs. For example, in (1) if E = {H } and F = {T }, then E ∪ F = {H, T } That is, E ∪ F would be the whole sample space S. In (2) if E = {1, 3, 5} and F = {1, 2, 3}, th ...
1986 - Quantitative Analysis of Analogy by Similarity
... at hand, i.e., we have no idea which of the known facts might be relevant, the theory does not apply. However, it still seems plausible that the most similar source is the best analogue. What has been lacking in previous theories of analogy by similarity is any attempt to justify this assumption; th ...
... at hand, i.e., we have no idea which of the known facts might be relevant, the theory does not apply. However, it still seems plausible that the most similar source is the best analogue. What has been lacking in previous theories of analogy by similarity is any attempt to justify this assumption; th ...
Uncertainty171
... There is always some atomic event true. if some atomic event is true, then all other other atomic events are false. Hence, there is exactly 1 atomic event true. ...
... There is always some atomic event true. if some atomic event is true, then all other other atomic events are false. Hence, there is exactly 1 atomic event true. ...
Continued misinterpretation of confidence intervals
... generates confidence intervals, and is said to have a confidence coefficient of X % if, in repeated sampling, X % of intervals would contain the true parameter value for all values of the true value (Neyman, 1937). The idea of a confidence procedure is conceptually very clear. The confidence coeffic ...
... generates confidence intervals, and is said to have a confidence coefficient of X % if, in repeated sampling, X % of intervals would contain the true parameter value for all values of the true value (Neyman, 1937). The idea of a confidence procedure is conceptually very clear. The confidence coeffic ...
Probability and Information Theory
... a person is from Germany given that they speak German is quite high, but if a randomly selected person is taught to speak German, their country of origin does not change. Computing the consequences of an action is called making an intervention query. Intervention queries are the domain of causal mod ...
... a person is from Germany given that they speak German is quite high, but if a randomly selected person is taught to speak German, their country of origin does not change. Computing the consequences of an action is called making an intervention query. Intervention queries are the domain of causal mod ...
Bayes` Rule With Python - James V Stone
... explanation of Bayes’ rule, using plausible and accessible examples. It is written specifically for readers who have little mathematical experience, but who are nevertheless willing to acquire the required mathematics on a ‘need to know’ basis. Lecturers (and authors) like to teach using a top-down ...
... explanation of Bayes’ rule, using plausible and accessible examples. It is written specifically for readers who have little mathematical experience, but who are nevertheless willing to acquire the required mathematics on a ‘need to know’ basis. Lecturers (and authors) like to teach using a top-down ...
Response
... Background: Some probability statements: Probability of randomly chosen card a heart is 0.25 Probability of randomly chosen student in a class getting A is 0.25, according to the professor. Probability of candidate being elected, according to an editorial, is 0.25. Question: Are these probabil ...
... Background: Some probability statements: Probability of randomly chosen card a heart is 0.25 Probability of randomly chosen student in a class getting A is 0.25, according to the professor. Probability of candidate being elected, according to an editorial, is 0.25. Question: Are these probabil ...
Bayes` Rule With R - James V Stone
... explanation of Bayes’ rule, using plausible and accessible examples. It is written specifically for readers who have little mathematical experience, but who are nevertheless willing to acquire the required mathematics on a ‘need to know’ basis. Lecturers (and authors) like to teach using a top-down ...
... explanation of Bayes’ rule, using plausible and accessible examples. It is written specifically for readers who have little mathematical experience, but who are nevertheless willing to acquire the required mathematics on a ‘need to know’ basis. Lecturers (and authors) like to teach using a top-down ...
probability, logic, and probability logic
... probability becomes a kind of modality. For objective interpretations such as the frequency and propensity theories, probability theory can be regarded as providing the logic of ‘chance’. By the lights of the subjective (Bayesian) interpretation, probability can be thought of as the logic of partial ...
... probability becomes a kind of modality. For objective interpretations such as the frequency and propensity theories, probability theory can be regarded as providing the logic of ‘chance’. By the lights of the subjective (Bayesian) interpretation, probability can be thought of as the logic of partial ...
On the Triviality of High-Order Probabilistic Beliefs
... richer than the one required to describe non-quantitative beliefs. Still, propositional modal logic suffices for this. The same alphabet described in the previous subsection is used, except that instead of the single modal operator B, there are now infinitely many modal operators, B p , one for each ...
... richer than the one required to describe non-quantitative beliefs. Still, propositional modal logic suffices for this. The same alphabet described in the previous subsection is used, except that instead of the single modal operator B, there are now infinitely many modal operators, B p , one for each ...
Bayes` Rule - James V Stone - The University of Sheffield
... This introductory text is intended to provide a straightforward explanation of Bayes’ rule, using plausible and accessible examples. It is written specifically for readers who have little mathematical experience, but who are nevertheless willing to acquire the required mathematics on a ‘need to know ...
... This introductory text is intended to provide a straightforward explanation of Bayes’ rule, using plausible and accessible examples. It is written specifically for readers who have little mathematical experience, but who are nevertheless willing to acquire the required mathematics on a ‘need to know ...
Declarations of Independence
... Nor is the problem limited to uncountable, or even infinite domains. Finite probability models can contain propositions that receive zero probability. While all contradictions must have zero probability, the converse is not true—even in finite spaces. For instance, rational agents (who may have cred ...
... Nor is the problem limited to uncountable, or even infinite domains. Finite probability models can contain propositions that receive zero probability. While all contradictions must have zero probability, the converse is not true—even in finite spaces. For instance, rational agents (who may have cred ...
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.