slides - John L. Pollock
... » formulated using free variables - prob(Fx/Gx) – need a theory of “direct inference” » The basic idea is that if we want to know the definite probability PROB(Fa), we look for the narrowest reference class (or strongest reference property) G such that we know the indefinite probability prob(Fx/Gx) ...
... » formulated using free variables - prob(Fx/Gx) – need a theory of “direct inference” » The basic idea is that if we want to know the definite probability PROB(Fa), we look for the narrowest reference class (or strongest reference property) G such that we know the indefinite probability prob(Fx/Gx) ...
doc - John L. Pollock
... S. Peirce was perhaps the first to make a suggestion of this sort. Similarly, the statistician R. A. Fisher, regarded by many as “the father of modern statistics”, identified probabilities with ratios in a “hypothetical infinite population, of which the actual data is regarded as constituting a rand ...
... S. Peirce was perhaps the first to make a suggestion of this sort. Similarly, the statistician R. A. Fisher, regarded by many as “the father of modern statistics”, identified probabilities with ratios in a “hypothetical infinite population, of which the actual data is regarded as constituting a rand ...
Comparative Value and the Weight of Reasons
... who wishes to aggregate the preferences, values, or judgments of different people, is quite complicated. A central issue is that reasons can conflict in different ways. Scanlon (1998) explains this point, writing, Desires can conflict in a practical sense by giving incompatible directives for action ...
... who wishes to aggregate the preferences, values, or judgments of different people, is quite complicated. A central issue is that reasons can conflict in different ways. Scanlon (1998) explains this point, writing, Desires can conflict in a practical sense by giving incompatible directives for action ...
De Finetti on uncertainty - Oxford Academic
... Singell, 1987), because probability is not an objective attribute of external events, but a property of the way individuals think about them. But as we will see, it can equally be argued that Knight’s estimates do not necessarily coincide with subjective probabilities even from an epistemic viewpoin ...
... Singell, 1987), because probability is not an objective attribute of external events, but a property of the way individuals think about them. But as we will see, it can equally be argued that Knight’s estimates do not necessarily coincide with subjective probabilities even from an epistemic viewpoin ...
Using Prospect Theory to Analyze New Risks
... to YA and PA, but then assume more pessimistic weighting for A than for K— Eqs. 3.3 and 3.4 implicitly assumed identical weightings. The probabilities 0.5 of YA and PA are subjective. The decision maker would adopt them as objective probabilities if he were ambiguity neutral, and so we call these su ...
... to YA and PA, but then assume more pessimistic weighting for A than for K— Eqs. 3.3 and 3.4 implicitly assumed identical weightings. The probabilities 0.5 of YA and PA are subjective. The decision maker would adopt them as objective probabilities if he were ambiguity neutral, and so we call these su ...
probability, logic, and probability logic
... As well as giving a (hypothetical) limiting relative frequency interpretation of probabilities of events, Reichenbach [45] gives an interpretation in terms of truth frequencies: the probability of truth of a statement of a certain type is the limiting relative frequency of statements of that type be ...
... As well as giving a (hypothetical) limiting relative frequency interpretation of probabilities of events, Reichenbach [45] gives an interpretation in terms of truth frequencies: the probability of truth of a statement of a certain type is the limiting relative frequency of statements of that type be ...
Why do we change whatever amount we found in the first
... It can be envisaged, however, that the sums in the two envelopes are not limited. This requires a more careful mathematical analysis, and also uncovers other possible interpretations of the problem. If, for example, the smaller of the two sums of money is considered equally likely to be one of infin ...
... It can be envisaged, however, that the sums in the two envelopes are not limited. This requires a more careful mathematical analysis, and also uncovers other possible interpretations of the problem. If, for example, the smaller of the two sums of money is considered equally likely to be one of infin ...
Stochastic Search and Surveillance Strategies for
... Kurt Plarre for his help in the sensor selection project. I thank Prof Jeff Moehlis for his encouragement, help, and support in the bifurcations project. I thank Prof Cédric Langbort and Prof Ruggero Carli for all the helpful discussions and their encouragement during the attention allocation proje ...
... Kurt Plarre for his help in the sensor selection project. I thank Prof Jeff Moehlis for his encouragement, help, and support in the bifurcations project. I thank Prof Cédric Langbort and Prof Ruggero Carli for all the helpful discussions and their encouragement during the attention allocation proje ...
Efficient Dynamic Allocation with Strategic Arrivals
... 2. The planner may not be aware of the nature of the arrival process, which allows here for correlations in arrival times. Thus, the planner is able to learn about future arrivals (and thus about future demand) from past arrivals. 3. Since our agents can optimally choose their arrival time, they wil ...
... 2. The planner may not be aware of the nature of the arrival process, which allows here for correlations in arrival times. Thus, the planner is able to learn about future arrivals (and thus about future demand) from past arrivals. 3. Since our agents can optimally choose their arrival time, they wil ...
BAYESIAN AND DOMINANT STRATEGY IMPLEMENTATION IN
... A direct mechanism consists of two maps per agent, a probability-of-trade function and a transfer function. Every agent, after observing her valuation, sends a report to the mechanism designer. Given the profile of reported valuations, the probability-of-trade function specifies the probability that ...
... A direct mechanism consists of two maps per agent, a probability-of-trade function and a transfer function. Every agent, after observing her valuation, sends a report to the mechanism designer. Given the profile of reported valuations, the probability-of-trade function specifies the probability that ...
Interpretations of Probability.pdf
... conceptual possibility. For example, suppose that we interpret ‘P’ as the truth function: it assigns the value 1 to all true sentences, and 0 to all false sentences. Then trivially, all the axioms come out true, so this interpretation is admissible. We would hardly count it as an adequate interpreta ...
... conceptual possibility. For example, suppose that we interpret ‘P’ as the truth function: it assigns the value 1 to all true sentences, and 0 to all false sentences. Then trivially, all the axioms come out true, so this interpretation is admissible. We would hardly count it as an adequate interpreta ...
2. Criteria of adequacy for the interpretations of
... probabilistic; but artificial examples aside, it is doubtful that the case ever arises. For example, we have a considerable fund of evidence on coin tossing from the results of our own experiments, the testimony of others, our knowledge of some of the relevant physics, and so on. In the second case, ...
... probabilistic; but artificial examples aside, it is doubtful that the case ever arises. For example, we have a considerable fund of evidence on coin tossing from the results of our own experiments, the testimony of others, our knowledge of some of the relevant physics, and so on. In the second case, ...
The Laws of Probability and the Law of the Land
... ,1Cohen's arguments as to the difficulty of quantifying the burden of persuasion in civil cases are considered in more detail in Kaye, The Paradox of the Gatecrasherand Other Stories, 1979 ARIz. ST. L.J. 101. The analysis in Lempert, supra note 6, implicitly helps resolve some of the other "anomalie ...
... ,1Cohen's arguments as to the difficulty of quantifying the burden of persuasion in civil cases are considered in more detail in Kaye, The Paradox of the Gatecrasherand Other Stories, 1979 ARIz. ST. L.J. 101. The analysis in Lempert, supra note 6, implicitly helps resolve some of the other "anomalie ...
Cross-Layer Optimization in TCP/IP networks - Netlab
... Here are our main results. In the case of pure dynamic routing, i.e., when link costs are the congestion prices generated by TCP–AQM, it turns out that we can interpret TCP/IP as a distributed primal-dual algorithm to maximize aggregate utility over both source rates (by TCP–AQM) and routes (by IP), ...
... Here are our main results. In the case of pure dynamic routing, i.e., when link costs are the congestion prices generated by TCP–AQM, it turns out that we can interpret TCP/IP as a distributed primal-dual algorithm to maximize aggregate utility over both source rates (by TCP–AQM) and routes (by IP), ...
Membership Functions and Probability Measures of Fuzzy Sets
... outcomes of a random phenomenon, but not about the uncertainty of classification (or the placement of an outcome in a given class), Zadeh (1986b) has claimed that “probability lacks sufficient expressiveness to deal with uncertainty in natural language.” In contrast, fuzzy set theory prescribes a ca ...
... outcomes of a random phenomenon, but not about the uncertainty of classification (or the placement of an outcome in a given class), Zadeh (1986b) has claimed that “probability lacks sufficient expressiveness to deal with uncertainty in natural language.” In contrast, fuzzy set theory prescribes a ca ...
Does Deliberation Crowd Out Prediction?
... connection between the two might not be very tight. This would make it possible for some probability assignments not to have any direct behavioural manifestations in betting dispositions. Still, to understand their arguments, we should concede to the supporters of the strong thesis this connection b ...
... connection between the two might not be very tight. This would make it possible for some probability assignments not to have any direct behavioural manifestations in betting dispositions. Still, to understand their arguments, we should concede to the supporters of the strong thesis this connection b ...
SOME NEW RESULTS IN THE KOLMOGOROV
... finite sequences determine the pair P t T since the measure of the atoms of yinT{P is determined. The Birkhoff ergodic theorem implies that if we look at a process long enough each fixed string of letters will occur with a fixed frequency. If T is ergodic (the only invariant sets have measure 0 or 1 ...
... finite sequences determine the pair P t T since the measure of the atoms of yinT{P is determined. The Birkhoff ergodic theorem implies that if we look at a process long enough each fixed string of letters will occur with a fixed frequency. If T is ergodic (the only invariant sets have measure 0 or 1 ...
Dual characterization of properties of risk measures on Orlicz hearts
... hearts. Then we give general conditions for monetary risk measures to be Gâteaux-differentiable, strictly monotone with respect to almost sure inequality, strictly convex modulo translation, strictly convex modulo comonotonicity, or monotone with respect to different stochastic orders. The theoreti ...
... hearts. Then we give general conditions for monetary risk measures to be Gâteaux-differentiable, strictly monotone with respect to almost sure inequality, strictly convex modulo translation, strictly convex modulo comonotonicity, or monotone with respect to different stochastic orders. The theoreti ...
MMPC Chapter 4
... standard deviation = 20. The lead time is 2 weeks and inventory replenishments are ordered weekly. a) If S = 220 and your inventory = 100 with 85 desks on order, how many desks will you order? (35) b) Suppose S = 220 and you are about to place an order and your inventory level – 160 with 65 desks on ...
... standard deviation = 20. The lead time is 2 weeks and inventory replenishments are ordered weekly. a) If S = 220 and your inventory = 100 with 85 desks on order, how many desks will you order? (35) b) Suppose S = 220 and you are about to place an order and your inventory level – 160 with 65 desks on ...
When Fully Informed States Make Good the Threat of War: Rational
... and Robinson changes in the cost of challenging the elite in power creates an incentive for the elite to renege on its promises when the cost of challenge is high.5 Revolutionary movements therefore have an incentive to challenge the elite when the cost of doing so is low. In a more recent analysis, ...
... and Robinson changes in the cost of challenging the elite in power creates an incentive for the elite to renege on its promises when the cost of challenge is high.5 Revolutionary movements therefore have an incentive to challenge the elite when the cost of doing so is low. In a more recent analysis, ...
On Individual Risk
... mathematical theory of counting. Since the focus is on the specific outcome of (say) a particular deal of cards or roll of a die, this classical conception is individualist. But questions as to the interpretation of the “probabilities” computed rarely raise their heads. If they do, it would typicall ...
... mathematical theory of counting. Since the focus is on the specific outcome of (say) a particular deal of cards or roll of a die, this classical conception is individualist. But questions as to the interpretation of the “probabilities” computed rarely raise their heads. If they do, it would typicall ...
Bruno de Finetti and Imprecision
... This paper pointed out what became an important research topic, concerning existence of agreeing or almost agreeing probabilities for comparative probability orderings. (See [18] for an excellent review.) The ideas expressed in [12] were not substantially modified in later writings. For instance, in ...
... This paper pointed out what became an important research topic, concerning existence of agreeing or almost agreeing probabilities for comparative probability orderings. (See [18] for an excellent review.) The ideas expressed in [12] were not substantially modified in later writings. For instance, in ...
When and why do people avoid unknown probabilities in decisions
... decision making in uncertain situations (Kahneman, Slovic & Tversky, 1982; Gigerenzer, 1996; Gigerenzer & Goldstein, 1996; Kahneman & Tversky, 1996). In this debate, one of the most prominent demonstrations of allegedly irrational decision making has been the ambiguity effect. This occurs when peopl ...
... decision making in uncertain situations (Kahneman, Slovic & Tversky, 1982; Gigerenzer, 1996; Gigerenzer & Goldstein, 1996; Kahneman & Tversky, 1996). In this debate, one of the most prominent demonstrations of allegedly irrational decision making has been the ambiguity effect. This occurs when peopl ...
Benchmarking real-valued acts
... the probability P (f β) that it meets her retirements needs, she needs to expand the set S to a larger set Ω. This example illustrates the following general ranking procedure. Given a set F of acts on a state space S, construct a benchmark β defined on a larger set Ω and a probability measure P on ...
... the probability P (f β) that it meets her retirements needs, she needs to expand the set S to a larger set Ω. This example illustrates the following general ranking procedure. Given a set F of acts on a state space S, construct a benchmark β defined on a larger set Ω and a probability measure P on ...
Probabilistic thinking and probability literacy in the context of risk
... personal feelings (such as risk aversion) should always be supported by defensible reasons. Again, mathematical competencies play neither an obvious nor a substantial role in Gal’s model of probabilistic literacy. Beyond, little is published on an explicit description of probabilistic thinking and t ...
... personal feelings (such as risk aversion) should always be supported by defensible reasons. Again, mathematical competencies play neither an obvious nor a substantial role in Gal’s model of probabilistic literacy. Beyond, little is published on an explicit description of probabilistic thinking and t ...