Members of random closed sets - University of Hawaii Mathematics
... Barmpalias et al. [2] introduced algorithmic randomness for closed sets. Subsequently Kjos-Hanssen [6] used algorithmically random Galton-Watson trees to obtain results on infinite subsets of random sets of integers. Here we show that the distributions studied by Barmpalias et al. and by Galton and ...
... Barmpalias et al. [2] introduced algorithmic randomness for closed sets. Subsequently Kjos-Hanssen [6] used algorithmically random Galton-Watson trees to obtain results on infinite subsets of random sets of integers. Here we show that the distributions studied by Barmpalias et al. and by Galton and ...
Lecture 6: Probability: Combinatorics
... whether an event should be associated with one distribution as opposed to the other. • Conversely, when two distributions are separated, the chance that an event will mistakenly be associated with the wrong one is very small. • For the fair coin problem, the distributions become more separated as th ...
... whether an event should be associated with one distribution as opposed to the other. • Conversely, when two distributions are separated, the chance that an event will mistakenly be associated with the wrong one is very small. • For the fair coin problem, the distributions become more separated as th ...
Context model inference for large or partially observable MDPs
... This was also the case in other tested environments. In general, the MMDP approach exhibits step-wise performance increases due to the fact that a distribution over model orders is maintained. 4.2. State representation The model creates an internal representation of the current system state. To see ...
... This was also the case in other tested environments. In general, the MMDP approach exhibits step-wise performance increases due to the fact that a distribution over model orders is maintained. 4.2. State representation The model creates an internal representation of the current system state. To see ...
Notes on Probabilistic Graphical Models 1
... The framework of probabilistic graphical models provides a general approach for this task. The approach is modelbased, allowing interpretable models to be constructed and then manipulated by reasoning algorithms. These models can also be learned automatically from data, allowing the approach to be u ...
... The framework of probabilistic graphical models provides a general approach for this task. The approach is modelbased, allowing interpretable models to be constructed and then manipulated by reasoning algorithms. These models can also be learned automatically from data, allowing the approach to be u ...
IOSR Journal of Mathematics (IOSR-JM)
... reader should note that two consecutive blocked intervals must always be separated by an interval of time during which the system is not blocked. In order to see this, we observe that at the end of a blocked period the blocking customer is released into unit II. There is therefore no customer in uni ...
... reader should note that two consecutive blocked intervals must always be separated by an interval of time during which the system is not blocked. In order to see this, we observe that at the end of a blocked period the blocking customer is released into unit II. There is therefore no customer in uni ...
Testing ±1-Weight Halfspaces
... We note that it follows from [6] that learning the class of ±1-weight halfspaces requires Ω(n/) queries. Thus, while some dependence on n is necessary for testing, our upper bound shows testing ±1-weight halfspaces can still be done more efficiently than learning. Although we prove our results spec ...
... We note that it follows from [6] that learning the class of ±1-weight halfspaces requires Ω(n/) queries. Thus, while some dependence on n is necessary for testing, our upper bound shows testing ±1-weight halfspaces can still be done more efficiently than learning. Although we prove our results spec ...
... one another by using a concept of duality introduced by Liggett 11. Backward theory in the presence of mutations in the forward process is well understood, as it requires the study of a marked Kingman’s tree see Tavaré 4, for a review. In the works of Neuhauser and Krone 12, there is also s ...
Math/Stats 342: Solutions to Homework
... one has a sum of 12, and in fact the number that have a sum of k ≤ 6 is k (and so Prob(S = k) = k/36), while the number that have a sum of k ≥ 6 is 12 − k (and so Prob(S = k) = (12 − k)/36 here). Note these probabilities are non-negative and sum to 1. Problem: Page 158: #10. Have n + m independent B ...
... one has a sum of 12, and in fact the number that have a sum of k ≤ 6 is k (and so Prob(S = k) = k/36), while the number that have a sum of k ≥ 6 is 12 − k (and so Prob(S = k) = (12 − k)/36 here). Note these probabilities are non-negative and sum to 1. Problem: Page 158: #10. Have n + m independent B ...
Spectral characterization of the optional quadratic varation process (revised vers ion) ET
... As is well known in the statistical analysis of time series in discrete or continuous time, t h e periodogram can be used for estimation problems in t h e frequency domain. It follows from t h e results of the present paper that the periodogram can also be used to estimate the variance of the innova ...
... As is well known in the statistical analysis of time series in discrete or continuous time, t h e periodogram can be used for estimation problems in t h e frequency domain. It follows from t h e results of the present paper that the periodogram can also be used to estimate the variance of the innova ...
Probability box
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A probability box (or p-box) is a characterization of an uncertain number consisting of both aleatoric and epistemic uncertainties that is often used in risk analysis or quantitative uncertainty modeling where numerical calculations must be performed. Probability bounds analysis is used to make arithmetic and logical calculations with p-boxes.An example p-box is shown in the figure at right for an uncertain number x consisting of a left (upper) bound and a right (lower) bound on the probability distribution for x. The bounds are coincident for values of x below 0 and above 24. The bounds may have almost any shapes, including step functions, so long as they are monotonically increasing and do not cross each other. A p-box is used to express simultaneously incertitude (epistemic uncertainty), which is represented by the breadth between the left and right edges of the p-box, and variability (aleatory uncertainty), which is represented by the overall slant of the p-box.