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  1. In statistics, the posterior probability expresses how likely a hypothesis is given a particular set of data.[1]
  2. Posterior probability is the probability an event will happen after all evidence or background information has been taken into account.[2]
  3. The posterior distribution is a way to summarize what we know about uncertain quantities in Bayesian analysis.[2]
  4. In other words, the posterior distribution summarizes what you know after the data has been observed.[2]
  5. Posterior probability is a conditional probability conditioned on randomly observed data.[3]
  6. In classification, posterior probabilities reflect the uncertainty of assessing an observation to particular class, see also Class membership probabilities.[3]
  7. While statistical classification methods by definition generate posterior probabilities, Machine Learners usually supply membership values which do not induce any probabilistic confidence.[3]
  8. A posterior probability, in Bayesian statistics, is the revised or updated probability of an event occurring after taking into consideration new information.[4]
  9. The posterior probability is calculated by updating the prior probability using Bayes' theorem.[4]
  10. Posterior probability distributions should be a better reflection of the underlying truth of a data generating process than the prior probability since the posterior included more information.[4]
  11. A posterior probability can subsequently become a prior for a new updated posterior probability as new information arises and is incorporated into the analysis.[4]
  12. For most problems encountered in fisheries stock assessment, it is impossible to evaluate the posterior distribution (Equation 1.5) analytically.[5]
  13. Let q denote the parameter vector and p( q ), the posterior probability of the parameter vector q .[5]
  14. q i : i=1,2,...} from the posterior distribution, p( q ), or to determine the relative posterior probabilities for a set of pre-specified vectors of parameters.[5]
  15. The posterior probability for each combination of the two parameters is then calculated using Equation (1.6).[5]
  16. This can be done by computing the quantiles of the posterior distribution.[6]
  17. Essentially this boils down to summarizing the posterior distribution by a single number.[6]
  18. When \(q\) is a continuous-valued variable, as here, the most common Bayesian point estimate is the mean (or expectation) of the posterior distribution, which is called the “posterior mean”.[6]
  19. The posterior probability is one of the quantities involved in Bayes' rule.[7]
  20. In sum, contrary to the common account, naive respondents do not perform well on tasks devised to improve their understanding of posterior probability.[8]
  21. Two notes are in order about the tasks that have documented the existence of an early understanding of prior and posterior probability (e.g., Task B and B').[8]
  22. …of all joint probabilities, the posterior probability is arrived at.[9]
  23. Posterior probability is the likelihood that the individual, whose genotype is uncertain, either carries the mutant gene or does not.[9]
  24. Range of the posterior probability of an interval over the ε-contamination class Γ={π=(1−ε)π 0 +εq:qεQ} is derived.[10]
  25. We show that the sup (resp. inf) of the posterior probability of an interval is attained by a prior which is equal to (1−ε)π 0 except in one interval (resp.[10]
  26. In Scott (2002) and Congdon (2006), a new method is advanced to compute posterior probabilities of models under consideration.[11]
  27. While it is indeed possible to approximate posterior probabilities based solely on MCMC outputs from single models, as demonstrated by Gelfand and Dey (1994) and Bartolucci et al.[11]
  28. Bayes' theorem can be used to estimate the posterior probabilities, that is, the probabilities that an email which is received as spam, really is spam, or is in fact legitimate.[12]
  29. A posterior probability is the probability of assigning observations to groups given the data.[13]
  30. If you know or can estimate these probabilities, a discriminant analysis can use these prior probabilities in calculating the posterior probabilities.[13]
  31. P(Θ|data) on the left hand side is known as the posterior distribution.[14]
  32. We don’t care about the normalising constant so we have everything we need to calculate the unnormalised posterior distribution.[14]
  33. Now we have the posterior distribution for the length of a hydrogen bond we can derive statistics from it.[14]
  34. One of the most common statistics calculated from the posterior distribution is the mode.[14]
  35. This approximation to the likelihood function was used because a full characterization of the posterior probability function had not yet been performed.[15]
  36. In this case the reconstruction is chosen to maximize the posterior probability and task performance involves using the posterior probability of the various alternatives as the decision variable.[15]
  37. The results demonstrate the improvement in detection performance that can be achieved when the full posterior probability function is incorporated into the decision variable.[15]
  38. Given any report r submitted to the CPS server, MLA guarantees that the posterior probability of each query content in r is larger than 0.[16]
  39. Posterior probability is a revised probability that takes into account new available information.[17]
  40. A description of the network structure is given first, followed by an explanation of the posterior probability-updating algorithm.[18]
  41. Individuals were assigned to the group with the largest posterior probability estimate.[18]
  42. Prior to observing x, this distribution is the prior probability p(h); after observing x, it is the posterior probability p(h x).[18]
  43. At the same time, neither effect size, nor confidence interval estimate, nor posterior probability can be used to exclude chance as an explanation of data.[18]
  44. There are many ways to summarize the posterior distribution of tree topologies and branch lengths.[19]
  45. The 50% majority consensus tree is a tree constructed so that it contains all of the clades that occur in at least 50% of the trees in the posterior distribution.[19]
  46. In other words it contains only the clades that have a posterior probability of >= 50%.[19]
  47. It has sometimes been used to describe the tree associated with the sampled state in the MCMC chain that has the highest posterior probability density.[19]
  48. We conclude that the posterior probability of H 0 provide a much more conservative quantification of the mode detection than the significance level.[20]
  49. In this contribution we show that the algorithm can also be used to estimate the posterior probability, or the confidence of its decision on each test instance.[21]
  50. Uniform prior probabilities allow a frequentist posterior probability distribution of a study result’s replication to be calculated conditional solely on the study’s observations.[22]
  51. Attempts have been made to calculate posterior probabilities by avoiding an explicitly Bayesian approach.[22]
  52. This will provide the posterior probability of each possible true result from Θ 1 to Q 101 .[22]
  53. The curve markers represent actual likelihood and posterior probabilities.[22]

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  • [{'LOWER': 'posterior'}, {'LEMMA': 'probability'}]
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  • [{'LOWER': 'relative'}, {'LOWER': 'frequency'}, {'LEMMA': 'probability'}]
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