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Population and Community: Count Variables
Published in Song S. Qian, Mark R. DuFour, Ibrahim Alameddine, Bayesian Applications in Environmental and Ecological Studies with R and Stan, 2023
Song S. Qian, Mark R. DuFour, Ibrahim Alameddine
As a result, θ and cannot be uniquely determined without proper prior distributions for two of these three parameters. Without knowing the true status (in this case, whether a snake is infected or not) made the problem difficult. However, if the unknown status is explicitly specified as an unknown parameter (e.g., for being infected and otherwise), the joint likelihood function of y for a snake is the joint probability of y,z and parameters , and fn in equation (1.4). The joint probability can be specified through the conditional probability formula
Fundamentals
Published in Arvind Kumar Bansal, Javed Iqbal Khan, S. Kaisar Alam, Introduction to Computational Health Informatics, 2019
Arvind Kumar Bansal, Javed Iqbal Khan, S. Kaisar Alam
Probability is strongly related to statistics because it is based upon computation of the percentage of an event occurring in a large sample set. Variable dependence (or independence) plays a major role in computing joint-probability of a multivariable event to occur. Conditional probability of an event to occur changes when the variables are dependent. Bayes' theorem equates absolute probabilities to conditional probabilities of two or more variable events, and has been used in many AI techniques including cause-and-effect based reasoning.
Building a Predictive Model of Toxicity
Published in Tiziana Rancati, Claudio Fiorino, Modelling Radiotherapy Side Effects, 2019
Sunan Cui, Randall K. Ten Haken, Issam El Naqa
Mathematically, a BN can be defined as an annotated acyclic graph that represents the joint probability distribution over a set of random variables X = (x1,…,xs), denoted as where graph G encodes random variables and dependence assumptions and denotes the set of parameters describing how the nodes depend on their parents. The joint probability is given by:
Fuzzy Bayesian estimation and consequence modeling of the domino effects of methanol storage tanks
Published in International Journal of Occupational Safety and Ergonomics, 2022
Mostafa Pouyakian, Fereydoon Laal, Mohammad Javad Jafari, Farshad Nourai, Sohag Kabir
Also, it can be concluded that: P(U) = joint probability. The chronological or sequential probability sequence of events will also be T1, T2 and T3. It is noteworthy that, if the domino effect does not occur, there is still a possibility of an accident in T3, which is the initial probability of T3. Therefore, L-NOR gates were used, the results of which can be seen in Table 7. Conditional probabilities between nodes in the previous step were calculated using the probit equations and used together with the initialtank probabilities to complete the CPTs and update the probabilities. Table 7 presents the probability of a domino accident caused by pool fire using the BTA and FBN methods at the first and second levels.
An optimal control chart for finite matrix sequences at some unknown change point
Published in Journal of Applied Statistics, 2021
Given a finite number of samples, τ be unknown. Therefore, the joint probability densities
Measuring association between nominal categorical variables: an alternative to the Goodman–Kruskal lambda
Published in Journal of Applied Statistics, 2018
Consider, for example, the joint probability distribution (or 2 × 3 table) X and Y so that a symmetric association measure should equal 1. Thus, a generic and symmetric association measure A should have the following property: (P8) A = 1 if and only if all nonzero probabilities only fall on a longest diagonal of the I × J table, irrespective of I and J. That is, A = 1 only when each row or each column contains at most one nonzero probability for any I × J contingency table (see, e.g. [15, pp. 568, 587–590, 3, pp. 385–386]). It is because of this property that Cramér's 5, p. 443]; although he used mean square contingency coefficient ([15, pp. 587–588, 3, p. 393, 20, pp. 46–47, 9]). From (29) and (30),