Examples of Bayesian information criterion in the following topics:
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- Usually, this takes the form of a sequence of $F$-tests; however, other techniques are possible, such as $t$-tests, adjusted $R$-square, Akaike information criterion, Bayesian information criterion, Mallows's $C_p$, or false discovery rate.
- Forward selection involves starting with no variables in the model, testing the addition of each variable using a chosen model comparison criterion, adding the variable (if any) that improves the model the most, and repeating this process until none improves the model.
- Backward elimination involves starting with all candidate variables, testing the deletion of each variable using a chosen model comparison criterion, deleting the variable (if any) that improves the model the most by being deleted, and repeating this process until no further improvement is possible.
- This problem can be mitigated if the criterion for adding (or deleting) a variable is stiff enough.
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- Bayesian inference provides further answers in the form of credible intervals.
- Ostensibly, the Bayesian approach offers intervals that (subject to acceptance of an interpretation of "probability" as Bayesian probability) offer the interpretation that the specific interval calculated from a given dataset has a certain probability of including the true value (conditional on the data and other information available).
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- Even in their basic "evaluative" capacity grades can be rich sources of information for students and educators alike.
- An essay, for example, which was characterized by very clear prose might receive an "A" for that criterion.
- If that same essay, however, was deeply unoriginal, it might receive a "C" for that criterion.
- And if it lacked documentation all together, it might receive a "D" or an "F" for that criterion.
- (She might weigh each criterion equally, or might assign the most important relatively more weight).
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- The second derivative test is a criterion for determining whether a given critical point is a local maximum or a local minimum.
- In calculus, the second derivative test is a criterion for determining whether a given critical point of a real function of one variable is a local maximum or a local minimum using the value of the second derivative at the point.
- It does not, however, provide information about inflection points.
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- Influence diagrams are directly applicable in group decisions because they allow incomplete sharing of information among team members to be modeled and for estimates to be made explicitly.
- She cannot have direct knowledge at the time of the decision what the weather will be, but she can gather information on the weather forecast or other climate patterns to help her make the choice of vacation location.
- Model potential decision alternatives through utilizing pro/con analysis, influence diagrams, decision trees and Bayesian networks
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- Notice that we are given sufficient information to quickly compute the probability of testing positive if a woman has breast cancer (1.00 − 0.11 = 0.89).
- Based on the information that the garage is full, there is a 56% probability that a sporting event is being held on campus that evening.
- Using this information, compute P(no event | the lot is full).
- This strategy of updating beliefs using Bayes' Theorem is actually the foundation of an entire section of statistics called Bayesian statistics.
- While Bayesian statistics is very important and useful, we will not have time to cover much more of it in this book.
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- The Statistical Significance Criterion Used in the Test: A significance criterion is a statement of how unlikely a positive result must be, if the null hypothesis of no effect is true, for the null hypothesis to be rejected.
- One easy way to increase the power of a test is to carry out a less conservative test by using a larger significance criterion, for example 0.10 instead of 0.05.
- An unstandardized (direct) effect size will rarely be sufficient to determine the power, as it does not contain information about the variability in the measurements.
- Let's say we look for a significance criterion of 0.05.
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- In simple linear regression, a criterion variable is predicted from one predictor variable.
- In multiple regression, the criterion is predicted by two or more variables.
- In multiple regression, it is often informative to partition the sums of squares explained among the predictor variables.
- Specifically, they are the differences between the actual scores on the criterion and the predicted scores.
- It is assumed that the relationship between each predictor variable and the criterion variable is linear.
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- It is useful to think of the condition as information we know to be true, and this information usually can be described as a known outcome or event.
- Suppose we were provided only the information in Table 2.13 on the preceding page, i.e. only probability data.
- Then if we took a sample of 1000 people, we would anticipate about 47% or 0.47 × 1000 = 470 would meet our information criterion.
- Similarly, we would expect about 28% or 0.28 × 1000 = 280 to meet both the information criterion and represent our outcome of interest.
- The complement still appears to work when conditioning on the same information.
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- The initial impetus for developing a classification of mental disorders in the United States was the need to collect statistical information.
- In this version, a clinical significance criterion was added to almost half of all the categories.
- This criterion required that symptoms cause "clinically significant distress or impairment in social, occupational, or other important areas of functioning."
- Notable changes include the change from autism and Asperger syndrome to a combined autism spectrum disorder; dropping the subtype classifications for variant forms of schizophrenia; dropping the "bereavement exclusion" for depressive disorders; a revised treatment and naming of gender-identity disorder to gender dysphoria; and changes to the criterion for post-traumatic stress disorder (PTSD).