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Glossary Archives

Moment Generating Function

Moment Generating Function: The moment generation function is associated with a probability distribution. The moment generating function can be used to generate moments. However, the main use of the moment generating function is not in generating moments but to help in characterizing a distribution. The moment generating function of a...

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Collaborative filtering

Collaborative filtering: Collaborative filtering algorithms are used to predict whether a given individual might like, or purchase, an item. One popular approach is to find a set of individuals (e.g. customers) whose item preferences (ratings) are similar to those of the given individual over a number of different items. The...

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Normal Distribution

Normal Distribution: The normal distribution is a probability density which is bell-shaped, symmetrical, and single peaked. The mean, median and mode coincide and lie at the center of the distribution. The two tails extend indefinitely and never touch the x-axis (asymptotic to the x-axis). A normal distribution is fully specified...

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Poisson Distribution

Poisson Distribution: The Poisson distribution is a discrete distribution, completely characterized by one parameter l:   p(x=k) =  lk k! e-l,   k=0,1,2,� (where k! = 1 x 2 x ... x k). Both the mean and the variance of Poisson distribution are equal to l. The Poisson distribution parameter l...

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Poisson Process

Statistical Glossary Poisson Process: A Poisson process is a random function U(t) which describes the number of random events in an interval [0,t] of time or space. The random events have the properties that (i) the probability of an event during a very small interval from t to t +...

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Posterior Probability

Posterior Probability: Posterior probability is a revised probability that takes into account new available information. For example, let there be two urns, urn A having 5 black balls and 10 red balls and urn B having 10 black balls and 5 red balls. Now if an urn is selected at...

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Prior and posterior probability (difference)

Prior and posterior probability (difference): Consider a population where the proportion of HIV-infected individuals is 0.01. Then, the prior probability that a randomly chosen subject is HIV-infected is Pprior = 0.01 . Suppose now a subject has been positive for HIV. It is known that specificity of the test is...

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Random Process

Statistical Glossary Random Process: A random process describes an experiment with outcomes being functions of a single continuous variable (e.g. time). See also Random Series, Random Field. Browse Other Glossary Entries

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Support Vector Machines

Support Vector Machines: Support vector machines are used in data mining (predictive modeling, to be specific) for classification of records, by learning from training data. Support vector machines use decision surfaces that separate records. They rely on optimization techniques to maximize separate margins between classes, and kernel functions to accommodate...

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t-distribution

t-distribution: A continuous distribution, with single peaked probability density symmetrical around the null value and a bell-curve shape. T-distribution is specified completely by one parameter - the number of degrees of freedom. If X and Y are independent random variables, X has the standard normal distribution and Y - chi-square...

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2-Tailed vs. 1-Tailed Tests

2-Tailed vs. 1-Tailed Tests: The purpose of a hypothesis test is to avoid being fooled by chance occurrences into thinking that the effect you are investigating (for example, a difference between treatment and control) is real. If you are investigating, say, the difference between an existing process and a (hopefully...

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Alternative Hypothesis

Alternative Hypothesis: In hypothesis testing, there are two competing hypotheses - the null hypothesis and the alternative hypothesis. The null hypothesis usually reflects the status quo (for example, the proposed new treatment is ineffective and the observed results are just due to chance variation). The hypothesis which competes with the...

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Analysis of Variance (ANOVA)

Analysis of Variance (ANOVA): A statistical technique which helps in making inference whether three or more samples might come from populations having the same mean; specifically, whether the differences among the samples might be caused by chance variation. Browse Other Glossary Entries

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Bonferroni Adjustment

Bonferroni Adjustment: Bonferroni adjustment is used in multiple comparison procedures to calculate an adjusted probability a of comparison-wise type I error from the desired probability aFW0 of family-wise type I error. The calculation guarantees that the use of the adjusted a in pairwise comparisons keeps the actual probability aFW of...

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Box´s M

Box´s M: Box´s M is a statistic which tests the homoscedasticity assumption in MANOVA - that is the assumption that all covariances are the same for any category. The results should be interpreted with caution because Box´s M is not robust - it is very sensitive to deviations from normality....

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