* Maximum likelihood, in estimation theory

The theory as first proposed used comparitative physiological evidence and the natural habits of animals when running, indicating the likelihood of this activity as a successful hunting method.

The theory for adoption of an innovation, called diffusion of innovations, considers the likelihood that an innovation will ever be adopted and the taxonomy of persons likely to adopt it or spur its adoption.

* Marginal likelihood, in Bayesian probability theory

The more truth Wigand tells, the greater the damage, the theory applied goes, and a greater likelihood that CBS will be faced by a multi-billion dollar lawsuit from Brown & Williamson.

In terms of α, this statement is equivalent to saying that " assuming the theory is true, the likelihood of obtaining the experimental result by coincidence is 0. 27 %" ( since 1 − erf ( 3 /√ 2 ) = 0. 0027 ) ( again depending on whether a one-tailed test or two-tailed test is appropriate ).

McKerrow argues against the likelihood of this theory.

These backlogs pose risks to the market ( both in theory and in all likelihood ), and they exacerbate other risks in the financial system.

An example is the Shtarkov normalized maximum likelihood code, which plays a central role in current MDL theory, but has no equivalent in Bayesian inference.

Visualisation of the Girsanov theorem — The left side shows a Wiener process with negative drift under a canonical measure P ; on the right side each path of the process is colored according to its likelihood under the martingale ( probability theory ) | martingale measure Q.

Another issue is opposition to campus " security fees " that some campuses impose on organizations hosting controversial or unpopular speakers on the theory that they should pay for extra security the colleges deem necessary due to the likelihood of demonstrations and disruption of the events.

Probability theory is used extensively in statistics, mathematics, science and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems.

In particular, Ted Grant deepened Trotsky's theory on " proletarian Bonapartism ": he foresaw the likelihood, in the 1945 – 1991 world situation, of the establishment of new bureaucratised " workers ' states " in backward countries, also on the basis of left-wing military coups and peasant guerrilla wars.

On television this is often done on the theory that involving the audience in the plot as soon as possible will reduce the likelihood of their switching away from a show during the opening commercial.

Papoulis also taught and developed subjects such as stochastic simulation, mean square estimation, likelihood tests, maximum entropy methods, Monte Carlo method, spectral representations and estimation, sampling theory, bispectrum and system identification, cyclostationary processes, deterministic signals in noise ( part of deterministic systems and dynamical system studies ), wave optics and the Wiener and Kalman filters.

In Bayesian probability theory, if the posterior distributions p ( θ | x ) are in the same family as the prior probability distribution p ( θ ), the prior and posterior are then called conjugate distributions, and the prior is called a conjugate prior for the likelihood.

: Salience refers to the likelihood that something will appear causal, in attribution theory.

Two generally true circumstances underlie the theory of thoughtful, therapeutic polypharmacy: ( 1 ) Drugs given for a single somatic locale act on biochemical mechanisms present throughout the body such that their nonlinear interactions can produce an ( unknown except empirically ) global physiological state of health ;( 2 ) The more independent variables, " handles ", to manipulate, the greater the likelihood of finding and stabilizing a small available parametric space of healthy function while minimizing unwanted effects.

In sum, the researchers strove to develop a theory that addressed the following: a person's likelihood to change his / her position, the likely direction of his / her attitude change, a person's tolerance of other positions, and the level of commitment to his / her own position.

The under-perception of rare events mentioned above is actually the opposite of the phenomenon originally described by Kahneman in " prospect theory " ( in their original experiments the likelihood of rare events is overestimated ).

The theory of Bayesian inference is used to derive the posterior distribution by combining the prior distribution and the likelihood function which represents the information obtained from the experiment.

His candidacy citation read: " Known throughout the world as co-author of the Neyman-Pearson theory of testing statistical hypotheses, and responsible for many important contributions to problems of statistical inference and methodology, especially in the development and use of the likelihood ratio criterion.

In the early 1960s, a theory was developed that small differences between homologous protein sequences ( sequences with a high likelihood of common ancestry ) could indicate the process and rate of evolutionary change on the molecular level.

This is done by using the item response function from item response theory to obtain a likelihood function of the examinee's ability.

* Hoaxes perpetrated by " scare tactics " appealing to the audience's subjectively rational belief that the expected cost of not believing the hoax ( the cost if its assertions are true times the likelihood of their truth ) outweighs the expected cost of believing the hoax ( cost if false times likelihood of falsity ), such as claims that a non-malicious but unfamiliar program on one's computer is malware

Amid outcry at the inaccuracy of the story, an apology was published by the paper on 24 July for making no attempt to verify the truth of any of their claims, publishing what they claimed to be the cover, criticising Rockstar for their alleged plans without questioning the likelihood, making no attempt to contact Rockstar before publishing, and obtaining statements from a grieving relative of one of Moat's victims.

Clarity of language, relative type size and proximity to the claim being qualified, and an absence of contrary claims that could undercut effectiveness, will maximize the likelihood that the qualifications and disclosures are appropriately clear and prominent.

By redefining the area of Australian territory that could be landed upon and then legitimately used for claims of asylum ( the migration zone ), and by removing any intercepted people to third countries for processing, future asylum seekers were deterred from making the dangerous journey, once they knew that their trip would in most likelihood not end up with a legitimate claim for asylum in Australia.

Since Adobe was unable to demonstrate a likelihood of success on both copyright and trademark claims, the Court denied Adobe's application for a preliminary injunction against SoftMan.

Though three of the four elements of the federal TRO standard, including irreparable harm, were clearly satisfied by Schiavo's imminent death, Whittemore did not believe the Schindlers ultimately had a substantial likelihood of prevailing, but instead found each of their claims " without merit.

The likelihood of claims was greatly increased by the vast numbers of passengers who constituted the flood of emigrants to North America and Australia in the second half of the century.

The most recent campaign makes claims about the likelihood of getting caught and the consequences of committing benefit fraud using ‘ And they thought they ’ d never be caught ’ as the leading slogan.

* Flood insurance only covers losses for the owner of the property, and claims are subject to caps, which further increases the likelihood that the property will be occupied by renters rather than the property owner.

The best index fossils are common, easy-to-identify at species level, and have a broad distribution — otherwise the likelihood of finding and recognizing one in the two sediments is minor.

Excessive disparities in income distribution emerging from private ownership are alleged by proponents of this system to lead to social instability that requires costly corrective measures in the form of social welfare and redistributive taxation and heavy administrative costs to administer them while weakening the incentive to work, inviting dishonesty and increasing the likelihood of tax evasion while reducing the overall efficiency of the market economy and necessitating government regulation over markets.

A likelihood function arises from a conditional probability distribution considered as a function of its distributional parameterization argument, conditioned on the data argument.

When is a conditional probability distribution and the loss function is the negative log likelihood:, then empirical risk minimization is equivalent to maximum likelihood estimation.

For the special case where is a joint probability distribution and the loss function is the negative log likelihood a risk minimization algorithm is said to perform generative training, because can be regarded as a generative model that explains how the data were generated.

The product of the prior and the likelihood, normalized, results in a posterior probability distribution that incorporates all the information known to date.

When considered a function of n for fixed N this is the probability distribution, but when considered a function of N for fixed n this is a likelihood function.

This likelihood function is not a probability distribution, because the total

When the logarithm of the likelihood ratio is used, the statistic is known as a log-likelihood ratio statistic, and the probability distribution of this test statistic, assuming that the null model is true, can be approximated using Wilks ' theorem.

It is clear that the CNML predictive distribution is strictly superior to the maximum likelihood plug-in distribution in terms of average Kullback – Leibler divergence for all sample sizes.

The best index fossils are common, easy-to-identify at species level, and have a broad distribution — otherwise the likelihood of finding and recognizing one in the two sediments is minor.

* The marginal likelihood ( sometimes also termed the evidence ) is the distribution of the observed data marginalized over the parameter ( s ), i. e..

By comparison, prediction in frequentist statistics often involves finding an optimum point estimate of the parameter ( s ) — e. g. by maximum likelihood or maximum a posteriori estimation ( MAP ) — and then plugging this estimate into the formula for the distribution of a data point.

Note that both types of predictive distributions have the form of a compound probability distribution ( as does the marginal likelihood ).

Auto-correlation can be reduced by increasing the jumping width ( the average size of a jump, which is related to the variance of the jumping distribution ), but this will also increase the likelihood of rejection of the proposed jump.

Least squares corresponds to the maximum likelihood criterion if the experimental errors have a normal distribution and can also be derived as a method of moments estimator.

* In a linear model, if the errors belong to a Normal distribution the least squares estimators are also the maximum likelihood estimators.

When including two suited hands with 5-4 distribution, two suiters have a high likelihood of occurrence, and the modern preemptive style is to incorporate such two-suited hands in the arsenal of preemptive openings.

In general, for a fixed set of data and underlying statistical model, the method of maximum likelihood selects values of the model parameters that produce a distribution that gives the observed data the greatest probability ( i. e., parameters that maximize the likelihood function ).

The results of the likelihood ratio ( the ratio of the fitted model to the saturated model ) will produce a negative value, so the product is multiplied by negative two times its natural logarithm to produce a value with an approximate chi-squared distribution.

More generally however, when maximum likelihood estimation does not coincide with minimum chi-squared estimation, the distribution will lie somewhere between a chi-squared distribution with and degrees of freedom ( See for instance Chernoff and Lehmann, 1954 ).