Note that this is expressed in words as " posterior is proportional to prior times likelihood ", or sometimes as " posterior

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

Note that power is the probability of finding a difference that does exist, as opposed to the likelihood of declaring a difference that does not exist ( which is known as a Type I error, or " false positive ").

Note that for the Cauchy distribution, neither the truncated mean, full sample mean or sample median represents a maximum likelihood estimator, nor are any as asymptotically efficient as the maximum likelihood estimator ; however, the maximum likelihood estimate is difficult to compute, leaving the truncated mean as a useful alternative.

Note that it may be not trivial to show that such derived estimator is the unique global maximizer for likelihood function.

Note, however, that the performance of likelihood is dependent on the quality of the model employed ; an incorrect model can produce a biased result.

Note that if the probability of error on a discrete memoryless channel is strictly less than one half, then minimum distance decoding is equivalent to maximum likelihood decoding, since if

Note that for any fixed w the function f ( x ) = F ( w x ) is computable ; thus the universality property states that all computable functions of one variable can be obtained in this fashion.

Note, however, that currying, while similar, is not the same operation as partial function application.

Note that after calling, we are left with a function that takes a single argument and returns another function, not a function that takes two arguments.

Note that the result of partial function application in this case is a function that takes two arguments.

Note that is a monotone function in γ and that the solution γ must satisfy.

Note that this derivation does assume that ƒ ( x ) is sufficiently differentiable and well-behaved ; specifically, that ƒ may be approximated by polynomials ; equivalently, that ƒ is a real analytic function of exponential type.

Note that for a Euclidean function that is so established there need not exist an effective method to determine q and r in ( EF1 ).

: is a spherical harmonic function of degree ℓ and order m. Note that the generalized Laguerre polynomials are defined differently by different authors.

Note that the operators operate on elements from the domain and range, respectively, of the " one-to-one " and " onto " function ƒ.

Note that parameters of a function are not necessarily in parentheses but separated by spaces.

Note the difference in passport color and function as per passport type.

Note that when N = R, the map dφ < sub > x </ sub >: T < sub > x </ sub > M → R coincides with the usual notion of the differential of the function φ.

Note that the waves shown here are real for illustrative purposes only whereas, in quantum mechanics the wave function is generally complex.

The Preliminary Note of Explanation did not in fact alter the value of the statement on collegiality in the text of Lumen Gentium: it " strengthened the adherence to the doctrine of the First Vatican Council on the primacy, but it did not subsequently strike out anything from the direct divine origin of the episcopal office and its function, and the responsibility of the College of Bishops for the Universal Church.

Note: This function may be integrated into the ET.

Note: The multiplexing function is performed in the D-4 framing structure by interleaving bits of consecutive bytes as they are presented from individual circuits into each D-4 frame.

Note 2: The FCC registration program contains no requirement that accepted terminal equipment be compatible with, or function with, the network.

Note that there exists an instance of Bayes ' theorem for each point in the Domain of a function | domain.

( Note that it is written as a relation, not as a function: T isn't written here as a function of M, L, and g .)

Note that searing in no way " locks in " moisture: moisture loss is simply a function of heat and time.

Note that also depends on.

Note that the error, e, depends not only on the estimator ( the estimation formula or procedure ), but on the sample.

Note that the sampling deviation, d, depends not only on the estimator, but on the sample.

Note that a substance's GWP depends on the timespan over which the potential is calculated.

( Note that the propagation of the prion depends on the presence of normally folded protein in which the prion can induce misfolding ; animals which do not express the normal form of the prion protein cannot develop nor transmit the disease.

Since we've assumed that we can infallibly identify programs for computing squares, we can determine whether t, which depends on a and i, is such a program, and that for every a and i ; thus we have obtained a program that decides whether program a halts on input i. Note that our halting-decision algorithm never executes t, but only passes its description to the squaring-identification program, which by assumption always terminates ; since the construction of the description of t can also be done in a way that always terminates, the halting-decision cannot fail to halt either.

Note that the power injected by the torque depends only on the instantaneous angular speed – not on whether the angular speed increases, decreases, or remains constant while the torque is being applied ( this is equivalent to the linear case where the power injected by a force depends only on the instantaneous speed – not on the resulting acceleration, if any ).

Signal processors, such as four-phase modems, cannot change the DSR, but the modulation rate depends on the line modulation scheme, in accordance with Note 4.

Note that the size of the columns depends loosely on the rate of cooling ; very rapid cooling may result in very small (< 1 cm diameter ) columns, while slow cooling is more likely to produce large columns.

Note that this definition of V depends on the gauge choice for the vector potential A ( the gradient of any scalar field can be added to A without changing B ).

Note that triviality also depends on context.

Note that this property holds only as long as other variables on which the intensive variable depends stay constant.

Note that the ( congruence ) closure of a binary relation depends on the operations in, not just on the carrier set.

Note that the conditional expected value is a random variable in its own right, whose value depends on the value of X.

Note: Given the non-linear nature of Invisible War, encountering certain plot elements depends on the actions of the player.

Note that the inner automorphism ( 1 ) does not depend on which such g is selected ; it depends only on g modulo H < sub > o </ sub >.

Note that, due to the principle of univariance, the firing of the cell depends upon only the number of photons absorbed.

Note that security depends also on the resistance of the blinding functions themselves to side-channel attacks.

Note that the adjoint of an operator depends on the scalar product considered on the dimensional complex or real space.

Note that the true distribution of the test statistic actually depends ( slightly ) on the two unknown variances: see Behrens – Fisher problem.

Note that, there is no clear distinction between obligate and non-obligate interaction, rather there exist a continuum between them which depends on various conditions e. g. pH, protein concentration etc.

Note that ellipticity only depends on the highest-order terms.

Note that some authors have defined an anticausal system as one that depends solely on future and present input values or, more simply, as a system that does not depend on past input values.