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The simple Bonferroni correction rejects only null hypotheses with p-value less than or equal to , in order to ensure that the FWER, i.e., the risk of rejecting one or more true null hypotheses (i.e., of committing one or more type I errors) is at most . The cost of this protection against type I errors is an increased risk of failing to reject ...
Prism dioptres. Prism correction is commonly specified in prism dioptres, a unit of angular measurement that is loosely related to the dioptre. Prism dioptres are represented by the Greek symbol delta (Δ) in superscript. A prism of power 1 Δ would produce 1 unit of displacement for an object held 100 units from the prism. [2]
The procedures of Bonferroni and Holm control the FWER under any dependence structure of the p-values (or equivalently the individual test statistics).Essentially, this is achieved by accommodating a `worst-case' dependence structure (which is close to independence for most practical purposes).
First the system is progressed in time to a mid-time-step position, solving the above transport equations for mass and momentum using a suitable advection method. This is denoted the predictor step. At this point an initial projection may be implemented such that the mid-time-step velocity field is enforced as divergence free.
A simple predictor–corrector method (known as Heun's method) can be constructed from the Euler method (an explicit method) and the trapezoidal rule (an implicit method). Consider the differential equation. and denote the step size by . First, the predictor step: starting from the current value , calculate an initial guess value via the Euler ...
MacCormack method. In computational fluid dynamics, the MacCormack method (/məˈkɔːrmæk ˈmɛθəd/) is a widely used discretization scheme for the numerical solution of hyperbolic partial differential equations. This second-order finite difference method was introduced by Robert W. MacCormack in 1969. [1] The MacCormack method is elegant ...
Newton's method in optimization. A comparison of gradient descent (green) and Newton's method (red) for minimizing a function (with small step sizes). Newton's method uses curvature information (i.e. the second derivative) to take a more direct route. In calculus, Newton's method (also called Newton–Raphson) is an iterative method for finding ...
For n ≥ 2, the n-dimensional Wiener process started at the origin is transient from its starting point: with probability one, i.e., X t > 0 for all t > 0. It is, however, neighbourhood-recurrent for n = 2, meaning that with probability 1, for any r > 0, there are arbitrarily large t with X t < r; on the other hand, it is truly transient for n > 2, meaning that X t ≥ r for all t ...