Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures used to analyze the differences among group means in a sample. ANOVA was developed by statistician and evolutionary biologist Ronald Fisher. In the ANOVA setting, the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether the population means of several groups are equal, and therefore generalizes the t-test to more than two groups. ANOVA is useful for comparing (testing) three or more group means for statistical significance. It is conceptually similar to multiple two-sample t-tests, but is more conservative, resulting in fewer type I errors, and is therefore suited to a wide range of practical problems.
In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a collection of random variables. Historically, the random variables were associated with or indexed by a set of numbers, usually viewed as points in time, giving the interpretation of a stochastic process representing numerical values of some system randomly changing over time, such as the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. They have applications in many disciplines including sciences such as biology, chemistry, ecology, neuroscience, and physics as well as technology and engineering fields such as image processing, signal processing, information theory, computer science, cryptography and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance.
In computer science, a semaphore is a variable or abstract data type used to control access to a common resource by multiple processes in a concurrent system such as a multitasking operating system. A semaphore is simply a variable. This variable is used to solve critical section problems and to achieve process synchronization in the multi processing environment. A trivial semaphore is a plain variable that is changed depending on programmer-defined conditions.
In statistics, an interaction may arise when considering the relationship among three or more variables, and describes a situation in which the effect of one causal variable on an outcome depends on the state of a second causal variable. Although commonly thought of in terms of causal relationships, the concept of an interaction can also describe non-causal associations. Interactions are often considered in the context of regression analyses or factorial experiments.
Branch and bound is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists of a systematic enumeration of candidate solutions by means of state space search: the set of candidate solutions is thought of as forming a rooted tree with the full set at the root. The algorithm explores branches of this tree, which represent subsets of the solution set. Before enumerating the candidate solutions of a branch, the branch is checked against upper and lower estimated bounds on the optimal solution, and is discarded if it cannot produce a better solution than the best one found so far by the algorithm.
In concurrent programming, a monitor is a synchronization construct that allows threads to have both mutual exclusion and the ability to wait (block) for a certain condition to become true. Monitors also have a mechanism for signaling other threads that their condition has been met. A monitor consists of a mutex (lock) object and condition variables. A condition variable is basically a container of threads that are waiting for a certain condition. Monitors provide a mechanism for threads to temporarily give up exclusive access in order to wait for some condition to be met, before regaining exclusive access and resuming their task.
In probability theory, the Lindley equation, Lindley recursion or Lindley processes is a discrete-time stochastic process An where n takes integer values and:
Proportional hazards models are a class of survival models in statistics. Survival models relate the time that passes, before some event occurs, to one or more covariates that may be associated with that quantity of time. In a proportional hazards model, the unique effect of a unit increase in a covariate is multiplicative with respect to the hazard rate. For example, taking a drug may halve one's hazard rate for a stroke occurring, or, changing the material from which a manufactured component is constructed may double its hazard rate for failure. Other types of survival models such as accelerated failure time models do not exhibit proportional hazards. The accelerated failure time model describes a situation where the biological or mechanical life history of an event is accelerated.
Recursive partitioning is a statistical method for multivariable analysis. Recursive partitioning creates a decision tree that strives to correctly classify members of the population by splitting it into sub-populations based on several dichotomous independent variables. The process is termed recursive because each sub-population may in turn be split an indefinite number of times until the splitting process terminates after a particular stopping criterion is reached.
In queueing theory, a discipline within the mathematical theory of probability, a fork–join queue is a queue where incoming jobs are split on arrival for service by numerous servers and joined before departure. The model is often used for parallel computations or systems where products need to be obtained simultaneously from different suppliers. The key quantity of interest in this model is usually the time taken to service a complete job. The model has been described as a "key model for the performance analysis of parallel and distributed systems." Few analytical results exist for fork–join queues, but various approximations are known.
In queueing theory, a discipline within the mathematical theory of probability, a fluid queue is a mathematical model used to describe the fluid level in a reservoir subject to randomly determined periods of filling and emptying. The term dam theory was used in earlier literature for these models. The model has been used to approximate discrete models, model the spread of wildfires, in ruin theory and to model high speed data networks. The model applies the leaky bucket algorithm to a stochastic source.
In queueing theory, a discipline within the mathematical theory of probability, a bulk queue is a general queueing model where jobs arrive in and/or are served in groups of random size. Batch arrivals have been used to describe large deliveries and batch services to model a hospital out-patient department holding a clinic once a week, a transport link with fixed capacity and an elevator.
In queueing theory, a discipline within the mathematical theory of probability, a D/M/1 queue represents the queue length in a system having a single server, where arrivals occur at fixed regular intervals and job service requirements are random with an exponential distribution. The model name is written in Kendall's notation. Agner Krarup Erlang first published a solution to the stationary distribution of a D/M/1 and D/M/k queue, the model with k servers, in 1917 and 1920.
In queueing theory, a discipline within the mathematical theory of probability, the flow-equivalent server method is a divide-and-conquer method to solve product form queueing networks inspired by Norton's theorem for electrical circuits. The network is successively split into two, one portion is reconfigured to a closed network and evaluated.
In queueing theory, a discipline within the mathematical theory of probability, the G/G/1 queue represents the queue length in a system with a single server where interarrival times have a general distribution and service times have a (different) general distribution. The evolution of the queue can be described by the Lindley equation.
In queueing theory, a discipline within the mathematical theory of probability, the decomposition method is an approximate method for the analysis of queueing networks where the network is broken into subsystems which are independently analyzed.
In queueing theory, a discipline within the mathematical theory of probability, a polling system or polling model is a system where a single server visits a set of queues in some order. The model has applications in computer networks and telecommunications, manufacturing and road traffic management. The term polling system was coined at least as early as 1968 and the earliest study of such a system in 1957 where a single repairman servicing machines in the British cotton industry was modelled.
