Jump to navigation Jump to search „Random“ redirects here. For a random Wikipedia article, see Special:Random. For information about Wikipedia’s random semi-Blind Robust Identification and Model Validation PDF feature, see Wikipedia:Random. Randomness is the lack of pattern or predictability in events.

Författare: Wenjing Ma.

We study a semi-blind robust identification

motivated from the fact that sometimes only partial

input data is exactly known. Derived from a

time-domain algorithm for robust identification, this

semi-blind robust identification

is stated as a non convex problem. We develop a

convex relaxation, by combining two variables into a

new variable, to reduce it to an LMI optimization

problem. Applying this convex relaxation, a

macro-economy modeling problem can be solved. The

problem of identification of Wiener Systems, a

special type of nonlinear systems, is analyzed from a

set-membership standpoint. We propose an algorithm

for time-domain based identification by pursuing a

risk-adjusted approach to reduce it to a convex

optimization problem. An arising non-trivial problem

in computer vision, tracking a human in a sequence of

frames, can be solved by modeling the plant as

Wiener system using the proposed identification

method. The book can serve as a reference for

financial engineers and finance-oriented

professionals in macro-economics and a textbook for

graduate courses on robust control theory and

macro-economics.

The fields of mathematics, probability, and statistics use formal definitions of randomness. In statistics, a random variable is an assignment of a numerical value to each possible outcome of an event space. This association facilitates the identification and the calculation of probabilities of the events. Random variables can appear in random sequences. Randomness is most often used in statistics to signify well-defined statistical properties.

Ancient fresco of dice players in Pompei. In ancient history, the concepts of chance and randomness were intertwined with that of fate. Many ancient peoples threw dice to determine fate, and this later evolved into games of chance. Most ancient cultures used various methods of divination to attempt to circumvent randomness and fate.

The Chinese of 3000 years ago were perhaps the earliest people to formalize odds and chance. The Greek philosophers discussed randomness at length, but only in non-quantitative forms. It was only in the 16th century that Italian mathematicians began to formalize the odds associated with various games of chance. The invention of the calculus had a positive impact on the formal study of randomness. The early part of the 20th century saw a rapid growth in the formal analysis of randomness, as various approaches to the mathematical foundations of probability were introduced. Although randomness had often been viewed as an obstacle and a nuisance for many centuries, in the 20th century computer scientists began to realize that the deliberate introduction of randomness into computations can be an effective tool for designing better algorithms. In some cases such randomized algorithms outperform the best deterministic methods.

In the 19th century, scientists used the idea of random motions of molecules in the development of statistical mechanics to explain phenomena in thermodynamics and the properties of gases. According to several standard interpretations of quantum mechanics, microscopic phenomena are objectively random. That is, in an experiment that controls all causally relevant parameters, some aspects of the outcome still vary randomly. The modern evolutionary synthesis ascribes the observed diversity of life to random genetic mutations followed by natural selection. Several authors also claim that evolution and sometimes development require a specific form of randomness, namely the introduction of qualitatively new behaviors. Instead of the choice of one possibility among several pre-given ones, this randomness corresponds to the formation of new possibilities.

As far as behavior is concerned, randomness is important if an animal is to behave in a way that is unpredictable to others. For instance, insects in flight tend to move about with random changes in direction, making it difficult for pursuing predators to predict their trajectories. The mathematical theory of probability arose from attempts to formulate mathematical descriptions of chance events, originally in the context of gambling, but later in connection with physics. Algorithmic information theory studies, among other topics, what constitutes a random sequence. The decimal digits of pi constitute an infinite sequence and „never repeat in a cyclical fashion.

Numbers like pi are also considered likely to be normal, which means their digits are random in a certain statistical sense. Pi certainly seems to behave this way. In the first six billion decimal places of pi, each of the digits from 0 through 9 shows up about six hundred million times. Yet such results, conceivably accidental, do not prove normality even in base 10, much less normality in other number bases.

In statistics, randomness is commonly used to create simple random samples. This lets surveys of completely random groups of people provide realistic data. Common methods of doing this include drawing names out of a hat or using a random digit chart. A random digit chart is simply a large table of random digits. In information science, irrelevant or meaningless data is considered noise. Noise consists of a large number of transient disturbances with a statistically randomized time distribution. In communication theory, randomness in a signal is called „noise“ and is opposed to that component of its variation that is causally attributable to the source, the signal.

In terms of the development of random networks, for communication randomness rests on the two simple assumptions of Paul Erdős and Alfréd Rényi who said that there were a fixed number of nodes and this number remained fixed for the life of the network, and that all nodes were equal and linked randomly to each other. The random walk hypothesis considers that asset prices in an organized market evolve at random, in the sense that the expected value of their change is zero but the actual value may turn out to be positive or negative. More generally, asset prices are influenced by a variety of unpredictable events in the general economic environment. Random selection can be an official method to resolve tied elections in some jurisdictions. Its use in politics is very old, as office holders in Ancient Athens were chosen by lot, there being no voting. Randomness can be seen as conflicting with the deterministic ideas of some religions, such as those where the universe is created by an omniscient deity who is aware of all past and future events. If the universe is regarded to have a purpose, then randomness can be seen as impossible.