Prognostic methods

Prognosis is in its wide sense the information about future. It can be seen as a forecast of future events and future development conditions. The characteristic feature of a prognosis is its variability arising from the possibility of setting the variant objectives and methods leading to their achievement, including the probabilistic character of a prognosis. The prognosis is always evaluated by its rate of reliability, which demands the specification of information requirements and requirements for data. Utilization in practice is always presumed at a prognosis setting it apart from prediction that is the part of a scientific work and from foresight that is the general ability of a human mind for thinking about future.

Predictive method for a certain problem is chosen depending on the amount (content) and uncertainty of input information [6]. The accessibility of the input information forms a key factor for the selection of a method. As standard method for prediction are re-spected: expert opinions, both implicit and explicit with the help of expert model

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systems; comparison; field experiment; mathematic simulation; visual simulation (lay-out, photography, film, 3D model); and physical simulation (noise, air-pollution, soil column etc.).

Predictive methods are expanded to formal and informal. Formal methods recognised as proved are: exact methods; statistic methods; experimental methods; and mathe-matic simulation. Informal approach represents an engineer assessment and applica-tion of analogy.

Individual formal work procedures form the wide category of technically-methodical ways of prediction. In practice, exact methods are enabled by the formulation of a real technical idea in several variants, by the measurement of relevant values on a map basis, calculation etc. Statistic methods come out of the assembled data (gathered pieces of information) significant for a certain problem and area (surroundings). There are used scientific basics of prognosticating, the theory of rising curves and the as-sessment of probable evolution trends. By the term “prognosis” we understand a prob-able statement about events that arise in some spatial or time interval. Scientific ap-proach distinguishes 3 fundamental alternatives of a methodical apap-proach: extrapola-tion or a normative method; synthesis or a morphological method; and intuitive or a theoretical method.

However, in practise we commonly combine the extrapolation with intuition or norma-tive method with a theoretical solution. Significant importance represents a so-called phenomenological projection of forecasts, where there are used both, the empiric ex-periences acquired in the field of a researched phenomenon and the information from the theory of growing models are used. If there is the evolution (i.e. rising or falling) of a certain quantity according to time without external interference, it can be supposed that the rate of evolution is a definite function of a variable. By solving of a relevant differential equation, the law of growth can be obtained.

Experimental methods and mathematical models differ in a feature that at mathemati-cal models there is a need for a strict formulation of cause and consequence, while by experimental methods these terms don’t have to be determined. But in both cases, it is necessary to schematize (simplify) the system leading to definition of relationship cause ---> consequence. Accomplishment of experiments is deemed indispensable in all cases where there aren’t basic data at a disposition. Basics in this field considered as satisfying are predicted data acquired by a mathematical simulation, laboratory ex-periments or exex-periments in situ. Favourite are comparative case studies and terrain pilot projects in similar natural and socio-ecological conditions. In the future, the gath-ered information of realized projects and practical testing of hypothesis (database) will be a significant help. Experimental methods are divided in: illustrative or physical mod-els symbolizing an affected environment; terrain (field) experiments; and laboratory experiments.

Illustrative models provide, in a certain measure, only the visual forecast of a future situation, whereas physical models provide this forecast in the measure of a physical process. Laboratory experiments simulate biological and biochemical process, but

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often in isolation from the overall ecosystem. The aim of the field experiments and tests is a research of the real changes in the area considered.

In mathematical models, the relations between cause and consequence are repre-sented by one or several mathematical equations. Mathematical models can be: em-pirical, processional or mixed. Empiric models are based on experiments or a repeated measurement; they employ the knowledge of statistical analysis and show the relation between cause and consequence without explicitly formulated interrelations (a model of a black box). Beside the general models, special models applicable in a real area or the certain type of surround are used.

Process models (internally descriptive) lie in an explicit definition of process either with-out a reference to time (stable, constant condition) or with one (dynamic evolution).

Complexity (algorithm) of models alters from simple ones that can be solved manually, to complex dynamic and stochastic models requiring a computing technology. In this context different types of models are used:

- distributional models determining a dimensional layout (e.g. source objects, protec-tive zones, primary point field allowing the digital model of a terrain etc.),

- models of a dimensional statistic arising from the supposition that all the elements of the selective files are placed in the coordinate system; models of dimensional modifications, which are primarily represented by models of variant diffusion pro-cesses of a different type (e.g. projection of the gradient orientation and rapidity of a diffusion process by a vector field calculation from the primary point field ), - distance-decay models allowing an exact determination of so-called divided

dis-tances, safe disdis-tances, zones of an increased hazard etc., by which they simplify the resolving about the localization of other investment projects demanding a spe-cial treatment (e.g. nurseries, playgrounds etc.).

It should be noted that the behaviour of entities based on forecast models based on as-sumptions:

- the conditions that prevailed in the past, needs also to apply in the future, - the largest observed phenomena in a given time interval are independent,

- the behaviour of the biggest phenomena in a given interval will be the same in the future as in the past.

Theoretical models based on the defined theories and their solution is a set of possible scenarios, with each scenario describes the behaviour of entities under certain conditions.

For success in practice, it needs to know the full set of conditions in which the tracked entity can occur, the complete set of possible scenarios of the behaviour of the entity, and also the occurrence frequency of each scenario. Due to lack the knowledge, there are the pos-sible sudden changes in conditions, which also mean sudden changes in the behaviour of the entity. This fact means that neither the probabilistic approaches applied methodically in practice since the mid-70's the years do not provide the correct prediction for the behaviour of the entities.

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From observation of the real world we know that extreme changes and extreme phenomena occur irregularly and sparse in time. Therefore, modelling the extreme phenomena does not use already from the 70's years the methods of mathematical statistics, but it goes from the law of large numbers, a distribution describing the fluctuation of random maxim (it is suitable for modelling the extreme phenomena using the distribution of Gumbel, Fréchet and Weibull, which represent the limit distribution of the maximum values of random variables).

The theory of extreme values needs to have a time series of phenomena and commonly is used since the mid of 80s. years for natural disasters, and in the last decade and in econ-omy. In the area of technologies, it is based on more of the Weibull distribution.

In the area of technology, in which there are simulated situations that are partly random and partly under control of the operator, from 50^th years of 20th century for support of decision targeted to the management of the possible behaviour of the entities there are used Markov´

processes based on Markov´ chains. It goes on the choice from several possible options, with each option consists of a Markov´ chain.

Bayesian network is a probabilistic model, which uses a graphical representation for dis-playing the probabilistic relationships among individual phenomena. It is used for the deter-mination of the likelihood of certain phenomena which arises from the base of the theory of probability. In general, the Bayesian Networks are used for modelling across different areas, support for decision-making and for probability calculation. Bayesian statistics is a branch of modern statistics, which works with the conditional probabilities and it allows to refine the probability of initial hypothesis, how to appear more relevant realities. The core of its math-ematical apparatus is the Bayes' theorem. While the classic statistics provides the proba-bility of an event based on the known fact from the past, Bayesian statistics is used where it is not possible. Therefore, it has a very extensive use, where it works with uncertain knowledge: in finance, in management, in medicine, in criminology, and also in detecting the spam. "Bayesian approach" also has great importance in mathematical logic and the theory.