Stationary Means Research Articles

Stationary local random countable sets over the Wiener noise

The times of Brownian local minima, maxima and their union are three distinct examples of local, stationary, dense, random countable sets associated with classical Wiener noise. Being local means, roughly, determined by the local behavior of the sample paths of the Brownian motion, and stationary means invariant relative to the Lévy shifts of the sample paths. We answer to the affirmative Tsirelson’s question, whether or not there are any others, and develop some general theory for such sets. An extra ingredient to their structure, that of an honest indexation, leads to a splitting result that is akin to the Wiener–Hopf factorization of the Brownian motion at the minimum (or maximum) and has the latter as a special case. Sets admitting an honest indexation are moreover shown to have the property that no stopping time belongs to them with positive probability. They are also minimal: they do not have any non-empty proper local stationary subsets. Random sets, of the kind studied in this paper, honestly indexed or otherwise, give rise to nonclassical one-dimensional noises, generalizing the noise of splitting. Some properties of these noises and the inter-relations between them are investigated. In particular, subsets are connected to subnoises.

Tracking a Maneuvering Object by Indirect Observations with Random Delays

A mathematical model for the target tracking problem is proposed. The model makes it possible to describe conditions when the time for an observer to receive the results of indirect observations of a moving object depends not only on the state of the observation environment but also on the state of the object itself. The source of such a model is the observation process, by stationary means, of an autonomous underwater vehicle, in which the time for obtaining up-to-date data depends on the unknown distance between the object and the observer. As part of the study of the problem, the equations of the optimal Bayesian filter are obtained. But this filter is not possible to implement. For practical purposes, it is proposed to use the conditionally minimax nonlinear filter, which has shown promising results in other complex tracking models. The conditions for the filter’s evaluation and its accuracy characteristics are given. A large-scale numerical experiment illustrating the filter’s operation and the observation system’s features with random delays are described.

ՃԱՆԱՊԱՐՀԱՅԻՆ ՑԱՆՑԻ ԳՈՐԾԱՐԿՈՒՄԸ ԲՐՈՆԶ-ԵՐԿԱԹԵԴԱՐՅԱՆ ՍՅՈՒՆԻՔՈՒՄ՝ ԽՈՇՈՐ ԲՆԱԿԱՎԱՅՐԱՅԻՆ ԱԳԼՈՄԵՐԱՑԻԱՆԵՐԻ ԳՈՅՈՒԹՅԱՆ ՊԱՅՄԱՆՆԵՐՈՒՄ (ՀԱՅ.) / THE FUNCTIONING OF THE ROAD NETWORK IN SYUNIK CONDITIONED BY EXISTENCE OF LARGE SETTLEMENT AGGLOMERATIONS DURING THE BRONZE AND IRON AGES

Since the 2nd millennium BC, in the Armenian Highlands and, in particular, in the Syunik- Artsakh region, a system of regions separated by natural boundaries is being formed. These settlement systems included a central fortified settlement, satellite settlements of an open type, economic and ideological infrastructure. Thus, a multifunctional complex was being formed, including fortification systems, economic and religious complexes. Naturally, the functioning of such complexes would be impossible without the existence of stationary means of communication. The roads connected not only separate areas of the Syunik region, but were also laid in the direction of high mountain pastures. The protection of the roads was carried out both by the construction of fortresses and watchtowers along the roads, and in the sense of sacred protection: i.e., location of cemeteries and places of worship along the roads. The functioning of an extensive road network ensured the viability of large settlement agglomerations, and also contributed to the formation of unions and confederations.

Soret Driven Instability in an Anisotropic Porous Layer Saturated by a Darcy-Maxwell Nanofluid

A theoretical and numerical study has been made of a Soret driven Darcy-Maxwell anisotropic porous medium filled with nanofluid. The linear theory of stability analysis is employed and the well-known normal mode procedure is used to test the stability/instability. It is established that stationary mode Rayleigh number independent from relaxation time parameter and modified particle-density increment. The modified particle-density increment does not affect the oscillatory Rayleigh number. A comparison between an isotropic porous medium and an anisotropic porous medium has been made. The presence of nanoparticles helps in early convection while the solute parameter tries to stop early convection. The solute parameter does not change its destabilizing nature with the Soret parameter although the Soret parameter creates resistance in early convection. Soret effect increases the stationary Rayleigh number means to delay the convection. The mechanical anisotropy parameter is responsible for early convection while thermal anisotropy parameters delay the convection.

Continuous‐time multi‐type Ehrenfest model and related Ornstein–Uhlenbeck diffusion on a star graph

We deal with a continuous‐time Ehrenfest model defined over an extended star graph, defined as a lattice formed by the integers of d semiaxis joined at the origin. The dynamics on each ray are regulated by linear transition rates, whereas the switching among rays at the origin occurs according to a general stochastic matrix. We perform a detailed investigation of the transient and asymptotic behavior of this process. We also obtain a diffusive approximation of the considered model, which leads to an Ornstein–Uhlenbeck diffusion process over a domain formed by semiaxis joined at the origin, named spider. We show that the approximating process possesses a truncated Gaussian stationary density. Finally, the goodness of the approximation is discussed through comparison of stationary distributions, means, and variances.

ОСОБЛИВОСТІ ВИКОРИСТАННЯ ПОЛІЦІЄЮ АВТОМОБІЛІВ-«ФАНТОМІВ» ЯК МОБІЛЬНИХ ТЕХНІЧНИХ ЗАСОБІВ У СИСТЕМІ ЗАБЕЗПЕЧЕННЯ БЕЗПЕКИ ДОРОЖНЬОГО РУХУ (НА ПРИКЛАДІ УКРАЇНИ)

The purpose of the article is to determine on the basis of the analysis of statistical data characterizing the state of road injuries in Ukraine, the main causes of road accidents; conducting a comparative description of existing technical means of speed control; description of the specifics of the use of removable (mobile) vehicles with integrated systems for automatic safety control (speed mode) on the roads by patrol police units. To achieve this goal, scientific methods were used, such as critical analysis of special literature and specification of current requirements of regulations in the field of road safety to control the speed limit; systematization of knowledge (information) from open Internet resources and generalization of existing approaches in popular science publications to solve the raised problem in Ukraine and in the world. Results. The norms of the current legislation have been determined and analysed, which provide the possibility of fixing violations of traffic rules at stationary posts and in automatic mode. Such categories of current legislation in the field of road safety, as “system for recording administrative offenses in the field of ensuring SRT in automatic node”, “technical means (control devices)”, the procedure for their application in accordance with the law. A comparative analysis of the use of “phantom” cars abroad was conducted. The tactical and technical characteristics of domestic patrol police vehicles, which control the speed of traffic due to the built-in integrated systems, are characterised. Some legal collisions that arise when using the above-mentioned mobile devices to control the speed limit on the roads are concretised. Conclusions were made on ensuring road safety as a complex problem that requires participation in its solution at various levels of many business entities and executive bodies; different ways of speed control on roads (stationary and mobile technical means) are noted; highlighted as one of the innovations in this area the application of “phantom” cars with integrated speed control systems; the presence of such “phantom” cars disciplines drivers and requires to comply the traffic rules be them anywhere on the road network.

Features of Phacosurgery in Macular Pathology. Part 2. Сapabilities of Optical Correction

Cataracts and age-related macular degeneration (AMD) are the leading causes of blindness worldwide. The main symptoms of AMD are: a gradual decrease in visual acuity to the hundredth, metamorphosis, the appearance of a central scotoma, which reduces the quality of life of the patients and leads to disability. Prosthetic and stationary means of optical rehabilitation, such as magnifiers for the visually impaired, glasses, video systems are cumbersome and poorly functional. An alternative correction option is intraocular vision devices that improve the patient’s quality of life. The review considers various types of intraocular implants, in particular, the intraocular telescope system (intraocular miniature telescope-IMT, IOL-VIP, IOL-AMD), Fresnel lens, Lipschitz lens, Scharioth macular lens (Scharioth macula lens, SML), EyeMax Mono, LENTIS ® MAX IOL LS-313 MF80. The use of high-tech devices for the correction of visual disturbances in AMD has opened a new direction in the rehabilitation of low vision. Further study and implementation of the latest generation of “macular” lenses will improve the quality of life of patients with advanced stages of AMD.

Synthesis of an algorithm for increasing the detection range of signals from radio-electronic means by means of radio control based on the estimated-correlation-compensation processing of signals with an unknown shape and additive noise in the receiving channel

In modern conditions of rapid development of telecommunication technologies radio engineering means of different function are used everywhere in all spheres of ability to live of the person. Thus organizational-technical systems of civil appointment and power departments use the wide nomenclature of radio-electronic means of various classes with a wide spectrum of parameters, kinds of radiations and operating modes. In turn, it causes formation of difficult electromagnetic conditions in administrative-industrial regions and their near environment. The primary goal of services of radio control in these conditions is control over correctness of use by organizational-technical systems of the allocated resource of a radiofrequency spectrum and the parameters radiating of radio-electronic means. One of the main difficulties with which means of radio control in the course of the analysis of electromagnetic conditions in the set territorial area face a considerable quantity of radiating radio-electronic means with various parameters in a wide range of the relation a signal/noise, and also presence of stirring influence of any hindrances is. These factors make rigid demands to indicators of quality of functioning of panoramic detectors-direction finders which make a basis of mobile and stationary means of radio control. One of the basic indicators of quality of panoramic detectors-direction finders of means of radio control is range of detection of the radio-electronic means, defined by the set level of sensitivity and demanded values of probabilities of detection and a false alarm. Authors in article result results of working out of algorithm of increase of range of detection of signals by means of radio control on the basis of an estimated-correlation-compensatory way of measurement and indemnification of average capacity of additive hindrances in the reception channel. By results of the researches spent in article it is shown that: the increase in average capacity of cumulative external inadvertent and deliberate hindrances for the set typical initial data leads in VHF a range to reduction of range of detection of radio-electronic means not less, than in 1,4 times from the demanded; at demanded value of probability of detection, for example, and probabilities of a false alarm, at relative level of external set of a hindrance the panoramic detectors-direction finder of means of radio control with the realised procedure of measurement and indemnification of average value of capacity (dispersion) of inadvertent, deliberate hindrances and internal noise allows to lower the requirement to the threshold relation a signal/(noise) (on pressure) more, than in 1,3 times that will allow to approach value of range of detection to a reference value.

ЗАСТОСУВАННЯ ТЕХНІЧНИХ ЗАСОБІВ СЛУЖБИ ПАЛЬНОГО ПІД ЧАС ЗАПРАВКИ ВІЙСЬКОВОЇ ТЕХНІКИ

In the conditions of modern combat and change of a tactical situation before officials of service of the fuel constantly there is a task on uninterrupted providing of military units with fueland lubricants. Refueling of military equipment can be carried out both at stationary gas stations through stationary means of refueling, and with the use of mobile individual or group means ofrefueling ground equipment. The use of certain technical means during the refueling of military equipment depends on the conditions of the situation as well as on the chosen method of refueling military equipment chosen by officials of the fuel service. Refueling of aircraft may be carried out through centralized refueling facilities at stationary aerodromes or at field aerodromes using automotive refueling equipment. According to the same principle, refueling of ships is organized, which are refueled both from stationary refueling facilities and bunker ships, as well as in the use of berthless refueling facilities on the unequipped coast. The use of certain technical means depends on the method of refueling equipment, which in turn depends on the conditions of the situation. Refueling of cars is organized based on the conditions. The use of certain technical means also depends on the conditions of the situation and the terms set aside for the organization of refueling. Machinery in refueling areas should be installed in such a way that the performance of refueling facilities is used to the fullest extent with minimal movement from place to place. In addition, it is necessary to have a site that allows simultaneous refueling of several cars and provides secrecy and reliable fire safety. In addition, any method of refueling military equipment must follow the procedure for refueling equipment in order to prevent fire safety measures, as well as damage to the quality of fuel during refueling. Keywords: methods of refueling military equipment, technical means of refueling equipment, field refueling equipment, berthless refueling equipment, group refueling equipment.

New Approaches to Assessing State of Insulating Material of Traction Electric Motors of Electric Locomotives

Increasing the efficiency of functioning of railway transport in the field of cargo and passenger transportation, reducing operating costs are immediately related at present to the cost of maintaining and restoring traction rolling stock. Optimization of operating costs is possible on the basis of the transition from a scheduled preventive system of repair of traction rolling stock, based on assessment of the average statistical level of its technical condition without considering peculiarities of the operating range, to a system of repair and maintenance based on the actual technical condition, objectively determined on the basis of creation and implementation of onboard, portable and stationary means of technical diagnostics of units and assemblies, of development of a data bank on the current state of electric locomotives and their units. Power plants belong to the basic elements and units of traction rolling stock structures. The reliability and service life of traction electric motors of electric locomotives, especially winding insulation, does not meet modern requirements, and the existing systems for diagnosing the state of winding insulation do not allow providing the required level of failure detection at an early stage. To qualitatively determine the wear category of the insulating material, new approaches have been developed. They are based on the method of IR spectrophotometry based on relative rate of transmittance of electromagnetic radiation in a gas atmosphere removed from the traction motor winding. This is the basis for development and implementation of onboard system for automated monitoring of the current state of the electric motor insulation and assessment of the residual resource.

Short-Range Forecasting of Coronavirus Disease 2019 (COVID-19) During Early Onset at Various Levels of Geographic Granularity Using Seven Different Methods

Background: The coronavirus disease 2019 (COVID-19) spread rapidly across the world since its appearance in Wuhan city, Hubei province, China in December 2019. We explore the effectiveness of forecasting methods during early onset for COVID-19 case counts over the upcoming seven-days at the county, health district, and state levels. Our goal is to assess which forecasting methods can aid decision makers about anticipated one-, three-, and seven-day case growth.Methods: We apply forecasting methods across VA’s counties and independent cities, its health districts, and the state using data reported by the The New York Times. We forecast one-, three-, and seven-days forward using: (1) a naïve approach; (2) Holt-Winters exponential smoothing (HW); (3) growth rate (Growth); (4) moving average (MA); (5) autoregressive (AR); (6) autoregressive moving average (ARMA); and (7) autoregressive integrated moving average (ARIMA). Using Median Absolute Error (MdAE) and Median Absolute Percentage Error (MdAPE), we compare the resulting 216698 forecasts to VA’s historical data through April 22, 2020.Findings: Single-day MA forecast with three-day lookback obtains the lowest MdAE and is statistically significantly different than 66 percent of evaluated alternatives at each geographic level. Furthermore, methods assuming stationary means of prior days’ case counts outperform methods with assumptions of weak- or non-stationarity. Finally, for an individual forecasting method, MdAPE evaluation reveals in most cases statistically significant differences across geographic levels demonstrating that there is not a one-size-fits-all solution to short-term COVID-19 forecasting.Interpretation: For decision makers applying short-term forecasts of COVID-19: (1) MA is an effective option for forecasting cumulative case counts one-, three-, and seven-days forward; (2) methods assuming stationarity of means in prior-observations are more effective than methods assuming weak- or non-stationary means; and (3) the intended level of geographic resolution should be a factor in selecting the appropriate forecasting method.Funding Statement: This work received no external funding.Declaration of Interests: All authors declare no competing interests.

Ergodicity Analysis and Antithetic Integral Control of a Class of Stochastic Reaction Networks with Delays

Delays are important phenomena arising in a wide variety of real-world systems, including biological ones, because of diffusion/propagation effects or as simplifying modeling elements. We propose here to consider delayed stochastic reaction networks, a class of networks that has received little attention until now. We demonstrate here that by restricting the delays to be phase-type distributed, one can represent the associated delayed reaction network as a reaction network with finite-dimensional state-space. In particular, we prove, for mass-action unimolecular and certain bimolecular networks, that the delayed stochastic reaction network is ergodic if and only if the delay-free network is ergodic as well. These results demonstrate that delays cause little to no harm to the ergodicity property of reaction networks as long as the delays are phase-type distributed, and this holds regardless of the complexity of their distribution. We also prove that the presence of those delays adds convolution terms in the moment equation but does not change the value of the stationary means compared to the delay-free case. The covariance, however, is influenced by the presence of the delays. Finally, the control of a certain class of delayed stochastic reaction network using a delayed antithetic integral controller is considered. It is proven that this controller achieves its goal provided that the delay-free network satisfies the conditions of ergodicity and output-controllability.

Dynamics of a stochastic multigroup SIQR epidemic model with standard incidence rates

In this paper, we consider a stochastic multigroup SIQR epidemic model with standard incidence rates. By using the stochastic Lyapunov function method, we establish sufficient conditions for the existence of a stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for extinction of the diseases. A stationary distribution means that all the individuals can be coexistent and persistent in the long term. Finally, some examples and numerical simulations are introduced to illustrate our theoretical results.

The Gaussian Graphical Model in Cross-Sectional and Time-Series Data

ABSTRACTWe discuss the Gaussian graphical model (GGM; an undirected network of partial correlation coefficients) and detail its utility as an exploratory data analysis tool. The GGM shows which variables predict one-another, allows for sparse modeling of covariance structures, and may highlight potential causal relationships between observed variables. We describe the utility in three kinds of psychological data sets: data sets in which consecutive cases are assumed independent (e.g., cross-sectional data), temporally ordered data sets (e.g., n = 1 time series), and a mixture of the 2 (e.g., n > 1 time series). In time-series analysis, the GGM can be used to model the residual structure of a vector-autoregression analysis (VAR), also termed graphical VAR. Two network models can then be obtained: a temporal network and a contemporaneous network. When analyzing data from multiple subjects, a GGM can also be formed on the covariance structure of stationary means—the between-subjects network. We discuss the interpretation of these models and propose estimation methods to obtain these networks, which we implement in the R packages graphicalVAR and mlVAR. The methods are showcased in two empirical examples, and simulation studies on these methods are included in the supplementary materials.

Adaptive output stationary average consensus for heterogeneous unknown linear multi‐agent systems

This study deals with the output stationary average consensus problem for heterogeneous linear multi-agent systems with unknown parameters under undirected or balanced directed networks. The output stationary average consensus means that the outputs of agents reach an agreement on the average of their initial outputs. Each agent is modelled as an unknown linear system of any order (which might extensively vary between the agents) with the relative degree one or two. The agent in the network has only access to its own output and the relative outputs of its neighbours. Based on a direct model reference adaptive control scheme, a novel decentralised adaptive output consensus protocol is proposed to ensure that the output of each agent converges to the output of its reference model, as well as reaching output stationary average consensus. Finally, an illustrative example is presented to better highlight the merit of the proposed protocol.

A method of using neural fuzzy models to determine the technical state of a diesel locomotive’s electrical equipment

Equipment for carrying out onboard diagnostics is an important component in systems for controlling the state and reliability of rolling stock, in particular, that of diesel locomotives. It makes it possible to monitor a locomotive’s service quality, to detect and predict changes in its technical state without interrupting the carriage process, and to efficiently use the high-cost stationary and local diagnostic means, as well as to correct service time and volume by taking into account the real technical state. Therefore, it is important to develop methods for determining the technical state of locomotive units by using an MCS-T(N,E) (micro-processor control system) locomotive’s diagnostic subsystem of a locomotive and software for processing the measurement data. The main aim of such a method is to monitor the technical state of a locomotive’s equipment and predict changes in it. At the present time, simplified diagnostic models are used to solve such problems. However, to increase the efficiency and reliability of the process of checking complicated objects such as a locomotive, it is necessary to use more complex diagnostic models based on artificial neural networks. A way to use a neural-network method and neural fuzzy diagnostic models for diagnosing the excitation system of traction generators of modern diesel locomotives is presented in this paper. Information collected by the MCS-TP subsystem is used as diagnostic information. It is transferred online to a remote diagnostic server. The method for diagnosing the excitation system of a traction generator is checked by processing the measurement information.

Fast Algorithm for Evaluating Critical Current of High-Temperature Superconducting Pancake Coil

Second-generation (2G) high-temperature superconducting (HTS) tapes are now capable of carrying very high transport current and promising for a wide range of applications. The critical current of HTS coils is important for applications, such as superconducting electric machines, superconducting magnetic energy storage, and superconducting magnets. Therefore, precisely and quickly calculating critical current of HTS coils is very important for designing HTS devices. This paper provides a fast algorithm for evaluating critical current of HTS pancake coil. The fast algorithm is realized through a stationary model, which is based on finite element method (FEM) software. The stationary model means that the model is solved by stationary study instead of time-dependent study. To validate this method, a pancake HTS coil was wound and its critical current was measured. Meanwhile, an axial symmetric stationary model was built according to the geometry of the measured HTS coil. By comparing measured and calculated results, the effectiveness of the stationary model was demonstrated. Moreover, the stationary model is compared with H formulation model. The calculated results by the two models are nearly the same. However, by using stationary calculation, the stationary model can remarkably speed up the computational process. Due to the advantage of calculating speed, the stationary model can be used to characterize and design large-scale HTS applications.

How Investors Set Valuation Ratios Using a Micro-Founded Gordon Asset Pricing Model

A Micro-Founded Gordon Asset Pricing Model (MF-GAPM) is developed that allows calculation of the current E/P of an equity using reported data. In the original Gordon Model, the discounting is done assuming constant growth and a constant discount rate, with the simple result E/P = r - g where r is the so-called required yield and g is the growth expectation. The MF-GAPM applies the standard CRRA utility methodology to the real-world problem of investors maximizing their real returns, but in contrast to common practice in academic finance where the growth is subject to stochastic fluctuations, the MF-GAPM assumes constant growth like the original Gordon Model. It is shown that the E/P that maximizes the utility of the investors lifetime return then reduces to E/P = (γ-1)*µ where µ is the growth expectation and γ is the curvature of the investors CRRA utility function. This result can be viewed as a micro-founded Gordon Model with required yield equal r = γ*µ. An Empirical Model (Empirical Model) is developed to identify the data variables that investors use to set the MF-GAPM’s assumed parameters. The Empirical Model identifies two broad classes of variables whose variation about their own stationary means explain the variation of E/P about its mean: a sentiment variable S_N and a trailing earnings growth variable EG_N. The two data variables suggest there are two types of investors: rational investors who trade on observed earnings growth and irrational investors who trade on sentiment. Noting the natural associations, the first-order expansions of the functional relationships µ = µ(EG_N) and γ = γ(S_N) provide direct links between the data variables and the parameters of the MF-GAPM. The direct links allow price forecasts to be made using only expectations for the future values of the data variables themselves – expectations about expectations are not required. The feasibility of forecasting prices considering the Model’s StdError is discussed. The lack of randomness in the observed historical earnings growth record is discussed in an Academic Addendum as the rational for abandoning the i.i.d. lognormal growth assumption. With the inclusion of both rational and irrational agents, the MF-GAPM seeks to integrate the classical and behavioral approaches to finance.

Biology in the Anthropocene: Challenges and insights from young fossil records

With overwhelming evidence of change in habitats, biologists today must assume that few, if any, study areas are natural and that biological variability is superimposed on trends rather than stationary means. Paleobiological data from the youngest sedimentary record, including death assemblages actively accumulating on modern land surfaces and seabeds, provide unique information on the status of present-day species, communities, and biomes over the last few decades to millennia and on their responses to natural and anthropogenic environmental change. Key advances have established the accuracy and resolving power of paleobiological information derived from naturally preserved remains and of proxy evidence for environmental conditions and sample age so that fossil data can both implicate and exonerate human stressors as the drivers of biotic change and permit the effects of multiple stressors to be disentangled. Legacy effects from Industrial and even pre-Industrial anthropogenic extirpations, introductions, (de)nutrification, and habitat conversion commonly emerge as the primary factors underlying the present-day status of populations and communities; within the last 2 million years, climate change has rarely been sufficient to drive major extinction pulses absent other human pressures, which are now manifold. Young fossil records also provide rigorous access to the baseline composition and dynamics of modern-day biota under pre-Industrial conditions, where insights include the millennial-scale persistence of community structures, the dominant role of physical environmental conditions rather than biotic interactions in determining community composition and disassembly, and the existence of naturally alternating states.

Change in Peat Coverage in Danish Cultivated Soils During the Past 35 Years

Mapping the spatial and temporal changes of peatland in farming systems is crucial to the study of soil quality and productivity and the modeling of the global carbon cycle (in relation to climate change). This study compiles a contemporary map (2010) of peatland coverage (according to Kyoto protocol) across the cultivated wetlands of Denmark and compares this actual map to a historical 1975 peat coverage map using simple indicator kriging. For the contemporary peatland mapping, extensive soil sampling databases consisting of 42,568 points with 32,817 historical samples and 9,751 contemporary samples were used. These databases contain partly categorical information on parent material (organic [peat, gytje] and mineral [sand, silt and clay]) and partly continuous data (soil organic carbon, in %) reclassified into organic and mineral soils (using 12% soil organic carbon as a cutoff value). In the simple indicator kriging procedure, the values 0 and 1 were assigned to the stationary means of the indicator codes to represent two hypotheses, that is, mineral and organic (peat) soils, respectively. The collected and analyzed contemporary unbiased organic samples (measured on different rectangular grid scales of 250, 275, and 500 m) in addition to some transformed historical organic samples (according to certain decision rules) were used to estimate the recent areal coverage of peat (2010) that was equivalent to 70,176 ha, and this estimate corresponds to an indicator kriging probability of 0.35. Results revealed there has been a total areal coverage loss of 35% (37,786 ha) of the Danish organic cultivated wetlands during a period of 35 years (map 1975 had 107,962-ha coverage of peat). The peat depletion is related to peat mining and agricultural drainage/tillage activities, rather than natural geological processes.