Random Field Approach Research Articles

A Random Field Approach to the Analysis of Field-Plot Experiments and Other Spatial Experiments

Several methods for the analysis of data from spatial experiments (e.g., agricultural field experiments) have recently been proposed. These methods attempt to account for the effect of spatial heterogeneity on the estimation of treatment contrasts; typically, this is accomplished indirectly by differencing or by using residuals from neighboring plots to construct covariates. We examine an alternative approach in which the spatial heterogeneity is modeled directly. The model underlying our approach is similar to the model underlying a geostatistical kriging analysis and, as in the latter model, the observations are regarded collectively as a partial realization of a random field. A randomization study of uniformity trial data suggests that the random field approach often provides more accurate estimates of treatment contrasts than nearest-neighbor approaches. In addition, the random field approach is devoid of ambiguities as to the handling of border plots and is generally more flexible than nearest-neighbor approaches.

A Random Field Approach to Transect Counts of Wildlife Populations

AbstractLine transect counting of a wildlife population is considered a sampling from a planar marked point process, where the marks describe the detectability of the animals. Sampling properties of transect counts and a new density estimator are derived from a counting process, which is a shot‐noise field induced by the marked point process. A general formula for the sampling variance of a transect is derived and applied to compare five common types of transects. Some stereological connections of transect sampling and density estimators are shown.

Transitions induced in a double minimum system by interaction with a quantum mechanical heat bath

A quantum mechanical treatment of a double minimum system interacting with a heat bath is presented for the purpose of interpreting experimental data on transfer kinetics in condensed hydrogen-bonded systems. The model describes the transfer motion in one or two dimensions. The heat bath is represented by a set of harmonic oscillators and the interaction by a term linear in the system coordinates and in the bath coordinates. Extending an earlier random field approach, the present treatment consistently accounts for the quantum nature of the total system. With crystalline benzoic acid dimer used as an example, the master equation for the populations of the energy levels of the hydrogen transfer motion is derived. Transition probabilities consistent with the principle of detailed balance are obtained, based on a representation with explicit off-diagonal tunnel interactions for pairs of states localized on different sides of the barrier and with diagonal terms describing the rearrangement of the heat bath as a consequence of the tunneling motion. The activation of the double minimum transfer process with increasing temperature is related to the excitation of the local vibrations in the two potential wells.

A Markov random field approach to data fusion and colour segmentation

A Markoman model is described which enables the data fusion and segmentation of multi-sensed images. The model is used to detect the boundaries and label the regions of a simple colour image. This is achieved by maximizing the conditional probability of all region labels and boundaries given an image. The assumption is made that the boundaries within a colour plane are related to those in other planes.

The effect of particle interactions on the initial susceptibility of a ferrofluid

The results are presented of a study of the variation of the initial susceptibility chi /sub 0/ of a ferrofluid with concentration. The applicability of chi /sub i/ (= chi /sub i//M/sub s/) is shown as a quality-control parameter for aggregation in magnetic fluids. An outline is presented of a random field approach to this many-fluid problem which predicts the general trend observed experimentally.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A random field approach to Bitterlich sampling

A random field approach to Bitterlich sampling

Consistency of random field specifications

In the random field approach to lattice gas models it has been shown that the one point conditional probabilities determine the finite set conditional probabilities under conditions of strict positivity and regularity. This paper considers the case when strict positivity does not obtain with families of conditional probabilities more general than the one-point conditional probabilities.

Behaviour of the charge carriers in slowly varying random field and semiphenomenological approach to the theory of electronic processes in disordered systems

A discussion is given of the behaviour of charged carriers in a disordered system with random nature of the field of force.