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ABSTRACT.
Existing methods for eliminating bias due to boundary overlap suffer some disadvantages in practical use, including the need to work outside the tract, restrictions on the kinds of boundaries to which they are applicable, and the possibility of significantly increased variance as a price for unbiasedness. We propose a new walkthrough method for reducing boundary overlap bias that diminishes or eliminates the need to work outside the tract and accommodates irregular boundaries easily. Under typical conditions, the walkthrough method eliminates the boundary overlap bias associated with most objects near the border and reduces it for the remaining objects. The walkthrough method is object-centered in conception and implementation, but the measurements required are simple. The walkthrough method complements existing methods for correcting boundary overlap bias and should prove especially helpful when conditions make existing methods difficult or impossible to use.
Key Words: Forest sampling, mirage, reflection, relascope, prism cruising.
FOR. SCI. 50(4):427-435.
THE POTENTIAL FOR BIAS DUE TO BOUNDARY OVERLAP exists in nearly all types of forest sampling. The problem arises whenever objects (trees, downed logs, etc.) within the population being sampled lie close to the boundary of the tract. Ordinarily, an object is measured if a sample point falls within that object's inclusion zone. If the inclusion zone extends beyond the tract boundary, then that object will have less than its nominal probability of being selected. Objects near the boundary will thus be underrepresented (in expectation) in the sample, and the usual estimators of attributes like density, basal area, and volume will be biased downward. As Gregoire (1982) has pointed out, bias occurs whether or not sample points actually fall near the boundary; because bias is a matter of expectation, it occurs whenever objects are sufficiently near the boundary to cause boundary overlap.
A number of useful methods for correcting bias due to boundary overlap have appeared in the literature or are used in practice (see, e.g., Schreuder et al. 1993 pp. 297-301). Of these, the most widely discussed in textbooks is the mirage method introduced by Schmid-Haas (1969). However, the inability of the mirage method to deal with irregular boundaries, and with linear or pocket inclusions such as roads or landings, presents a severe limitation to its use in some settings (lies...