Simultaneous unbiased estimates of multiple downed wood attributes in perpendicular distance sampling

2008 ◽  
Vol 38 (7) ◽  
pp. 2044-2051 ◽  
Author(s):  
Mark J. Ducey ◽  
Michael S. Williams ◽  
Jeffrey H. Gove ◽  
Harry T. Valentine
Keyword(s):  
Surface Area ◽  
Unbiased Estimator ◽  
Distance Sampling ◽  
Area Coverage ◽  
Unbiased Estimation ◽  
General Design ◽  
Perpendicular Distance ◽  
Simple Measurement ◽  
Unbiased Estimates ◽  
Downed Wood

Perpendicular distance sampling (PDS) is a fast probability-proportional-to-size method for inventory of downed wood. However, previous development of PDS had limited the method to estimating only one variable (such as volume per hectare, or surface area per hectare) at a time. Here, we develop a general design-unbiased estimator for PDS. We then show how that estimator can be used to develop simple measurement protocols that allow simultaneous, unbiased estimation of multiple downed wood variables, including logs per hectare, length of logs per hectare, surface area or area coverage per hectare, and volume per hectare.

Assessing surface area of coarse woody debris with line intersect and perpendicular distance sampling

2005 ◽  
Vol 35 (4) ◽  
pp. 949-960 ◽  
Author(s):  
M S Williams ◽  
M J Ducey ◽  
J H Gove
Keyword(s):  
Surface Area ◽  
Coarse Woody Debris ◽  
Mean Squared Error ◽  
Woody Debris ◽  
Distance Sampling ◽  
Field Work ◽  
Single Measurement ◽  
Stem Form ◽  
Important Conclusion ◽  
Perpendicular Distance

Coarse woody debris (CWD) plays an important role in many terrestrial and aquatic ecosystem processes. In recent years, a number of new methods have been proposed to sample CWD. Of these methods, perpendicular distance sampling (PDS) is one of the most efficient methods for estimating CWD volume in terms of both estimator variance and field effort. This study extends the results for PDS to the estimation of the surface area of CWD. The PDS estimator is also compared to two line intersect sampling (LIS) estimators, where one of the LIS estimators requires the measurement of surface area on each log and the other estimates surface area using a single measurement of log circumference at the point of intersection between the log and the line. The first estimator approximates the true surface area by assuming either a conic or parabolic stem form and requires measurements of the end diameters of each log, which is more time consuming than a single measurement. The performance of the three estimators was compared using a computer simulation. The results of the simulation indicate that, given the same number of pieces of CWD sampled at each point, equal variances can be achieved with PDS using sample sizes that range from about 10% to in excess of 100% the size of a comparable LIS estimator. When the LIS estimators were compared, the estimator that required the measurement of surface area was only about 3%–6% more efficient than the alternative estimator, but the bias associated with assuming a conic or parabolic stem form ranged from roughly 5% to 15%. We conclude that PDS will generally outperform either of the LIS estimators. Another important conclusion is that the LIS estimator based on a measured surface area is likely to have a higher mean squared error than an LIS estimator that employs a single measurement of circumference. Thus, LIS sampling strategies that require the least amount of field work will often have the smallest mean square error.

Design-unbiased estimation for point-to-tree distance sampling

2006 ◽  
Vol 36 (6) ◽  
pp. 1407-1414 ◽  
Author(s):  
Christoph Kleinn ◽  
František Vilčko
Keyword(s):  
Unbiased Estimator ◽  
Distance Sampling ◽  
Spatial Arrangement ◽  
Field Application ◽  
Unbiased Estimation ◽  
Stem Density ◽  
Sample Point ◽  
Statistical Point ◽  
Tree Distance ◽  
Inclusion Zone

Point-to-tree distance sampling designs, sometimes also referred to as k-tree sampling or fixed-count sampling, are practical response design options for field sampling in forest inventories and ecological surveys. While practitioners accept and use several approaches to estimate stem density and other stand attributes, a major concern from a statistical point of view is the lack of a general unbiased estimator for this class of sampling strategies. In this paper we analyse point-to-tree distance sampling in the framework of design-based probabilistic sampling and present an unbiased estimator valid for estimation of any stand attribute. This estimator draws upon the idea of defining an inclusion zone around each tree. A tree is taken as a sample tree if a selected sample point falls into its inclusion zone. The size of the inclusion zone is therefore a measure of the individual tree's inclusion probability when sampling is done with random sample points. Once the inclusion probabilities are known for all sampled trees, the Horwitz-Thompson estimator can be used as an unbiased estimator for any stand variable. In point-to-tree distance sampling, the inclusion zone of a particular tree depends exclusively on the spatial arrangement of the neighbouring trees. Such inclusion zones are determined by k-order Voronoi polygons, where k is the number of trees being sampled per sample point. The approach, however, requires the positions of the k sample trees and a number of surrounding trees to be mapped. Field application is therefore difficult, but a comparison of plot designs by simulation studies in fully mapped stands can now also be done with an unbiased estimator for k-tree sampling.

Extracting surface area coverage by superimposing 3D scan data

1999 ◽  
Author(s):  
Peng Li ◽  
Brian D. Corner ◽  
Steven Paquette
Keyword(s):  
Surface Area ◽  
Area Coverage ◽  
3D Scan ◽  
Scan Data

Unbiased Estimation of Total Rural Loans Advanced and Incurred in an Indian State Along with Unbiased Estimation of Variance in Estimation

2017 ◽  
Vol 69 (1) ◽  
pp. 71-75
Author(s):  
Arijit Chaudhuri
Keyword(s):  
Sampling Technique ◽  
Unbiased Estimation ◽  
Approximately Unbiased ◽  
Rural Farmers ◽  
Statistical Institute ◽  
Indian State ◽  
Unbiased Estimates ◽  
Indian Statistical ◽  
Year 2000 ◽  
Estimation Of Variance

Around the year 2000, the problem of reconciling the estimate of loans advanced by the banks and the estimate of loans incurred by the rural farmers was studied in the Indian Statistical Institute. Some approximately unbiased estimates were examined along with approximately unbiased estimates of their approximate variances. Utilizing “Constrained Network” sampling technique exactly unbiased counterparts are presented as alternatives.

scholarly journals Distance-limited perpendicular distance sampling for coarse woody debris: theory and field results

2012 ◽  
Vol 86 (1) ◽  
pp. 119-128 ◽  
Author(s):  
M. J. Ducey ◽  
M. S. Williams ◽  
J. H. Gove ◽  
S. Roberge ◽  
R. S. Kenning
Keyword(s):  
Coarse Woody Debris ◽  
Woody Debris ◽  
Distance Sampling ◽  
Perpendicular Distance

A line intersect distance sampling strategy for downed wood inventory

2008 ◽  
Vol 38 (8) ◽  
pp. 2262-2273 ◽  
Author(s):  
David L.R. Affleck
Keyword(s):  
Sampling Error ◽  
Distance Sampling ◽  
Sampling Strategy ◽  
Primary Interest ◽  
Sampling Protocol ◽  
Forest Fuels ◽  
Unbiased Estimators ◽  
Transect Sampling ◽  
Selection Protocol ◽  
Unbiased Estimates

Perpendicular distance sampling (PDS) has emerged as a compelling alternative to line intersect sampling (LIS) for the inventory of forest fuels and other downed woody materials (DWM), particularly where the aggregate volume of DWM is of primary interest. This article develops a selection protocol and design-unbiased estimators for a new probability proportional-to-volume sampling strategy, termed line intersect distance sampling (LIDS). LIDS combines the distance sampling protocol of PDS with the transect sampling protocol of LIS and provides unbiased estimates of aggregate DWM volume from counts of selected logs or log fragments. Simulations indicate that LIDS along multidirectional (e.g., Y-shaped) transects should perform similarly to PDS in terms of sampling error; however, it remains unclear how LIDS and PDS compare with LIS, especially when interest is attached to multiple DWM population parameters. It is argued that LIDS will be most useful in reducing implementation errors, particularly detection errors, relative to PDS under limited visibility field conditions.

Estimating the Carbon in Coarse Woody Debris with Perpendicular Distance Sampling

2008 ◽  
pp. 73-87 ◽  
Author(s):  
Harry T. Valentine ◽  
Jeffrey H. Gove ◽  
Mark J. Ducey ◽  
Timothy G. Gregoire ◽  
Michael S. Williams
Keyword(s):  
Coarse Woody Debris ◽  
Woody Debris ◽  
Distance Sampling ◽  
Perpendicular Distance

Temperature and Nutrient Effects on Campylobacter jejuni Attachment on Multispecies Biofilms on Stainless Steel

2008 ◽  
Vol 71 (2) ◽  
pp. 271-278 ◽  
Author(s):  
SHERIASE Q. SANDERS ◽  
JOSEPH F. FRANK ◽  
JUDY W. ARNOLD
Keyword(s):  
Stainless Steel ◽  
Surface Area ◽  
Campylobacter Jejuni ◽  
Intestinal Tract ◽  
Fluorescent Protein ◽  
Area Coverage ◽  
Epifluorescence Microscopy ◽  
Nutrient Effects ◽  
Green Fluorescent ◽  
Multispecies Biofilms

Campylobacter jejuni is a thermophilic microaerophilic pathogen that is commonly found in the intestinal tract of chickens. In this study, attachment of C. jejuni 1221gfp in biofilms on stainless steel was assessed at various temperatures and with reduced nutrients. Bacteria collected from a saline rinse of processed broiler chicken carcasses were used to form initial biofilms. The whole carcass rinse (WCR) biofilms were formed by incubation of the bacteria for 16 h at 13, 20, 37, and 42°C on stainless steel coupons in tryptic soy broth (TSB). The resulting biofilms were stained with Hoechst 33258 stain and visualized by epifluorescence microscopy. WCR biofilms formed at 13°C yielded the highest surface area coverage (47.6%), and the lowest coverage (2.1%) was attained at 42°C. C. jejuni transformed to produce green fluorescent protein (gfp) was allowed to attach to the preexisting biofilms (from WCR incubated for 16 h) at each of the four temperatures, and attached cells were enumerated by visualization with an epifluorescence microscope. Attachment of C. jejuni 1221gfp did not significantly differ (P > 0.05) among the four temperatures. C. jejuni 1221gfp was cultured only from coupons with biofilms formed at 13 and 20°C. For nutrient limitation experiments, WCR biofilms were allowed to grow in 10- and 50-fold diluted TSB at 20 and 37°C for 48 h. The WCR biofilm surface area coverage (approximately 2%) was greater at 37°C than at 20°C for both TSB concentrations. C. jejuni 1221gfp was incubated with the WCR biofilm for 48 h at 20 and 37°C, and attached cells were enumerated. Attachment was significantly higher (P < 0.05) only for the treatments with 1:10 TSB at 20°C and 1:50 TSB at 37°C. Under reduced-nutrient conditions, C. jejuni 1221gfp was cultured only from biofilms formed at 20°C. Under the conditions tested, the attachment of C. jejuni 1221gfp on stainless steel and biofilms was affected by a combination of temperature and nutrient availability, but C. jejuni culturability was affected solely by temperature.

scholarly journals Unbiased estimation of the gradient of the log-likelihood in inverse problems

2021 ◽  
Vol 31 (3) ◽  
Author(s):  
Ajay Jasra ◽  
Kody J. H. Law ◽  
Deng Lu
Keyword(s):  
Numerical Approximation ◽  
Unbiased Estimation ◽  
Finite Variance ◽  
Multilevel Monte Carlo ◽  
Gradient Algorithms ◽  
Log Likelihood ◽  
Bayesian Inverse Problem ◽  
Unbiased Estimates ◽  
The Cost ◽  
Single Processor

AbstractWe consider the problem of estimating a parameter $$\theta \in \Theta \subseteq {\mathbb {R}}^{d_{\theta }}$$ θ ∈ Θ ⊆ R d θ associated with a Bayesian inverse problem. Typically one must resort to a numerical approximation of gradient of the log-likelihood and also adopt a discretization of the problem in space and/or time. We develop a new methodology to unbiasedly estimate the gradient of the log-likelihood with respect to the unknown parameter, i.e. the expectation of the estimate has no discretization bias. Such a property is not only useful for estimation in terms of the original stochastic model of interest, but can be used in stochastic gradient algorithms which benefit from unbiased estimates. Under appropriate assumptions, we prove that our estimator is not only unbiased but of finite variance. In addition, when implemented on a single processor, we show that the cost to achieve a given level of error is comparable to multilevel Monte Carlo methods, both practically and theoretically. However, the new algorithm is highly amenable to parallel computation.

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