antithetic variate to facilitate upper-stem height measurements for critical height sampling with importance sampling
Critical height sampling (CHS) estimates cubic volume per unit area by multiplying the sum of critical heights measured on trees tallied in a horizontal point sample (HPS) by the HPS basal area factor. One of the barriers to practical application of CHS is the fact that trees near the field location...
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| Published in | Canadian journal of forest research Vol. 43; no. 12; pp. 1151 - 1161 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Ottawa, ON
NRC Research Press
01.12.2013
National Research Council of Canada Canadian Science Publishing NRC Research Press |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1208-6037 0045-5067 1208-6037 |
| DOI | 10.1139/cjfr-2013-0279 |
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| Abstract | Critical height sampling (CHS) estimates cubic volume per unit area by multiplying the sum of critical heights measured on trees tallied in a horizontal point sample (HPS) by the HPS basal area factor. One of the barriers to practical application of CHS is the fact that trees near the field location of the point-sampling sample point have critical heights that occur quite high on the stem, making them difficult to view from the sample point. To surmount this difficulty, use of the âantithetic variateâ associated with the critical height together with importance sampling from the cylindrical shells integral is proposed. This antithetic variate will be u = (1 â b/B), where b is the cross-sectional area at âborderlineâ condition and B is the treeâs basal area. The cross-sectional area at borderline condition b can be determined with knowledge of the HPS gauge angle by measuring the distance to the sample tree. When the antithetic variate u is used in importance sampling, the upper-stem measurement will be low on tree stems close to the sample point and high on tree stems distant from the sample point, enhancing visibility and ease of measurement from the sample point. Computer simulations compared HPS, CHS, CHS with importance sampling (ICHS), ICHS and an antithetic variate (AICHS), and CHS with paired antithetic varariates (PAICHS) and found that HPS, ICHS, AICHS, and PAICHS were very nearly equally precise and were more precise than CHS. These results are favorable to AICHS, since it should require less time than either PAICHS or ICHS and is not subject to individual-tree volume equation bias. |
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| AbstractList | Critical height sampling (CHS) estimates cubic volume per unit area by multiplying the sum of critical heights measured on trees tallied in a horizontal point sample (HPS) by the HPS basal area factor. One of the barriers to practical application of CHS is the fact that trees near the field location of the point-sampling sample point have critical heights that occur quite high on the stem, making them difficult to view from the sample point. To surmount this difficulty, use of the âantithetic variateâ associated with the critical height together with importance sampling from the cylindrical shells integral is proposed. This antithetic variate will be u = (1 â b/B), where b is the cross-sectional area at âborderlineâ condition and B is the treeâs basal area. The cross-sectional area at borderline condition b can be determined with knowledge of the HPS gauge angle by measuring the distance to the sample tree. When the antithetic variate u is used in importance sampling, the upper-stem measurement will be low on tree stems close to the sample point and high on tree stems distant from the sample point, enhancing visibility and ease of measurement from the sample point. Computer simulations compared HPS, CHS, CHS with importance sampling (ICHS), ICHS and an antithetic variate (AICHS), and CHS with paired antithetic varariates (PAICHS) and found that HPS, ICHS, AICHS, and PAICHS were very nearly equally precise and were more precise than CHS. These results are favorable to AICHS, since it should require less time than either PAICHS or ICHS and is not subject to individual-tree volume equation bias. Critical height sampling (CHS) estimates cubic volume per unit area by multiplying the sum of critical heights measured on trees tallied in a horizontal point sample (HPS) by the HPS basal area factor. One of the barriers to practical application of CHS is the fact that trees near the field location of the point-sampling sample point have critical heights that occur quite high on the stem, making them difficult to view from the sample point. To surmount this difficulty, use of the "antithetic variate" associated with the critical height together with importance sampling from the cylindrical shells integral is proposed. This antithetic variate will be u = (1 - b/B), where b is the cross-sectional area at "borderline" condition and B is the tree's basal area. The cross-sectional area at borderline condition b can be determined with knowledge of the HPS gauge angle by measuring the distance to the sample tree. When the antithetic variate u is used in importance sampling, the upper-stem measurement will be low on tree stems close to the sample point and high on tree stems distant from the sample point, enhancing visibility and ease of measurement from the sample point. Computer simulations compared HPS, CHS, CHS with importance sampling (ICHS), ICHS and an antithetic variate (AICHS), and CHS with paired antithetic varariates (PAICHS) and found that HPS, ICHS, AICHS, and PAICHS were very nearly equally precise and were more precise than CHS. These results are favorable to AICHS, since it should require less time than either PAICHS or ICHS and is not subject to individual-tree volume equation bias.Original Abstract: L'echantillonnage de la hauteur critique (EHC) permet d'estimer le volume de bois par unite de surface en multipliant la somme des hauteurs critiques mesurees sur les arbres inventories dans un echantillonnage horizontal par point (EHP) par le facteur de prisme de l'EHP. L'un des obstacles a l'application pratique de l'EHC vient du fait que les arbres proches de l'emplacement du point d'echantillonnage ont des hauteurs critiques qui se situent assez haut sur la tige. Ceci rend les hauteurs critiques difficilement visibles a partir du point d'echantillonnage. On suggere de surmonter cette difficulte en utilisant la << variable antithetique >> associee a la hauteur critique dans l'echantillonnage par importance basee sur l'integrale d'enveloppes cylindriques. Cette variable antithetique sera u = (1 - b/B) ou b est la section transversale a la limite de demarcation et B est la surface terriere de l'arbre. La section transversale a la limite de demarcation b peut etre determinee avec le facteur de prisme de l'EHP en mesurant la distance de l'arbre echantillonne. Lorsque la variable antithetique u est utilisee dans l'echantillonnage par importance, la mesure en haut de la tige est abaissee pour les arbres proches du point d'echantillonnage et haussee pour les arbres eloignes du point d'echantillonnage. La mesure a partir du point d'echantillonnage se trouve ainsi facilitee par une meilleure visibilite de la hauteur critique. Des simulations sur ordinateur ont permis de comparer l'EHP, l'echantillonnage de la hauteur critique (EHC), l'EHC avec l'echantillonnage par importance (EHCP), l'EHCP avec une variable antithetique (EHCPA) et l'echantillonnage de la hauteur critique avec des variables antithetiques appariees (EHCAA). Les comparaisons ont permis de constater que l'EHP, l'EHCP, l'EHCPA et l'EHCAA avaient pratiquement la meme precision et qu'ils etaient plus precis que l'EHC. Ces resultats privilegient l'EHCPA qui requiert moins de temps que l'EHCAA ou l'EHCP et qui n'est pas sujet au biais de l'equation de volume des arbres individuels. [Traduit par la Redaction] Critical height sampling (CHS) estimates cubic volume per unit area by multiplying the sum of critical heights measured on trees tallied in a horizontal point sample (HPS) by the HPS basal area factor. One of the barriers to practical application of CHS is the fact that trees near the field location of the point-sampling sample point have critical heights that occur quite high on the stem, making them difficult to view from the sample point. To surmount this difficulty, use of the "antithetic variate" associated with the critical height together with importance sampling from the cylindrical shells integral is proposed. This antithetic variate will be u = (1 - b/B), where b is the cross-sectional area at "borderline" condition and B is the tree's basal area. The cross-sectional area at borderline condition b can be determined with knowledge of the HPS gauge angle by measuring the distance to the sample tree. When the antithetic variate u is used in importance sampling, the upper-stem measurement will be low on tree stems close to the sample point and high on tree stems distant from the sample point, enhancing visibility and ease of measurement from the sample point. Computer simulations compared HPS, CHS, CHS with importance sampling (ICHS), ICHS and an antithetic variate (AICHS), and CHS with paired antithetic varariates (PAICHS) and found that HPS, ICHS, AICHS, and PAICHS were very nearly equally precise and were more precise than CHS. These results are favorable to AICHS, since it should require less time than either PAICHS or ICHS and is not subject to individual-tree volume equation bias. Resume: L'echantillonnage de la hauteur critique (EHC) permet d'estimer le volume de bois par unite de surface en multipliant la somme des hauteurs critiques mesurees sur les arbres inventories dans un echantillonnage horizontal par point (EHP) par le facteur de prisme de l'EHP. L'un des obstacles a l'application pratique de l'EHC vient du fait que les arbres proches de l'emplacement du point d'echantillonnage ont des hauteurs critiques qui se situent assez haut sur la tige. Ceci rend les hauteurs critiques difficilement visibles a partir du point d'echantillonnage. On suggere de surmonter cette difficulte en utilisant la ≪ variable antithetique [much greater than] associee a la hauteur critique dans l'echantillonnage par importance basee sur l'integrale d'enveloppes cylindriques. Cette variable antithetique sera u = (1 - b/B) ou b est la section transversale a la limite de demarcation et B est la surface terriere de l'arbre. La section transversale a la limite de demarcation b peut etre determinee avec le facteur de prisme de l'EHP en mesurant la distance de l'arbre echantillonne. Lorsque la variable antithetique u est utilisee dans l'echantillonnage par importance, la mesure en haut de la tige est abaissee pour les arbres proches du point d'echantillonnage et haussee pour les arbres eloignes du point d'echantillonnage. La mesure a partir du point d'echantillonnage se trouve ainsi facilitee par une meilleure visibilite de la hauteur critique. Des simulations sur ordinateur ont permis de comparer l'EHP, l'echantillonnage de la hauteur critique (EHC), l'EHC avec l'echantillonnage par importance (EHCP), l'EHCP avec une variable antithetique (EHCPA) et l'echantillonnage de la hauteur critique avec des variables antithetiques appariees (EHCAA). Les comparaisons ont permis de constater que l'EHP, l'EHCP, l'EHCPA et l'EHCAA avaient pratiquement la meme precision et qu'ils etaient plus precis que l'EHC. Ces resultats privilegient l'EHCPA qui requiert moins de temps que l'EHCAA ou l'EHCP et qui n'est pas sujet au biais de l'equation de volume des arbres individuels. [Traduit par la Redaction] Critical height sampling (CHS) estimates cubic volume per unit area by multiplying the sum of critical heights measured on trees tallied in a horizontal point sample (HPS) by the HPS basal area factor. One of the barriers to practical application of CHS is the fact that trees near the field location of the point-sampling sample point have critical heights that occur quite high on the stem, making them difficult to view from the sample point. To surmount this difficulty, use of the “antithetic variate” associated with the critical height together with importance sampling from the cylindrical shells integral is proposed. This antithetic variate will be u = (1 − b/B), where b is the cross-sectional area at “borderline” condition and B is the tree’s basal area. The cross-sectional area at borderline condition b can be determined with knowledge of the HPS gauge angle by measuring the distance to the sample tree. When the antithetic variate u is used in importance sampling, the upper-stem measurement will be low on tree stems close to the sample point and high on tree stems distant from the sample point, enhancing visibility and ease of measurement from the sample point. Computer simulations compared HPS, CHS, CHS with importance sampling (ICHS), ICHS and an antithetic variate (AICHS), and CHS with paired antithetic varariates (PAICHS) and found that HPS, ICHS, AICHS, and PAICHS were very nearly equally precise and were more precise than CHS. These results are favorable to AICHS, since it should require less time than either PAICHS or ICHS and is not subject to individual-tree volume equation bias. Critical height sampling (CHS) estimates cubic volume per unit area by multiplying the sum of critical heights measured on trees tallied in a horizontal point sample (HPS) by the HPS basal area factor. One of the barriers to practical application of CHS is the fact that trees near the field location of the point-sampling sample point have critical heights that occur quite high on the stem, making them difficult to view from the sample point. To surmount this difficulty, use of the "antithetic variate" associated with the critical height together with importance sampling from the cylindrical shells integral is proposed. This antithetic variate will be u = (1 - b/B), where b is the cross-sectional area at "borderline" condition and B is the tree's basal area. The cross-sectional area at borderline condition b can be determined with knowledge of the HPS gauge angle by measuring the distance to the sample tree. When the antithetic variate u is used in importance sampling, the upper-stem measurement will be low on tree stems close to the sample point and high on tree stems distant from the sample point, enhancing visibility and ease of measurement from the sample point. Computer simulations compared HPS, CHS, CHS with importance sampling (ICHS), ICHS and an antithetic variate (AICHS), and CHS with paired antithetic varariates (PAICHS) and found that HPS, ICHS, AICHS, and PAICHS were very nearly equally precise and were more precise than CHS. These results are favorable to AICHS, since it should require less time than either PAICHS or ICHS and is not subject to individual-tree volume equation bias. Critical height sampling (CHS) estimates cubic volume per unit area by multiplying the sum of critical heights measured on trees tallied in a horizontal point sample (HPS) by the HPS basal area factor. One of the barriers to practical application of CHS is the fact that trees near the field location of the point-sampling sample point have critical heights that occur quite high on the stem, making them difficult to view from the sample point. To surmount this difficulty, use of the "antithetic variate" associated with the critical height together with importance sampling from the cylindrical shells integral is proposed. This antithetic variate will be u = (1 - b/B), where b is the cross-sectional area at "borderline" condition and B is the tree's basal area. The cross-sectional area at borderline condition b can be determined with knowledge of the HPS gauge angle by measuring the distance to the sample tree. When the antithetic variate u is used in importance sampling, the upper-stem measurement will be low on tree stems close to the sample point and high on tree stems distant from the sample point, enhancing visibility and ease of measurement from the sample point. Computer simulations compared HPS, CHS, CHS with importance sampling (ICHS), ICHS and an antithetic variate (AICHS), and CHS with paired antithetic varariates (PAICHS) and found that HPS, ICHS, AICHS, and PAICHS were very nearly equally precise and were more precise than CHS. These results are favorable to AICHS, since it should require less time than either PAICHS or ICHS and is not subject to individual-tree volume equation bias. [PUBLICATION ABSTRACT] |
| Abstract_FL | L’échantillonnage de la hauteur critique (EHC) permet d’estimer le volume de bois par unité de surface en multipliant la somme des hauteurs critiques mesurées sur les arbres inventoriés dans un échantillonnage horizontal par point (EHP) par le facteur de prisme de l’EHP. L’un des obstacles à l’application pratique de l’EHC vient du fait que les arbres proches de l’emplacement du point d’échantillonnage ont des hauteurs critiques qui se situent assez haut sur la tige. Ceci rend les hauteurs critiques difficilement visibles à partir du point d’échantillonnage. On suggère de surmonter cette difficulté en utilisant la « variable antithétique » associée à la hauteur critique dans l’échantillonnage par importance basée sur l’intégrale d’enveloppes cylindriques. Cette variable antithétique sera u = (1 − b/B) où b est la section transversale à la limite de démarcation et B est la surface terrière de l’arbre. La section transversale à la limite de démarcation b peut être déterminée avec le facteur de prisme de l’EHP en mesurant la distance de l’arbre échantillonné. Lorsque la variable antithétique u est utilisée dans l’échantillonnage par importance, la mesure en haut de la tige est abaissée pour les arbres proches du point d’échantillonnage et haussée pour les arbres éloignés du point d’échantillonnage. La mesure à partir du point d’échantillonnage se trouve ainsi facilitée par une meilleure visibilité de la hauteur critique. Des simulations sur ordinateur ont permis de comparer l’EHP, l’échantillonnage de la hauteur critique (EHC), l’EHC avec l’échantillonnage par importance (EHCP), l’EHCP avec une variable antithétique (EHCPA) et l’échantillonnage de la hauteur critique avec des variables antithétiques appariées (EHCAA). Les comparaisons ont permis de constater que l’EHP, l’EHCP, l’EHCPA et l’EHCAA avaient pratiquement la même précision et qu’ils étaient plus précis que l’EHC. Ces résultats privilégient l’EHCPA qui requiert moins de temps que l’EHCAA ou l’EHCP et qui n’est pas sujet au biais de l’équation de volume des arbres individuels. [Traduit par la Rédaction] |
| Audience | Academic |
| Author | Lynch, Thomas B Jeffrey H. Gove |
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| Cites_doi | 10.1139/x99-119 10.1093/forestscience/41.1.194 10.1017/S0305004100031455 10.1201/9780203498880 10.1139/x86-231 10.1016/S0378-1127(00)00601-0 10.5558/tfc49136-3 10.1139/x03-056 10.1139/x92-042 10.1002/9780470316511 10.1139/x86-096 10.1139/x01-147 10.1093/forestscience/22.3.289 10.1139/x87-219 10.1016/j.foreco.2012.06.014 |
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| Keywords | Facilitation Critical value Forestry Samplings Height Sampling Stem |
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| Snippet | Critical height sampling (CHS) estimates cubic volume per unit area by multiplying the sum of critical heights measured on trees tallied in a horizontal point... |
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| SubjectTerms | basal area Bias Biological and medical sciences Computer simulation equations Forestry Fundamental and applied biological sciences. Psychology Methods Monte Carlo method Observations Plant growth Sampling stand basal area Statistical sampling Stems Stems (Botany) Trees |
| Title | antithetic variate to facilitate upper-stem height measurements for critical height sampling with importance sampling |
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