Bayesian Evaluation of Smartphone Applications for Forest Inventories in Small Forest Holdings
Abstract
:1. Introduction
2. Materials and Methods
2.1. Study Area and Field Measurements
2.2. Bayesian and Frequentist Paired Sample t-Test
2.3. Bayesian Informative Hypothesis Evaluation (Bain)
3. Results
3.1. Differences in the Number of Stems per Hectare between TRESTIMA and MOTI
3.2. Differences in Stand Basal Area between TRESTIMA and MOTI
3.3. Informative Hypotheses
4. Discussion
5. Conclusions
Funding
Acknowledgments
Conflicts of Interest
References
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Paired Sample t-Test | The Bain Paired Sample t-Test | |||
---|---|---|---|---|
Hypotheses | H0: NTRESTIMA = NMOTI. The null hypothesis that the population mean of differences in N between the two applications equals. 0. | H0: GTRESTIMA = GMOTI. The null hypothesis that the population mean of differences in G between the two applications equals 0. | H2: NTRESTIMA > NMOTI. The hypothesis that the population mean of the TRESTIMA estimates is greater than the population mean of the MOTI estimates. | H2: GTRESTIMA > GMOTI. The hypothesis that the population mean of the TRESTIMA estimates is greater than the population mean of the MOTI estimates. |
H1: NTRESTIMA ≠ NMOTI. Two-sided alternative hypothesis that the population mean of differences in N between the two applications does not equal 0. | H1: GTRESTIMA ≠ GMOTI. Two-sided alternative hypothesis that the population mean of differences in G between the two applications does not equal 0. | H3: NTRESTIMA < NMOTI. The hypothesis that the population mean of the TRESTIMA estimates is lower than the population mean of the MOTI estimates. | H3: GTRESTIMA < GMOTI. The hypothesis that the population mean of the TRESTIMA estimates is lower than the population mean of the MOTI estimates. | |
Bayesian approach | BF01 in Bayesian paired sample t-test | BF23 in the Bayesian informative hypotheses evaluation (bain) paired sample t-test | ||
BFab: The bigger the BFab, the greater the strength of the belief that Ha is true. | ||||
Frequentist approach | p-value in paired sample t-test, the Vovk–Sellke maximum p –ratio (VS-MPR) and the Frequentist type I error probability (α(p)) | N/A | ||
p-value: The smaller the p-value, the smaller the probability of the t-statistic being more extreme than or equal to the observed t in the test. | N/A | |||
VS–MPR: The bigger the VS–MPR, the more likely it is that the p-value occurs under H1 than under H0. | ||||
α(p): The bigger the α(p), the greater the probability of false rejection of H0. |
N | Mean | Median | SD | SE | p-Value of Shapiro–Wilk | |
---|---|---|---|---|---|---|
TRESTIMA_N (/ha) | 4 | 924.5 | 947.5 | 130.4 | 65.2 | 0.77 |
MOTI_N (/ha) | 4 | 618.8 | 593.5 | 112.5 | 56.3 | 0.42 |
TRESTIMA_N–MOTI_N (/ha) | 4 | 305.8 | 308.0 | 149.7 | 74.8 | 0.43 |
TRESTIMA_G (m2/ha) | 4 | 39.8 | 40.7 | 8.2 | 4.1 | 0.86 |
MOTI_G (m2/ha) | 4 | 34.0 | 31.5 | 8.5 | 4.3 | 0.36 |
TRESTIMA_G–MOTI_G (m2/ha) | 4 | 5.8 | 4.0 | 5.0 | 2.5 | 0.19 |
TRESTIMA_G (m2/ha) | 61 | 41.2 | 41.2 | 15.3 | 2.0 | 0.37 |
MOTI_G (m2/ha) | 61 | 35.5 | 34.0 | 11.7 | 1.5 | 0.00 |
TRESTIMA_G–MOTI_G (m2/ha) | 61 | 5.7 | 7.6 | 17.7 | 2.3 | 0.71 |
95% CI for Effect Size | ||||||||
---|---|---|---|---|---|---|---|---|
Test | Statistic | df | p | VS-MPR 1 | Effect Size | Lower | Upper | |
TRESTIMA_N−MOTI_N | Student | 4.09 | 3 | 0.03 | 3.83 | 2.04 | 0.19 | 3.85 |
Wilcoxon | 1.83 | 0.13 | 1.42 | 1.00 | 1.00 | 1.00 | ||
TRESTIMA_G−MOTI_G | Student | 2.28 | 3 | 0.11 | 1.54 | 1.14 | −0.21 | 2.41 |
Sign | 1.5 | 0.13 | 1.42 | 1.00 | 1.00 | 1.00 | ||
TRESTIMA_G−MOTI_G | Student | 2.52 | 60 | 0.01 | 6.00 | 0.32 | 0.06 | 0.58 |
Hypothesis 1 | n | BF | Posterior Probability |
---|---|---|---|
H2: NTRESTIMA > NMOTI | 4 | 45,529.8 | 0.9999 |
H3: NTRESTIMA < NMOTI | 4 | 0.0000 | |
H2: GTRESTIMA > GMOTI | 4 | 88.1 | 0.9888 |
H3: GTRESTIMA < GMOTI | 4 | 0.0112 | |
H2: GTRESTIMA > GMOTI | 61 | 168.5 | 0.9941 |
H3: GTRESTIMA < GMOTI | 61 | 0.0059 |
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Ficko, A. Bayesian Evaluation of Smartphone Applications for Forest Inventories in Small Forest Holdings. Forests 2020, 11, 1148. https://doi.org/10.3390/f11111148
Ficko A. Bayesian Evaluation of Smartphone Applications for Forest Inventories in Small Forest Holdings. Forests. 2020; 11(11):1148. https://doi.org/10.3390/f11111148
Chicago/Turabian StyleFicko, Andrej. 2020. "Bayesian Evaluation of Smartphone Applications for Forest Inventories in Small Forest Holdings" Forests 11, no. 11: 1148. https://doi.org/10.3390/f11111148