Bayesian functional regression as an alternative statistical analysis of high-throughput phenotyping data of modern agriculture

Montesinos-López, Abelardo; Montesinos-López, Osval A.; de los Campos, Gustavo; Crossa, José; Burgueño, Juan; Luna-Vazquez, Francisco Javier

doi:10.1186/s13007-018-0314-7

Plant Methods

Table 4 Prediction accuracy of grain yield with Pearson’s correlation for the 7 proposed methods, under BayesA, BayesB and Bayes Lasso (BL) for three numbers of basis (5, 29 and 51)

From: Bayesian functional regression as an alternative statistical analysis of high-throughput phenotyping data of modern agriculture

Method	Parameter	BayesA									BayesB									BayesLasso									Average
		Number of basis									Number of basis									Number of basis
		5			29			51			5			29			51			5			29			51
		Pearson’s correlation									Pearson’s correlation									Pearson’s correlation
M1	Mean	0.501	a	A	0.501	a	A	0.501	a	A	0.510	a	A	0.510	a	A	0.510	a	A	0.494	a	A	0.494	a	A	0.494	a	A	0.501	a
	SE	0.022			0.022			0.022			0.020			0.020			0.020			0.022			0.022			0.022			0.021
M2	Mean	0.469	a	A	0.499	a	A	0.511	a	A	0.476	a	A	0.507	a	A	0.508	a	A	0.474	a	A	0.498	a	A	0.504	a	A	0.494	a
	SE	0.023			0.024			0.021			0.027			0.020			0.023			0.216			0.022			0.024			0.023
M3	Mean	0.486	a	A	0.508	a	A	0.508	a	A	0.485	a	A	0.507	a	A	0.503	a	A	0.482	a	A	0.504	a	A	0.504	a	A	0.499	a
	SE	0.020			0.025			0.025			0.020			0.024			0.026			0.020			0.026			0.026			0.024
M4	Mean	0.482	a	A	0.503	a	A	0.510	a	A	0.482	a	A	0.504	a	A	0.513	a	A	0.478	a	A	0.497	a	A	0.506	a	A	0.497	a
	SE	0.023			0.023			0.024			0.023			0.024			0.025			0.023			0.025			0.021			0.024
M5	Mean	0.486	a	A	0.505	a	A	0.507	a	A	0.487	a	A	0.511	a	A	0.513	a	A	0.483	a	A	0.505	a	A	0.496	a	A	0.499	a
	SE	0.012			0.024			0.024			0.020			0.025			0.025			0.021			0.021			0.026			0.023
M6	Mean	0.470	a	A	0.499	a	A	0.510	a	A	0.476	a	A	0.500	a	A	0.511	a	A	0.474	a	A	0.498	a	A	0.504	a	A	0.493	a
	SE	0.022			0.024			0.021			0.027			0.023			0.022			0.022			0.022			0.024			0.023
M7	Mean	0.486	a	A	0.508	a	A	0.507	a	A	0.485	a	A	0.509	a	A	0.505	a	A	0.482	a	A	0.504	a	A	0.504	a	A	0.499	a
	SE	0.020			0.025			0.024			0.020			0.025			0.023			0.020			0.026			0.026			0.023
		Implementation Time									Implementation Time									Implementation Time
M1	Mean_T	30.911	a	A	30.911	a	A	30.911	a	A	30.911	a	A	30.911	a	A	30.911	a	A	30.911	a	A	30.911	a	A	30.911	a	A	30.911	a
	SE_T	2.16			2.16			2.16			2.16			2.16			2.16			2.16			2.16			2.16			2.16
M2	Mean_T	9.180	c	C	11.233	c	C	11.106	de	A	10.170	c	B	12.160	c	B	11.093	c	A	12.720	c	A	15.340	b	A	9.900	c	A	11.430	c
	SE_T	0.08			0.05			0.08			0.02			0.2			0.54			0.03			0.08			0.22			1.02
M3	Mean_T	9.230	c	B	10.826	c	C	10.910	e	A	9.893	c	B	12.176	c	B	10.973	c	A	12.190	c	A	15.113	bc	A	9.840	c	A	11.240	c
	SE_T	0.2			0.22			0.06			0.1			0.2			0.64			0.34			0.17			0.07			1
M4	Mean_T	30.110	a	B	29.920	a	AB	27.186	b	A	30.110	a	B	26.746	b	B	26.310	b	AB	36.213	a	A	32.083	a	A	21.390	b	B	28.890	ab
	SE_T	1.08			1			0.05			0.9			0.03			0.94			1.46			0.78			1.73			2.46
M5	Mean_T	26.720	b	B	26.426	b	B	26.633	c	A	26.620	b	B	26.463	b	B	26.030	b	A	32.390	b	A	31.776	a	A	21.463	b	B	27.170	b
	SE_T	0.08			0.14			0.18			0.13			0.2			0.6			0.3			0.8			1.62			1.87
M6	Mean_T	8.060	c	C	9.423	c	C	11.353	d	A	8.676	c	B	10.433	d	B	11.980	c	A	10.806	c	A	13.360	bc	A	10.256	c	A	10.480	c
	SE_T	0.1			0.11			0.05			0.06			0.11			0.27			0.14			0.04			1.85			1.05
M7	Mean_T	7.970	c	C	9.610	c	C	11.196	de	A	8.796	c	B	10.583	d	B	11.973	c	A	10.943	c	A	13.083	c	A	10.060	c	A	10.460	c
	SE_T	0.16			0.07			0.03			0.08			0.04			0.7			0.05			0.25			1.66			1.01

Mean is the average Pearson’s correlation and SE is the standard error. Mean_T and SE_T are the average and standard error (in seconds) for implementing each scenario. The average column was calculated across the numbers of basis of the three methods by row. Different lowercase letters by the columns indicate statistical differences between methods with the Tukey test at 5% level of significance. Different uppercase letters by the rows indicate statistical differences between regularization methods with the Tukey test at 5% level of significance

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ISSN: 1746-4811

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