Table 1. Prior distributions for key parameters in trend model to predict radar counts for Marbled Murrelet in British Columbia, Canada.

For the normal distribution, the 1^st parameter is the mean and the 2^nd parameter is the precision (1/ variance). For the gamma distribution, these are α and β. For the uniform these are the lower and upper bounds. For the lognormal the 1^st parameter is the natural logarithm of the median, and the 2^nd is the precision in the natural logarithm of the random variable.

Parameter	Description	Distribution	1 st param.	2 nd param.
aR	Day of year effect	Normal	0	10000
cR	Day of year effect	Normal	0	0.01
σR	Residual error variance for each region R	Gamma	0.01	0.01
t	Radar tilt coefficient	Normal	0	1
σY	Hyper parameter for standard deviation of year effects	Log-normal	2.303	1.5625
Y R,y	Year effect	Normal	0	σY
μ bo	Hyper parameter for mean of intercepts	Uniform	1	2000
σ bo	Hyper parameter for standard deviation of intercepts	Log-normal	3.91	1.5625
μ b1	Hyper parameter for mean of slopes	Normal	0	0.0001
σ b1	Hyper parameter for standard deviation of slopes	Log-normal	2.30	1.5625
bo,s	Mean count for site	Log-normal	μ bo	σ bo
b1,s	Slope for site	Normal	μ b1	σ b1