### Schwaferts & Augustin 2019 ### ### Imprecise Hypothesis-based Bayesian ### ### Decision Making with Simple Hypotheses. ### ### Electronic Appendix: Example ### # parameters n = 10 m = 10 N = n + m x = 9 y = 5 z = x + y # hypotheses: 0.5 vs [0.75 , 0.9] # lower bounds of LR LR_x_U = dbinom(x,n, 0.5) / dbinom(x,n, 0.75) LR_y_U = dbinom(y,m, 0.5) / dbinom(y,m, 0.9) LR_z_U = dbinom(z,N, 0.5) / dbinom(z,N, 0.9) # upper bounds of LR LR_x_L = dbinom(x,n, 0.5) / dbinom(x,n, 0.9) LR_y_L = dbinom(y,m, 0.5) / dbinom(y,m, 0.75) LR_z_L = dbinom(z,N, 0.5) / dbinom(z,N, 0.75) # imprecise likelihood ratios c(LR_x_L, LR_x_U) c(LR_y_L, LR_y_U) c(LR_z_L, LR_z_U) # updating inconsistency c(LR_y_L * LR_x_L, LR_y_U* LR_x_U) c(LR_z_L, LR_z_U) c(4.214 * 0.025, 165.4 * 0.052) # for paper: using rounded values # imprecise loss function k_L = 8 k_U = 20 # imprecise prior odds pi_L = 1 pi_U = 4 # imprecise ratio of expected posterior losses for x c(pi_L * k_L * LR_x_L, pi_U * k_U * LR_x_U) # imprecise ratio of expected posterior losses for x and y # with inconsistencies c(pi_L * k_L * LR_y_L * LR_x_L, pi_U * k_U * LR_y_U * LR_x_U) c(pi_L * k_L * 4.214 * 0.025, pi_U * k_U * 165.4 * 0.052) # for paper # imprecise ratio of expected posterior losses for z c(pi_L * k_L * LR_z_L, pi_U * k_U * LR_z_U) # arbitrary precise parameters pi = 1 k = k_L # hypotheses: 0.5 vs. 0.8 # precise likelihood ratio for x LR_x = dbinom(x,n, 0.5) / dbinom(x,n, 0.8) LR_x # precise ratio of expected posterior losses for x pi * k * LR_x