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Compute likelihood for the two-tap scenario with equal spatial variance

likelihood_2Tap_EqVar.Rd

The function computes likelihood values for the given trajectory. The code refers to the two-tap model with equal variance (spatial uncertainty) for both taps as described in Goldreich & Tong (2013), given in Formula A11.

Usage

likelihood_2Tap_EqVar(x1m, x2m, x1, x2, sigma_s)

Arguments

x1m

measured/sensed or hypothetical position of tap 1 for which the likelihood (p given the other parameters) is computed

x2m

measured/sensed or hypothetical position of tap 2

x1

(real) position of tap 1

x2

(real) position of tap 1

sigma_s

spatial uncertainty (given as a standard deviation) for the taps (same sd assumed for both positions)

Value

likelihood values (see article for details or the vignette on the two-tap scenario). If x1 and x2 are vectors, a vector of likelihood values is returned.

References

Goldreich & Tong, 2013, Frontiers in Psychology

Examples

require(rabBITS)

#XXX Example 1: compute a single point estimate XXX
likelihood_2Tap_EqVar(x1m=2, x2m=4, x1=1, x2=2, sigma_s=1)
#> [1] 0.01306423

#XXX Example 2: plot a likelihood function for combinations of tap 1 and 2 XXX
library(ggplot2)
x1_range <- c(0, 10) #range for taps
x2_range <- c(0, 10)

x1_res <- 100 #resolution for graphs
x2_res <- 100

likelihoodMat <- expand.grid(x1=seq(x1_range[1], x1_range[2], length.out=x1_res), x2=seq(x2_range[1], x2_range[2], length.out=x2_res))
likelihoodMat$l <- likelihood_2Tap_EqVar(x1m=2, x2m=4, x1=likelihoodMat$x1, x2=likelihoodMat$x2, sigma_s=1)
ggplot(likelihoodMat, aes(x=x1, y=x2, fill=l)) +
  geom_raster() +
  coord_fixed() +
  ggtitle("likelihood")