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Compute parameters of the posterior distribution for the two-tap scenario with unequal spatial variance

posterior_params_2Tap_UneqVar.Rd

The function computes parameters of the 2-dimensional posterior distrbution, namely, the posterior modes for both dimensions (corresponding to taps 1 and tap 2), the variance, and correlation. The code refers to the two-tap model with unequal variance (spatial uncertainties) for both taps as described in Goldreich & Tong (2013), given in Formula A19.

Usage

posterior_params_2Tap_UneqVar(x1m, x2m, time_t, sigma_s1, sigma_s2, sigma_v)

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

time_t

speed prior (in units of space per time; given as a standard deviation)

sigma_s1

spatial uncertainty (given as a standard deviation) for tap 1

sigma_s2

spatial uncertainty (given as a standard deviation) for tap 2

sigma_v

speed prior (in units of space per time; given as a standard deviation)

Value

a list containing the posterior modes, the variances, and the correlation.

References

Goldreich & Tong, 2013, Frontiers in Psychology

Examples

#posterior parameters for the given parameters...
posterior_params_2Tap_UneqVar(x1m=2, x2m=4, time_t=0.1, sigma_s=1, sigma_s2=2, sigma_v=10)
#> $x1_star
#> [1] 2.333333
#> 
#> $x2_star
#> [1] 2.666667
#> 
#> $x1_sigma_square
#> [1] 0.8333333
#> 
#> $x2_sigma_square
#> [1] 1.333333
#> 
#> $correlation
#> [1] 0.6324555
#>