Table 4:
Fitting results for quadratic variance models (Model #4 in Table 1) in both straight and circular tunnel tasks on Zhou and Ren’s steering law dataset. For each type of distribution, we use Steering law (Equation 1) to predict the mean (or location) parameter, and quadratic variance model (#4) to predict the variance (or scale) parameter, as explained in Table 2. a and b are parameters of Steering law, and c, and d are parameters of variance models. Parameter estimations are shown in mean and 95% credible interval of posterior distributions. Fitness results are reported in AIC and WAIC metrics.
| Distribution Model | Model Parameters (Mean and 95% Credible Interval) | Information Criteria | ||||||
|---|---|---|---|---|---|---|---|---|
| Variance Model | Distribution Type | a | b | c | d | k | AIC | WAIC |
|
σ2 = c + d · ID2 (Straight tunnel) |
Gaussian | 0.53 [0.47, 0.59] | 0.029 [0.026, 0.032] | 0.133 [0.111, 0.158] | 0.0002 [0.0002, 0.0003] | N/A | 12252.0 | 12249.2 |
| Truncated Gaussian | 0.492 [0.424, 0.557] | 0.029 [0.026, 0.033] | 0.162 [0.13, 0.201] | 0.0002 [0.0001, 0.0003] | N/A | 12223.2 | 12220.7 | |
| Lognormal | 0.526 [0.465, 0.589] | 0.029 [0.026, 0.033] | 0.14 [0.102, 0.182] | 0.0003 [0.0002, 0.0005] | N/A | 12128.4 | 12124.3 | |
| Gamma | 0.532 [0.475, 0.587] | 0.029 [0.025, 0.032] | 0.12 [0.097, 0.146] | 0.0002 [0.0002, 0.0003] | N/A | 12120.5 | 12116.2 | |
| Extreme value | 0.512 [0.452, 0.569] | 0.03 [0.026, 0.033] | 0.111 [0.088, 0.137] | 0.0003 [0.0002, 0.0004] | N/A | 12129.4 | 12124.9 | |
| exGaussian | 0.44 [0.377, 0.5] | 0.035 [0.031, 0.04] | 0.06 [0.037, 0.086] | 0.00006 [0.00004, 0.00008] | 0.04 [0.04, 0.05] | 12193.7 | 12194.7 | |
|
σ2 = c + d · ID2 (Circular tunnel) |
Gaussian | 0.646 [0.552, 0.74] | 0.085 [0.08, 0.09] | 0.419 [0.356, 0.489] | 0.0004 [0.0003, 0.0006] | N/A | 13058.7 | 13055.4 |
| Truncated Gaussian | 0.587 [0.48, 0.69] | 0.086 [0.081, 0.092] | 0.483 [0.406, 0.574] | 0.0003 [0.0002, 0.0005] | N/A | 13040.1 | 13039.9 | |
| Lognormal | 0.608 [0.509, 0.71] | 0.087 [0.081, 0.093] | 0.36 [0.274, 0.463] | 0.0008 [0.0005, 0.0011] | N/A | 12959.3 | 12957.5 | |
| Gamma | 0.637 [0.545, 0.73] | 0.085 [0.08, 0.091] | 0.344 [0.276, 0.417] | 0.0006 [0.0004, 0.0008] | N/A | 12954.4 | 12951.5 | |
| Extreme value | 0.55 [0.46, 0.65] | 0.091 [0.085, 0.097] | 0.258 [0.196, 0.327] | 0.0011 [0.0009, 0.0014] | N/A | 12974.1 | 12971.1 | |
| exGaussian | 0.342 [0.131, 0.652] | 0.107 [0.085, 0.124] | 0.119 [0.001, 0.369] | 0.0002 [0.00006, 0.0004] | 0.03 [0.02, 0.05] | 13039.6 | 13074.5 | |