I have implemented two models for signal detection theory, namely I defined two likelihoods f_1(y|\theta), and f_2(y|\theta), where y denotes data and \theta a model parameter.
The data y consists of 6 non-netagive valued random variables, i.e., y=(H_1,H_2,H_3,F_1,F_2,F_3) which can be displayed by the following table.
Consider two datasets y_1 and y_2, one of which is obtained as the perturvation of the other.
data y_1
Confidence Level | Number of True Positives | Number of False Positives |
---|---|---|
3 = definitely present | H_{3}=97 | F_{3}=0 |
2 = equivocal | H_{2}=32 | F_{2}=\color{red}{0} |
1 = questionable | H_{1}=31 | F_{1}=74 |
data y_2
Confidence Level | Number of True Positives | Number of False Positives |
---|---|---|
3 = definitely present | H_{3}=97 | F_{3}=0 |
2 = equivocal | H_{2}=32 | F_{2}=\color{red}{1} |
1 = questionable | H_{1}=31 | F_{1}=74 |
Because these two datasets are similar, so I expect that the posterior estimates is also similar. But, in one model f_1(y|\theta), the estimates or posterior distribution is unstable and esimates (such as posterior means or posterior variance) are dramtically changed as follows.
Estimates for data y_1
Param name | mean | se_mean | sd |
---|---|---|---|
z[1] | -5.924416e-01 | 1.185005e-02 | 0.12219574 |
z[2] | 8.760078e+305 | NaN | Inf |
z[3] | 1.860283e+306 | NaN | Inf |
Estimates for data y_2
Param name | mean | se_mean | sd |
---|---|---|---|
z[1] | -6.197717e-01 | 6.744095e-03 | 1.213770e-01 |
z[2] | 2.440500e+00 | 4.749197e-02 | 5.032560e-01 |
z[3] | 6.120099e+00 | 1.652269e-01 | 1.383218e+00 |
So, I want to quantify this robustness.
So my question is :
Is there any famous way to show this robustness?
or any charcteristics for robustness or books?
The codes is open to public, if necesarry, I show it.
To tell the truth, my new model has robustness, so I want to show this robusness as a venefit of my new model.
Is there another question on Bayesian analysis.
In the above fitting, some constant posterior chains appear, then R hat is NaN, but when I visualize the estimates with constant chains, the estimates looks reasonable, because the fitted curve are close to data-points. So, How should we consider these constant chains.
So, another question is:
Are fitted estimates not reliable if it includes constant chains?