包含一系列离散值的JAGS模型的Stan版本 - 是否可能?

时间:2015-01-15 12:43:20

标签: bayesian mcmc stan

我试图在斯坦运行这个模型。我有一个正在运行的JAGS版本(返回高度自相关的参数),我知道如何将其表示为双指数(具有两个速率)的CDF,这可能会毫无问题地运行。但是,我想将此版本作为类似但更复杂的模型的起点。

到目前为止,我怀疑Stan这样的模型是不可能的。也许是因为通过取一个布尔值的总和引入的离散性,Stan可能无法计算梯度。

有没有人知道是这种情况,还是我在这个模型中以错误的方式做了其他事情?我将我得到的错误粘贴到模型代码下面。

非常感谢提前 扬

Model:

data {
    int y[11]; 
    int reps[11];
    real soas[11]; 

}
parameters {
    real<lower=0.001,upper=0.200> v1;
    real<lower=0.001,upper=0.200> v2;

}


model {
    real dif[11,96];
    real cf[11];

    real p[11];

    real t1[11,96];
    real t2[11,96];

    for (i in 1:11){
        for (r in 1:reps[i]){     
            t1[i,r]  ~ exponential(v1);
            t2[i,r]  ~ exponential(v2);
            dif[i,r] <-  (t1[i,r]+soas[i]<=(t2[i,r]));

            }
        cf[i] <- sum(dif[i]);
        p[i]  <-cf[i]/reps[i];
        y[i] ~ binomial(reps[i],p[i]); 
    }

}

这是一些虚拟数据:

psy_dat = { 
         'soas' :  numpy.array(range(-100,101,20)),
            'y' :  [47, 46, 62, 50, 59, 47, 36, 13, 7, 2, 1],
         'reps' :  [48, 48, 64, 64, 92, 92, 92, 64, 64, 48, 48]
          }

以下是错误:

DIAGNOSTIC(S) FROM PARSER:
Warning (non-fatal): Left-hand side of sampling statement (~) contains a non-linear transform of a parameter or local variable.
You must call increment_log_prob() with the log absolute determinant of the Jacobian of the transform.
Sampling Statement left-hand-side expression:
get_base1(get_base1(t1,i,"t1",1),r,"t1",2) ~ exponential_log(...)
Warning (non-fatal): Left-hand side of sampling statement (~) contains a non-linear transform of a parameter or local variable.
You must call increment_log_prob() with the log absolute determinant of the Jacobian of the transform.
Sampling Statement left-hand-side expression:
get_base1(get_base1(t2,i,"t2",1),r,"t2",2) ~ exponential_log(...)

在运行时:

Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
 stan::prob::exponential_log(N4stan5agrad3varE): Random variable is nan:0, but must not be nan!
 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
 Rejecting proposed initial value with zero density.


Initialization between (-2, 2) failed after 100 attempts. 
 Try specifying initial values, reducing ranges of constrained values, or   reparameterizing the model

以下是该模型的JAGS版本:

   model {
   for ( n in 1 : N  ) { 
     for (r in 1 : reps[n]){
       t1[r,n] ~ dexp(v1)
       t2[r,n] ~ dexp(v2)
       c[r,n] <- (1.0*((t1[r,n]+durs[n])<=t2[r,n]))
     } 
     p[n] <- max((min(sum(c[,n]) /  (reps[n]),0.99999999999999)),   1-0.99999999999999)) 
     y[n] ~ dbin(p[n],reps[n])
   }

   v1 ~ dunif(0.0001,0.2)
   v2 ~ dunif(0.0001,0.2)
   }

关于min()和max():请参阅此帖子https://stats.stackexchange.com/questions/130978/observed-node-inconsistent-when-binomial-success-rate-exactly-one?noredirect=1#comment250046_130978

1 个答案:

答案 0 :(得分:1)

我仍然不确定你想要估计什么型号(如果你发布JAGS代码最好),但你上面的东西在Stan中不起作用。在您必须声明然后定义对象的意义上,Stan更接近C ++。在Stan程序中,您有两个声明 real t1[11,96]; real t2[11,96]; 但没有t1t2的定义。因此,当你这样做时,他们会被NaN初始化 t1[i,r] ~ exponential(v1); 被解析为类似的东西 for(i in 1:11) for(r in 1:reps[i]) lp__ += log(v1) - v1 * NaN 其中lp__是一个内部符号,它保存了log-posterior的值,后者变为NaN,并且不能对参数进行Metropolis风格的更新。

也许您认为t1t2是未知参数,在这种情况下,它们应该在parameters块中声明。以下[EDITED] Stan程序是有效的并且应该有效,但它可能不是您想到的程序(它对我来说没有多大意义,dif中的不连续性可能会阻止Stan采样从这个后验分布有效)。 data { int<lower=1> N; int y[N]; int reps[N]; real soas[N]; } parameters { real<lower=0.001,upper=0.200> v1; real<lower=0.001,upper=0.200> v2; real t1[N,max(reps)]; real t2[N,max(reps)]; } model { for (i in 1:N) { real dif[reps[i]]; for (r in 1:reps[i]) { dif[r] <- (t1[i,r]+soas[i]) <= t2[i,r]; } y[i] ~ binomial(reps[i], (1.0 + sum(dif)) / (1.0 + reps[i])); } to_array_1d(t1) ~ exponential(v1); to_array_1d(t2) ~ exponential(v2); }