Problems in connecting two different distributions with each other for a regression of Markov model.

9 views
Skip to first unread message

Jan Münch

unread,
May 23, 2017, 8:42:20 AM5/23/17
to Stan users mailing list
Hey Stan Team and discussion participians,
one of my toy models for inferencing Markov Models of Ion channels Looks like this. (See below)
It works fine. (As long as I exclude probabilties = 0 or 1 for the binominal Distribution. The derivative of the log probabilty seems to be infinit there.?)

But in the real data I not going to see y_t but some y_gaus ~ normal(y_t, sigma). Are finitie mixtures here the right way to go? Are there better ways?

My data will be something like

p(t) = 1- exp(-theta*t)+....
n_open ~ Binomial(N_channel, p(t))
I ~ normal(Const * n_open, sigma)

I would like to infer p(t) via Theta  (or more complex Sums of exponentials)  and n_open and N_channel even though they are discrete. The const will probably come from different Data.

Thanks alot for any hints.

Jan Münch



data {

int<lower=1> N_data; // number of data points
int<lower=0, upper = 1000> y_t[N_data]; // array observations ever element bigger als 0 to 20 binomainal draw(20, theta)
real<lower=0, upper = 10> time[N_data];
int N_channel;
}

transformed data{ // ... declarations ... statements ...
}

parameters { // The parameters we want to inference by via Stan
simplex[2] mu;
real<lower = 0, upper = 5> theta[2];
}

transformed parameters { // ... declarations ... statements ...


real<lower = 0, upper = 1> probabilty[N]; // fitted values

for(i in 1:N)
probabilty[i] = 1 - mu[1] * exp(-theta[1] * time[i])- mu[2]* exp(-theta[2]*time[i]);


}

model {
theta[1] ~ uniform(0.0,3);
theta[2] ~ uniform(2.0,5);
y_t ~ binomial(N_channel, probabilty);
//y_gaus ~ normal(y_t,sigma);

}
generated quantities { // ... declarations ... statements ...


}
"""
Reply all
Reply to author
Forward
0 new messages