# Define Dirichlet parameters in advance settings

**URL:** <https://discourse.mc-stan.org/t/define-dirichlet-parameters-in-advance-settings/32348>\
**Category:** Modeling\
**Tags:** dirichlet-multinomial\
**Created:** [August 4, 2023, 12:41am UTC](https://discourse.mc-stan.org/t/define-dirichlet-parameters-in-advance-settings/32348 "2023-08-04T00:41:09Z")\
**Posts on this page:** 20\
**Page:** 1

<div class="post-metadata">

**Author:** ![niro](https://avatars.discourse-cdn.com/v4/letter/n/bb73d2/32.png) [@niro](https://discourse.mc-stan.org/u/niro)\
**Post date:** [August 4, 2023, 12:41am UTC](https://discourse.mc-stan.org/t/define-dirichlet-parameters-in-advance-settings/32348/1 "2023-08-04T00:41:09Z")

</div>

Hello,

I am trying to fit a model with Dirichlet prior. However, my parameter specification is quite complex. I have three parameters, let’s say w, r and m. These three follows Dirichlet prior. For all these three parameters should be defined i times. In-other words, my parameters are wi, ri and mi where i=1:400. I can fit this prior easily as follows. (theta\_1 = (wi, ri, mi))

```stan
Data{
row_vector [3] beta1;
}
parameters {
    
     simplex [3] theta_1 [400];
  
}

model {
  // Define priors  
  theta_1 ~ dirichlet(beta1);
  
dat ~ tenismodel(theta_1);

}

```

I have done this. Now I want an advance setting than above. I want to fit parameters, theta\_1 = (wi ^j, ri^j, mi^j) . Now I have both superscript j and subscript i. As an example, when i = 1 and j = 2 I want to have parameters:

[w1^1, w1^2, r1^1, r1^2, m1^1, m1^2]

I tried to explain my problem as much as I can. If anyone have an idea how we can implement these parameter settings in stan please let me know. I really appreciate your help.

Thank You.

---

<div class="post-metadata">

**Author:** ![jsocolar](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/jsocolar/32/2486_2.png) [@jsocolar](https://discourse.mc-stan.org/u/jsocolar)\
**Post date:** [August 4, 2023, 1:17am UTC](https://discourse.mc-stan.org/t/define-dirichlet-parameters-in-advance-settings/32348/2 "2023-08-04T01:17:19Z")

</div>

I’m not 100% sure from your description what you need. Is it this (for an illustrative case where `j` ranges from 1 to 10): `simplex[3] theta_1[400, 10]`?

Note that in newer versions of Stan, this would be written as `array[400, 10] simplex[3] theta_1`

---

<div class="post-metadata">

**Author:** ![niro](https://avatars.discourse-cdn.com/v4/letter/n/bb73d2/32.png) [@niro](https://discourse.mc-stan.org/u/niro)\
**Post date:** [August 4, 2023, 2:31am UTC](https://discourse.mc-stan.org/t/define-dirichlet-parameters-in-advance-settings/32348/3 "2023-08-04T02:31:45Z")

</div>

Thanks jsocolar for the reply. Does this `simplex[3] theta_1[400, 10]` means, each parameter repeats 10 times for all 400 cases?.

---

<div class="post-metadata">

**Author:** ![jsocolar](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/jsocolar/32/2486_2.png) [@jsocolar](https://discourse.mc-stan.org/u/jsocolar)\
**Post date:** [August 4, 2023, 2:10pm UTC](https://discourse.mc-stan.org/t/define-dirichlet-parameters-in-advance-settings/32348/4 "2023-08-04T14:10:56Z")

</div>

This means that there are 4000 3-simplexes, with each simplex indexed by i and j

---

<div class="post-metadata">

**Author:** ![niro](https://avatars.discourse-cdn.com/v4/letter/n/bb73d2/32.png) [@niro](https://discourse.mc-stan.org/u/niro)\
**Post date:** [August 4, 2023, 5:35pm UTC](https://discourse.mc-stan.org/t/define-dirichlet-parameters-in-advance-settings/32348/5 "2023-08-04T17:35:56Z")

</div>

Thanks, I will run this and check is that what I want.

---

<div class="post-metadata">

**Author:** ![niro](https://avatars.discourse-cdn.com/v4/letter/n/bb73d2/32.png) [@niro](https://discourse.mc-stan.org/u/niro)\
**Post date:** [August 6, 2023, 12:11pm UTC](https://discourse.mc-stan.org/t/define-dirichlet-parameters-in-advance-settings/32348/6 "2023-08-06T12:11:32Z")

</div>

Hi Jsocolar,

I tried this method and still I am getting an error. “Ill-typed arguments to ‘~’ statement. No distribution ‘dirichlet’ was found with the correct signature.”

Think this is because my beta1. I supplied it as an vector in R. `b1 <- c(rep(0.0078, 81), rep(0.0913,81), rep(0.9009,81))`. How do we need to supply beta 1 to the model?. Is that a matrix?.

> [@niro](#):
>
> ```no-highlight
> 
> Data{
> row_vector [3] beta1;
> }
> parameters {
>     
> simplex [3] theta_1 [400, 81];
>   
> }
> model {
> // Define priors  
> theta_1 ~ dirichlet(beta1);
>   
> dat ~ tenismodel(theta_1);
> 
> }
> 
> ```

---

<div class="post-metadata">

**Author:** ![jsocolar](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/jsocolar/32/2486_2.png) [@jsocolar](https://discourse.mc-stan.org/u/jsocolar)\
**Post date:** [August 6, 2023, 4:57pm UTC](https://discourse.mc-stan.org/t/define-dirichlet-parameters-in-advance-settings/32348/7 "2023-08-06T16:57:29Z")

</div>

It’s hard to say for sure since you are just showing parts of your model definition, but most straightforwardly, `beta1` would also be a 400 x 81 array of 3-vectors.

---

<div class="post-metadata">

**Author:** ![niro](https://avatars.discourse-cdn.com/v4/letter/n/bb73d2/32.png) [@niro](https://discourse.mc-stan.org/u/niro)\
**Post date:** [August 7, 2023, 12:04am UTC](https://discourse.mc-stan.org/t/define-dirichlet-parameters-in-advance-settings/32348/8 "2023-08-07T00:04:22Z")

</div>

Hi Jsocolar,

This following is my full code.

```stan

// Create user define function

functions{

  real tenismodel_lpdf(matrix dat, vector[] theta, vector[] alpha, int[] ServerID, int[] ReceiverID, int[] t1,
  int[] t2, int[] t3){

  vector[rows(dat)] prob;
  real t;
  real x;
  int s;
  int re;
  real out;
  real a;
  real f;
  real ws;
  real rs;
  real ms;
  real wr;
  real rr;
  real mr;
  real pr;
    
  for (i in 1:rows(dat)){
    
    t <- dat[i, 1];
    x <- dat[i, 2];
    s <- ServerID[i];
    re <- ReceiverID[i];
    a <- theta[s, 1];
    f <- theta[s, 2];

    
    if(x == -1){
      
      prob[i] <- f; 
      
    }else if(t == 1){
      
      prob[i] <- a^x * f^(1 - x);

    }else if(fmod(t, 2) == 0){
     
     vector [t1[i]] p1 ;

     for(j in 1:t1[i]) {
       
        rs <- alpha[s, j];
        rr <- alpha[re, j];
        
        p1[j] <- (rr)^(2*j) * (rs)^(2*j + 1);
     }
     
       pr <- prod(p1);
      
        ws <- alpha[s, 1];
        ms <- alpha[s, 3];
        wr <- alpha[re, 1];
        mr <- alpha[re, 3];
      prob[i] <- ((1- a - f) * pr * (mr)^x * (wr)^(1-x)); 
    
    }else {
      
      vector [t2[i]] p1;
     
     for(j in 1:t2[i]) {
       
        rs <- alpha[s, j];
        rr <- alpha[re, j];
        
        p1[j] <- (rr)^(2*j);
     }
     
     vector [t3[i]] p2;
     
     for(j in 1:t3[i]) {
       
        rs <- alpha[s, j];
        rr <- alpha[re, j];
        
        p2[j] <- (rs)^(2*j + 1);
     }
     
     pr <- prod(p1) * prod(p2);
     ws <- alpha[s, 1];
     ms <- alpha[s, 3];
     wr <- alpha[re, 1];
     mr <- alpha[re, 3];
     
       prob[i] <- ((1- a - f) * pr * (ms)^(1 - x) * (ws)^x);
    }
  }

  out <- sum(log(prob));
  return out;

 }
}

// The input data is a vector 'y' of length 'N'.
data {
  int N; // number of observations (rally lengths)
  int M; // number of players
  int t1; // number of touches
  int t2; // number of touches
  int t3; // number of touches
  matrix [N, 2] dat; // touches, indicator, servereID and receiverID 
  int ServerID [N];
  int ReceiverID [N];
  int <lower = 2> m; 
  row_vector [3] beta1;
  row_vector [3] beta2;

}

parameters {
    
     simplex [m] theta_1 [M, 81];
     
     simplex [m] theta_2 [M, 81];
  
}

// The model to be estimated.
model {
  // Define priors

  
  theta_1 ~ dirichlet(beta1);

  theta_2 ~ dirichlet(beta2);

  dat ~ tenismodel(theta_1, theta_2, ServerID, ReceiverID, t1, t2, t3);

}

```

To feed values for the model, I use the following R code:

```plaintext

fit_model3 <- stan(file = 'R/model_3.stan',
                   data = list(N = len, M = num_players,
                               dat = as.matrix(men_data),
                               ServerID = ServerID,
                               ReceiverID = ReceiverID,
                               m = 3,
                               beta1 = b1,
                               beta2 = b2,
                               t1 = t1,
                               t2 = t2, t3 = t3), 
                   chains = 1, iter = 1000)

```

where my b1 and b2 are:

```plaintext
vector_1 <- rep(0.0078, 81)
vector_2 <- rep(0.0913,81)
vector_3 <- rep(0.9009,81)
b1<- array(c(vector_1,vector_2, vector_3))
b2<- array(c(vector_1,vector_2, vector_3))

```

I do not think the way I defined b1 and b2 is correct.

---

<div class="post-metadata">

**Author:** ![jsocolar](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/jsocolar/32/2486_2.png) [@jsocolar](https://discourse.mc-stan.org/u/jsocolar)\
**Post date:** [August 7, 2023, 12:17am UTC](https://discourse.mc-stan.org/t/define-dirichlet-parameters-in-advance-settings/32348/9 "2023-08-07T00:17:53Z")

</div>

Which dirichlet parameters are meant to apply to which elements of `theta_1`?

---

<div class="post-metadata">

**Author:** ![niro](https://avatars.discourse-cdn.com/v4/letter/n/bb73d2/32.png) [@niro](https://discourse.mc-stan.org/u/niro)\
**Post date:** [August 7, 2023, 12:39am UTC](https://discourse.mc-stan.org/t/define-dirichlet-parameters-in-advance-settings/32348/10 "2023-08-07T00:39:36Z")

</div>

For theta\_1, m is number of parameters, which is 3; M are the number of players and 81 is how many time each parameter repeats. According to my example, i = M and j = 81.

---

<div class="post-metadata">

**Author:** ![jsocolar](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/jsocolar/32/2486_2.png) [@jsocolar](https://discourse.mc-stan.org/u/jsocolar)\
**Post date:** [August 7, 2023, 2:04am UTC](https://discourse.mc-stan.org/t/define-dirichlet-parameters-in-advance-settings/32348/11 "2023-08-07T02:04:52Z")

</div>

> [@niro](#):
>
> For theta\_1, m is number of parameters

Right now `theta_1` involves m\times M \times 81 parameters. Are you now saying that it should contain only 3 parameters, or do you still mean 3 parameters for each of the m \times M elements? Do you wish for all of those M \times m simplexes to all have the same Dirichlet prior whose parameters are given by the single 3-vector `beta_1`?

---

<div class="post-metadata">

**Author:** ![niro](https://avatars.discourse-cdn.com/v4/letter/n/bb73d2/32.png) [@niro](https://discourse.mc-stan.org/u/niro)\
**Post date:** [August 7, 2023, 2:37am UTC](https://discourse.mc-stan.org/t/define-dirichlet-parameters-in-advance-settings/32348/12 "2023-08-07T02:37:41Z")

</div>

Yes, I have three parameters in my model. As an example I have three parameters a, b, c. I want a to have aij where i = M and j = 81. Also, bij again i = M and j = 81 and cij where i = M and j = 81. Is this possible? . I think this statement is true ‘’ Do you wish for all of those  
M  
×  
m  
simplexes to all have the same Dirichlet prior whose parameters are given by the single 3-vector beta\_1?‘’

---

<div class="post-metadata">

**Author:** ![jsocolar](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/jsocolar/32/2486_2.png) [@jsocolar](https://discourse.mc-stan.org/u/jsocolar)\
**Post date:** [August 7, 2023, 3:58am UTC](https://discourse.mc-stan.org/t/define-dirichlet-parameters-in-advance-settings/32348/13 "2023-08-07T03:58:19Z")

</div>

I think the most straight forward solution here is not to worry about vectorizing and to write

```stan
for(i in 1:m){
  for(j in 1:M){
    theta_1[i,j] ~ dirichlet(beta_1);
  }
}

```

---

<div class="post-metadata">

**Author:** ![niro](https://avatars.discourse-cdn.com/v4/letter/n/bb73d2/32.png) [@niro](https://discourse.mc-stan.org/u/niro)\
**Post date:** [August 8, 2023, 1:17pm UTC](https://discourse.mc-stan.org/t/define-dirichlet-parameters-in-advance-settings/32348/14 "2023-08-08T13:17:12Z")

</div>

Hi Jscolar,

```stan

data {
  int N; // number of observations (rally lengths)
  int M; // number of players
  int t1; // number of touches
  int t2; // number of touches
  int t3; // number of touches
  int K;
  matrix [N, 2] dat; // touches, indicator, servereID and receiverID 
  int ServerID [N];
  int ReceiverID [N];
  int <lower = 2> m; 
  row_vector [3] beta1;
  row_vector [3] beta2;

}

parameters {
    
     simplex [m] theta_1 [M];
     
     simplex [m] theta_2 [M];
  
}

// The model to be estimated.
model {
  // Define priors

  for(i in 1:M){
  for(j in 1:K){
    theta_1[i,j] ~ dirichlet(beta1);
  }
}

  for(i in 1:M){
  for(j in 1:K){
    theta_2[i,j] ~ dirichlet(beta2);
  }
}

  dat ~ tenismodel(theta_1, theta_2, ServerID, ReceiverID, t1, t2, t3);

}

```

No I gave beta1 and beta2 as vectors in R. “beta1 ← c(0.0815, 0.3814, 0.5371)  
beta2 ← c(0.0715, 0.7424, 0.1861)”.

But I am getting the same error. The error is:

`Ill-typed arguments to '~' statement. No distribution 'dirichlet' was found with the correct signature.`

What am I doing in correct when defining Dirichlet parameters?. My M is number of players; which is i and my K is j ; how many times each parameter repeats. That means each of the three parameters in beta1 is repeating K times.

---

<div class="post-metadata">

**Author:** ![ssp3nc3r](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/ssp3nc3r/32/120_2.png) [@ssp3nc3r](https://discourse.mc-stan.org/u/ssp3nc3r)\
**Post date:** [August 8, 2023, 1:41pm UTC](https://discourse.mc-stan.org/t/define-dirichlet-parameters-in-advance-settings/32348/15 "2023-08-08T13:41:01Z")

</div>

You have a few problems here.

On the error, the signature for the [dirichlet distribution takes vectors](https://mc-stan.org/docs/functions-reference/dirichlet-distribution.html), not row vectors.

Once you resolve the above compile error, and assuming the rest is ok to compile, you will also have a runtime error for dimension mismatch between your data declaration `row_vector[3] beta1` and what you are giving the model with `b1`, which is a longer than 3 vector.

---

<div class="post-metadata">

**Author:** ![jsocolar](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/jsocolar/32/2486_2.png) [@jsocolar](https://discourse.mc-stan.org/u/jsocolar)\
**Post date:** [August 8, 2023, 1:48pm UTC](https://discourse.mc-stan.org/t/define-dirichlet-parameters-in-advance-settings/32348/16 "2023-08-08T13:48:44Z")

</div>

> [@ssp3nc3r](#):
>
> On the error, the signature for the [dirichlet distribution takes vectors](https://mc-stan.org/docs/functions-reference/dirichlet-distribution.html), not row vectors.

From the doc:

```no-highlight
The Dirichlet probability functions are overloaded to allow the simplex θ 
and prior counts (plus one) α to be vectors or row vectors (or to mix the 
two types).

```

---

<div class="post-metadata">

**Author:** ![ssp3nc3r](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/ssp3nc3r/32/120_2.png) [@ssp3nc3r](https://discourse.mc-stan.org/u/ssp3nc3r)\
**Post date:** [August 8, 2023, 1:57pm UTC](https://discourse.mc-stan.org/t/define-dirichlet-parameters-in-advance-settings/32348/17 "2023-08-08T13:57:47Z")

</div>

Ah, I think you have theta as an array of simplexes,

> [@niro](#):
>
> `simplex [m] theta_2 [M];`

but you loop through theta twice, leaving only a real for the dirichlet, which expects the simplex,

```no-highlight
for(i in 1:M){
  for(j in 1:K){
    theta_1[i,j] ~ dirichlet(beta1);
  }
}

```

---

<div class="post-metadata">

**Author:** ![jsocolar](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/jsocolar/32/2486_2.png) [@jsocolar](https://discourse.mc-stan.org/u/jsocolar)\
**Post date:** [August 8, 2023, 2:10pm UTC](https://discourse.mc-stan.org/t/define-dirichlet-parameters-in-advance-settings/32348/18 "2023-08-08T14:10:37Z")

</div>

@niro previously you had theta as a 2-dimensional array of 3-simplexes, but now you have a 1-dimensional array of 3-simplexes. Which do you intend?

---

<div class="post-metadata">

**Author:** ![niro](https://avatars.discourse-cdn.com/v4/letter/n/bb73d2/32.png) [@niro](https://discourse.mc-stan.org/u/niro)\
**Post date:** [August 8, 2023, 2:41pm UTC](https://discourse.mc-stan.org/t/define-dirichlet-parameters-in-advance-settings/32348/19 "2023-08-08T14:41:10Z")

</div>

Jscolar, I think I should explain my question again. May be it is not clear here. This is what I want.

Let’s say I have four players in my data set, i.e M = 4, and I need to estimate three parameters for each of these players (m = 3). Let’s say they are a, b, c. These three parameters should repeat for each player 2 times (k = 2). So my “a” would be;

player 1 - a11, a12  
player2- a21, a22  
player3- a31, a32  
player4- a41, a42

Also, for next parameter b;

player 1 - b11, b12  
player2- b21, b22  
player3- b31, b32  
player4- b41, b42

For the last one c also as above.

So I need to set prior distribution of these to Dirichlet distribution. This is my problem.

---

<div class="post-metadata">

**Author:** ![jsocolar](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/jsocolar/32/2486_2.png) [@jsocolar](https://discourse.mc-stan.org/u/jsocolar)\
**Post date:** [August 8, 2023, 3:58pm UTC](https://discourse.mc-stan.org/t/define-dirichlet-parameters-in-advance-settings/32348/20 "2023-08-08T15:58:03Z")

</div>

Yup, so in your most recent Stan code, you declared a one-dimensional array of simplexes, but what you want is a two-dimensional array of simplexes.

[Next page](https://discourse.mc-stan.org/t/define-dirichlet-parameters-in-advance-settings/32348.md?page=2)