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Symbolic Multivariate Distribution

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2

$begingroup$

If I try to input a symbolic multivariate distribution, I do not get a useful result.

PDF[MultinormalDistribution[m, S], x]



(* During evaluation of MultinormalDistribution::vrprm: The value m at position 1 in MultinormalDistribution[m,S] is expected to be a list of real numbers. *)



(* During evaluation of MultinormalDistribution::vrprm: The value m at position 1 in MultinormalDistribution[m,S] is expected to be a list of real numbers.*)

(* PDF[MultinormalDistribution[m, S], x] *)

Clearly, Mathematica could return an appropriate symbolic expression. Is there any way of making it do so?

probability-or-statistics symbolic

share|improve this question

asked 2 hours ago

mikadomikado

6,9371929

$endgroup$

add a comment | 

2

$begingroup$

If I try to input a symbolic multivariate distribution, I do not get a useful result.

PDF[MultinormalDistribution[m, S], x]



(* During evaluation of MultinormalDistribution::vrprm: The value m at position 1 in MultinormalDistribution[m,S] is expected to be a list of real numbers. *)



(* During evaluation of MultinormalDistribution::vrprm: The value m at position 1 in MultinormalDistribution[m,S] is expected to be a list of real numbers.*)

(* PDF[MultinormalDistribution[m, S], x] *)

Clearly, Mathematica could return an appropriate symbolic expression. Is there any way of making it do so?

probability-or-statistics symbolic

share|improve this question

asked 2 hours ago

mikadomikado

6,9371929

$endgroup$

add a comment | 

$begingroup$

If I try to input a symbolic multivariate distribution, I do not get a useful result.

PDF[MultinormalDistribution[m, S], x]



(* During evaluation of MultinormalDistribution::vrprm: The value m at position 1 in MultinormalDistribution[m,S] is expected to be a list of real numbers. *)



(* During evaluation of MultinormalDistribution::vrprm: The value m at position 1 in MultinormalDistribution[m,S] is expected to be a list of real numbers.*)

(* PDF[MultinormalDistribution[m, S], x] *)

Clearly, Mathematica could return an appropriate symbolic expression. Is there any way of making it do so?

probability-or-statistics symbolic

share|improve this question

asked 2 hours ago

mikadomikado

6,9371929

$endgroup$

PDF[MultinormalDistribution[m, S], x]



(* During evaluation of MultinormalDistribution::vrprm: The value m at position 1 in MultinormalDistribution[m,S] is expected to be a list of real numbers. *)



(* During evaluation of MultinormalDistribution::vrprm: The value m at position 1 in MultinormalDistribution[m,S] is expected to be a list of real numbers.*)

(* PDF[MultinormalDistribution[m, S], x] *)

share|improve this question

asked 2 hours ago

mikadomikado

6,9371929

share|improve this question

asked 2 hours ago

mikadomikado

6,9371929

asked 2 hours ago

mikadomikado

6,9371929

asked 2 hours ago

mikadomikado

6,9371929

1 Answer
1

active

oldest

votes

5

$begingroup$

You need to supply Mathematica with the structure of your variables:

(* dimension of distribution *)

n = 2;



PDF[

 MultinormalDistribution[

  Array[Subscript[m, ##] &, n],

  Array[Subscript[S, Sequence @@ Sort@{##}] &, {n, n}]

  ],

 Array[Subscript[x, ##] &, n]

 ]

We use Array to construct variables of the form Subscript[var,i,j,…] (you can of course use any other form that is more convenient). Note that S is explicitly made symmetric by sorting the indices. The code works without this, but this way there are no "fake" parameters.

Note: As pointed out by @BobHanlon in the comments, Subscript can often cause issues if used blindly. For actual use, it is much safer to simply use indexed variables such as Array[x, n].

share|improve this answer

edited 20 mins ago

answered 2 hours ago

Lukas LangLukas Lang

7,44011032

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Rather than using subscripted variables, I recommend using indexed variables and then using Format to display the indexed variables as subscripted variables. Subscripted variables tend to cause problems in solvers.
  $endgroup$
  – Bob Hanlon
  28 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I am aware of that - I just thought that for a quick demonstration, it would be good enough and it's easy to read. But I will add a comment to the answer to point out potential issues.
  $endgroup$
  – Lukas Lang
  25 mins ago
  

  
  
  
  

add a comment | 

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5

$begingroup$

You need to supply Mathematica with the structure of your variables:

(* dimension of distribution *)

n = 2;



PDF[

 MultinormalDistribution[

  Array[Subscript[m, ##] &, n],

  Array[Subscript[S, Sequence @@ Sort@{##}] &, {n, n}]

  ],

 Array[Subscript[x, ##] &, n]

 ]

We use Array to construct variables of the form Subscript[var,i,j,…] (you can of course use any other form that is more convenient). Note that S is explicitly made symmetric by sorting the indices. The code works without this, but this way there are no "fake" parameters.

Note: As pointed out by @BobHanlon in the comments, Subscript can often cause issues if used blindly. For actual use, it is much safer to simply use indexed variables such as Array[x, n].

share|improve this answer

edited 20 mins ago

answered 2 hours ago

Lukas LangLukas Lang

7,44011032

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Rather than using subscripted variables, I recommend using indexed variables and then using Format to display the indexed variables as subscripted variables. Subscripted variables tend to cause problems in solvers.
  $endgroup$
  – Bob Hanlon
  28 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I am aware of that - I just thought that for a quick demonstration, it would be good enough and it's easy to read. But I will add a comment to the answer to point out potential issues.
  $endgroup$
  – Lukas Lang
  25 mins ago
  

  
  
  
  

add a comment | 

5

$begingroup$

You need to supply Mathematica with the structure of your variables:

(* dimension of distribution *)

n = 2;



PDF[

 MultinormalDistribution[

  Array[Subscript[m, ##] &, n],

  Array[Subscript[S, Sequence @@ Sort@{##}] &, {n, n}]

  ],

 Array[Subscript[x, ##] &, n]

 ]

We use Array to construct variables of the form Subscript[var,i,j,…] (you can of course use any other form that is more convenient). Note that S is explicitly made symmetric by sorting the indices. The code works without this, but this way there are no "fake" parameters.

Note: As pointed out by @BobHanlon in the comments, Subscript can often cause issues if used blindly. For actual use, it is much safer to simply use indexed variables such as Array[x, n].

share|improve this answer

edited 20 mins ago

answered 2 hours ago

Lukas LangLukas Lang

7,44011032

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Rather than using subscripted variables, I recommend using indexed variables and then using Format to display the indexed variables as subscripted variables. Subscripted variables tend to cause problems in solvers.
  $endgroup$
  – Bob Hanlon
  28 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I am aware of that - I just thought that for a quick demonstration, it would be good enough and it's easy to read. But I will add a comment to the answer to point out potential issues.
  $endgroup$
  – Lukas Lang
  25 mins ago
  

  
  
  
  

add a comment | 

$begingroup$

You need to supply Mathematica with the structure of your variables:

(* dimension of distribution *)

n = 2;



PDF[

 MultinormalDistribution[

  Array[Subscript[m, ##] &, n],

  Array[Subscript[S, Sequence @@ Sort@{##}] &, {n, n}]

  ],

 Array[Subscript[x, ##] &, n]

 ]

We use Array to construct variables of the form Subscript[var,i,j,…] (you can of course use any other form that is more convenient). Note that S is explicitly made symmetric by sorting the indices. The code works without this, but this way there are no "fake" parameters.

Note: As pointed out by @BobHanlon in the comments, Subscript can often cause issues if used blindly. For actual use, it is much safer to simply use indexed variables such as Array[x, n].

share|improve this answer

edited 20 mins ago

answered 2 hours ago

Lukas LangLukas Lang

7,44011032

$endgroup$

(* dimension of distribution *)

n = 2;



PDF[

 MultinormalDistribution[

  Array[Subscript[m, ##] &, n],

  Array[Subscript[S, Sequence @@ Sort@{##}] &, {n, n}]

  ],

 Array[Subscript[x, ##] &, n]

 ]

share|improve this answer

edited 20 mins ago

answered 2 hours ago

Lukas LangLukas Lang

7,44011032

answered 2 hours ago

Lukas LangLukas Lang

7,44011032

answered 2 hours ago

Lukas LangLukas Lang

7,44011032