Symbolic Multivariate Distribution
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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
asked 3 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
asked 3 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
asked 3 hours ago
mikadomikado
6,9371929
$endgroup$
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
probability-or-statistics symbolic
asked 3 hours ago
mikadomikado
6,9371929
asked 3 hours ago
mikadomikado
6,9371929
asked 3 hours ago
mikadomikado
6,9371929
asked 3 hours ago
mikadomikado
6,9371929
asked 3 hours ago
mikadomikado
6,9371929
6,9371929
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
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].
answered 2 hours ago
Lukas LangLukas Lang
7,45011032
$endgroup$
$begingroup$
Rather than using subscripted variables, I recommend using indexed variables and then usingFormatto display the indexed variables as subscripted variables. Subscripted variables tend to cause problems in solvers.
$endgroup$
– Bob Hanlon
35 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
31 mins ago
$begingroup$
A very useful answer, but I was hoping for an expression that worked in terms of vector and matrix inputs (of unspecified dimension).
$endgroup$
– mikado
2 mins ago
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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].
answered 2 hours ago
Lukas LangLukas Lang
7,45011032
$endgroup$
$begingroup$
Rather than using subscripted variables, I recommend using indexed variables and then usingFormatto display the indexed variables as subscripted variables. Subscripted variables tend to cause problems in solvers.
$endgroup$
– Bob Hanlon
35 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
31 mins ago
$begingroup$
A very useful answer, but I was hoping for an expression that worked in terms of vector and matrix inputs (of unspecified dimension).
$endgroup$
– mikado
2 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].
answered 2 hours ago
Lukas LangLukas Lang
7,45011032
$endgroup$
$begingroup$
Rather than using subscripted variables, I recommend using indexed variables and then usingFormatto display the indexed variables as subscripted variables. Subscripted variables tend to cause problems in solvers.
$endgroup$
– Bob Hanlon
35 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
31 mins ago
$begingroup$
A very useful answer, but I was hoping for an expression that worked in terms of vector and matrix inputs (of unspecified dimension).
$endgroup$
– mikado
2 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].
answered 2 hours ago
Lukas LangLukas Lang
7,45011032
$endgroup$
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].
answered 2 hours ago
Lukas LangLukas Lang
7,45011032
edited 27 mins ago
answered 2 hours ago
Lukas LangLukas Lang
7,45011032
answered 2 hours ago
Lukas LangLukas Lang
7,45011032
answered 2 hours ago
Lukas LangLukas Lang
7,45011032
7,45011032
$begingroup$
Rather than using subscripted variables, I recommend using indexed variables and then usingFormatto display the indexed variables as subscripted variables. Subscripted variables tend to cause problems in solvers.
$endgroup$
– Bob Hanlon
35 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
31 mins ago
$begingroup$
A very useful answer, but I was hoping for an expression that worked in terms of vector and matrix inputs (of unspecified dimension).
$endgroup$
– mikado
2 mins ago
add a comment |
$begingroup$
Rather than using subscripted variables, I recommend using indexed variables and then usingFormatto display the indexed variables as subscripted variables. Subscripted variables tend to cause problems in solvers.
$endgroup$
– Bob Hanlon
35 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
31 mins ago
$begingroup$
A very useful answer, but I was hoping for an expression that worked in terms of vector and matrix inputs (of unspecified dimension).
$endgroup$
– mikado
2 mins ago
$begingroup$
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
35 mins ago
$begingroup$
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
35 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
31 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
31 mins ago
$begingroup$
A very useful answer, but I was hoping for an expression that worked in terms of vector and matrix inputs (of unspecified dimension).
$endgroup$
– mikado
2 mins ago
$begingroup$
A very useful answer, but I was hoping for an expression that worked in terms of vector and matrix inputs (of unspecified dimension).
$endgroup$
– mikado
2 mins ago
add a comment |
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