Plotting absorbing state probabilities from state 1
I have the following transition matrix:
[ScriptCapitalP] = DiscreteMarkovProcess[1, {{0., 0.5, 0., 0., 0.5, 0., 0., 0., 0., 0.}, {0., 0., 0.5, 0., 0., 0.5, 0., 0., 0., 0.}, {0., 0., 0., 0.5, 0., 0., 0.5, 0., 0., 0.}, {0., 0., 0., 1., 0., 0., 0., 0., 0., 0.}, {0., 0., 0., 0., 0., 0.5, 0., 0.5, 0., 0.}, {0., 0., 0., 0., 0., 0., 0.5, 0., 0.5, 0.}, {0., 0., 0., 0., 0., 0., 1., 0., 0., 0.}, {0., 0., 0., 0., 0., 0., 0., 0., 0.5, 0.5}, {0., 0., 0., 0., 0., 0., 0., 0., 1., 0.}, {0., 0., 0., 0., 0., 0., 0., 0., 0., 1.}}]
Visually, it looks as shown at the bottom.
Looking at the graph, I can see the absorbing states easily, and I can calculate individual probabilities of reaching a particular absorbing state from state 1. For example, from state 1 to state 9:
PDF[[ScriptCapitalP][∞], 9]
However, this manual process is hardly practical with larger matrices.
So, what I wish to achieve is an automatic computation of all absorbing state probabilities from state 1, so that I can finally plot these.
How might that be achieved?
plotting markov-chains markov-process
edited Dec 1 at 16:32
kglr
176k9198404
asked Dec 1 at 14:38
user120911
58418
add a comment |
I have the following transition matrix:
[ScriptCapitalP] = DiscreteMarkovProcess[1, {{0., 0.5, 0., 0., 0.5, 0., 0., 0., 0., 0.}, {0., 0., 0.5, 0., 0., 0.5, 0., 0., 0., 0.}, {0., 0., 0., 0.5, 0., 0., 0.5, 0., 0., 0.}, {0., 0., 0., 1., 0., 0., 0., 0., 0., 0.}, {0., 0., 0., 0., 0., 0.5, 0., 0.5, 0., 0.}, {0., 0., 0., 0., 0., 0., 0.5, 0., 0.5, 0.}, {0., 0., 0., 0., 0., 0., 1., 0., 0., 0.}, {0., 0., 0., 0., 0., 0., 0., 0., 0.5, 0.5}, {0., 0., 0., 0., 0., 0., 0., 0., 1., 0.}, {0., 0., 0., 0., 0., 0., 0., 0., 0., 1.}}]
Visually, it looks as shown at the bottom.
Looking at the graph, I can see the absorbing states easily, and I can calculate individual probabilities of reaching a particular absorbing state from state 1. For example, from state 1 to state 9:
PDF[[ScriptCapitalP][∞], 9]
However, this manual process is hardly practical with larger matrices.
So, what I wish to achieve is an automatic computation of all absorbing state probabilities from state 1, so that I can finally plot these.
How might that be achieved?
plotting markov-chains markov-process
edited Dec 1 at 16:32
kglr
176k9198404
asked Dec 1 at 14:38
user120911
58418
add a comment |
I have the following transition matrix:
[ScriptCapitalP] = DiscreteMarkovProcess[1, {{0., 0.5, 0., 0., 0.5, 0., 0., 0., 0., 0.}, {0., 0., 0.5, 0., 0., 0.5, 0., 0., 0., 0.}, {0., 0., 0., 0.5, 0., 0., 0.5, 0., 0., 0.}, {0., 0., 0., 1., 0., 0., 0., 0., 0., 0.}, {0., 0., 0., 0., 0., 0.5, 0., 0.5, 0., 0.}, {0., 0., 0., 0., 0., 0., 0.5, 0., 0.5, 0.}, {0., 0., 0., 0., 0., 0., 1., 0., 0., 0.}, {0., 0., 0., 0., 0., 0., 0., 0., 0.5, 0.5}, {0., 0., 0., 0., 0., 0., 0., 0., 1., 0.}, {0., 0., 0., 0., 0., 0., 0., 0., 0., 1.}}]
Visually, it looks as shown at the bottom.
Looking at the graph, I can see the absorbing states easily, and I can calculate individual probabilities of reaching a particular absorbing state from state 1. For example, from state 1 to state 9:
PDF[[ScriptCapitalP][∞], 9]
However, this manual process is hardly practical with larger matrices.
So, what I wish to achieve is an automatic computation of all absorbing state probabilities from state 1, so that I can finally plot these.
How might that be achieved?
plotting markov-chains markov-process
edited Dec 1 at 16:32
kglr
176k9198404
asked Dec 1 at 14:38
user120911
58418
I have the following transition matrix:
[ScriptCapitalP] = DiscreteMarkovProcess[1, {{0., 0.5, 0., 0., 0.5, 0., 0., 0., 0., 0.}, {0., 0., 0.5, 0., 0., 0.5, 0., 0., 0., 0.}, {0., 0., 0., 0.5, 0., 0., 0.5, 0., 0., 0.}, {0., 0., 0., 1., 0., 0., 0., 0., 0., 0.}, {0., 0., 0., 0., 0., 0.5, 0., 0.5, 0., 0.}, {0., 0., 0., 0., 0., 0., 0.5, 0., 0.5, 0.}, {0., 0., 0., 0., 0., 0., 1., 0., 0., 0.}, {0., 0., 0., 0., 0., 0., 0., 0., 0.5, 0.5}, {0., 0., 0., 0., 0., 0., 0., 0., 1., 0.}, {0., 0., 0., 0., 0., 0., 0., 0., 0., 1.}}]
Visually, it looks as shown at the bottom.
Looking at the graph, I can see the absorbing states easily, and I can calculate individual probabilities of reaching a particular absorbing state from state 1. For example, from state 1 to state 9:
PDF[[ScriptCapitalP][∞], 9]
However, this manual process is hardly practical with larger matrices.
So, what I wish to achieve is an automatic computation of all absorbing state probabilities from state 1, so that I can finally plot these.
How might that be achieved?
plotting markov-chains markov-process
plotting markov-chains markov-process
edited Dec 1 at 16:32
kglr
176k9198404
asked Dec 1 at 14:38
user120911
58418
edited Dec 1 at 16:32
kglr
176k9198404
asked Dec 1 at 14:38
user120911
58418
edited Dec 1 at 16:32
kglr
176k9198404
edited Dec 1 at 16:32
kglr
176k9198404
edited Dec 1 at 16:32
kglr
176k9198404
176k9198404
asked Dec 1 at 14:38
user120911
58418
asked Dec 1 at 14:38
user120911
58418
asked Dec 1 at 14:38
user120911
58418
58418
add a comment |
add a comment |
1 Answer
1
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oldest
votes
You can use MarkovProcessProperties
absorbingStateProbs1[p_] := Extract @@ (MarkovProcessProperties[
p, #] & /@ {"ReachabilityProbability", "AbsorbingClasses"});
absorbingStateProbs1@[ScriptCapitalP]
{0.125, 0.375, 0.375, 0.125}
Alternatively,
absorbingStateProbs2[p_] := PDF[p[∞], #] & /@
Flatten[MarkovProcessProperties[p, "AbsorbingClasses"]]
absorbingStateProbs2@[ScriptCapitalP]
{0.125, 0.375, 0.375, 0.125}
answered Dec 1 at 16:44
kglr
176k9198404
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
You can use MarkovProcessProperties
absorbingStateProbs1[p_] := Extract @@ (MarkovProcessProperties[
p, #] & /@ {"ReachabilityProbability", "AbsorbingClasses"});
absorbingStateProbs1@[ScriptCapitalP]
{0.125, 0.375, 0.375, 0.125}
Alternatively,
absorbingStateProbs2[p_] := PDF[p[∞], #] & /@
Flatten[MarkovProcessProperties[p, "AbsorbingClasses"]]
absorbingStateProbs2@[ScriptCapitalP]
{0.125, 0.375, 0.375, 0.125}
answered Dec 1 at 16:44
kglr
176k9198404
add a comment |
You can use MarkovProcessProperties
absorbingStateProbs1[p_] := Extract @@ (MarkovProcessProperties[
p, #] & /@ {"ReachabilityProbability", "AbsorbingClasses"});
absorbingStateProbs1@[ScriptCapitalP]
{0.125, 0.375, 0.375, 0.125}
Alternatively,
absorbingStateProbs2[p_] := PDF[p[∞], #] & /@
Flatten[MarkovProcessProperties[p, "AbsorbingClasses"]]
absorbingStateProbs2@[ScriptCapitalP]
{0.125, 0.375, 0.375, 0.125}
answered Dec 1 at 16:44
kglr
176k9198404
add a comment |
You can use MarkovProcessProperties
absorbingStateProbs1[p_] := Extract @@ (MarkovProcessProperties[
p, #] & /@ {"ReachabilityProbability", "AbsorbingClasses"});
absorbingStateProbs1@[ScriptCapitalP]
{0.125, 0.375, 0.375, 0.125}
Alternatively,
absorbingStateProbs2[p_] := PDF[p[∞], #] & /@
Flatten[MarkovProcessProperties[p, "AbsorbingClasses"]]
absorbingStateProbs2@[ScriptCapitalP]
{0.125, 0.375, 0.375, 0.125}
answered Dec 1 at 16:44
kglr
176k9198404
You can use MarkovProcessProperties
absorbingStateProbs1[p_] := Extract @@ (MarkovProcessProperties[
p, #] & /@ {"ReachabilityProbability", "AbsorbingClasses"});
absorbingStateProbs1@[ScriptCapitalP]
{0.125, 0.375, 0.375, 0.125}
Alternatively,
absorbingStateProbs2[p_] := PDF[p[∞], #] & /@
Flatten[MarkovProcessProperties[p, "AbsorbingClasses"]]
absorbingStateProbs2@[ScriptCapitalP]
{0.125, 0.375, 0.375, 0.125}
answered Dec 1 at 16:44
kglr
176k9198404
answered Dec 1 at 16:44
kglr
176k9198404
answered Dec 1 at 16:44
kglr
176k9198404
answered Dec 1 at 16:44
kglr
176k9198404
176k9198404
add a comment |
add a comment |
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