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#76 2014-09-10 09:16:10

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Markov chains

Okay, thank you. Very good work.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#77 2014-09-10 09:18:16

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: Markov chains

You're welcome. It wasn't that hard, though.

I think I might be able to reduce it to 5 states.

Edit: This should work too:

Last edited by anonimnystefy (2014-09-10 10:13:29)


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#78 2014-09-10 10:17:03

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Markov chains

Did you enter the answer for a check?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#79 2014-09-10 10:23:08

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: Markov chains

Long time ago, it's correct.

Also, I checked, the above matrix is working.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#80 2014-09-10 10:24:04

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Markov chains

Okay, I am off and thanks for the help.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#81 2014-09-10 10:25:29

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: Markov chains

No problem, see you later.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#82 2014-09-10 12:25:46

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
Website

Re: Markov chains

After I insert that big matrix in M, what do I do?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#83 2014-09-10 12:29:46

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: Markov chains

Hm, you won't be needing all of it at once.

First, take out the rows and columns that correspond to the absorbing states. I'll call that new matrix Q. You need to calculate


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#84 2014-09-10 12:40:38

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
Website

Re: Markov chains

What is I?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#85 2014-09-10 12:46:04

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: Markov chains

An identity matrix.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#86 2014-09-10 12:49:33

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Markov chains

Post#1 gave you the M commands.

M = ({
    {0, 4/5, 0, 0, 0, 0, 0, 0, 1/5},
    {0, 0, 1/2, 0, 0, 0, 1/2, 0, 0},
    {1/10, 0, 0, 9/10, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 4/5, 0, 0, 0, 1/5},
    {0, 0, 0, 1/2, 0, 0, 0, 1/2, 0},
    {0, 0, 0, 0, 0, 0, 4/5, 0, 1/5},
    {0, 0, 0, 0, 0, 1/10, 0, 9/10, 0},
    {0, 0, 0, 0, 0, 0, 0, 1, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 1}
   });
P2 = DiscreteMarkovProcess[1, M];
PDF[P2[\[Infinity]], 8]
PDF[P2[\[Infinity]], 9]

For the smaller one:

M = ({
    {1/25, 9/25, 2/5, 0, 1/5},
    {0, 2/5, 0, 2/5, 1/5},
    {0, 0, 2/25, 9/10, 1/50},
    {0, 0, 0, 1, 0},
    {0, 0, 0, 0, 1}
   });
P2 = DiscreteMarkovProcess[1, M];
PDF[P2[\[Infinity]], 4]
PDF[P2[\[Infinity]], 5]

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#87 2014-09-10 22:38:47

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
Website

Re: Markov chains

Thanks.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#88 2014-09-11 01:15:10

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: Markov chains

The only thing left bugging me is how to bobbym's simulation.

Maybe l, instead of picking them uniformely from the [1,33] interval, we should pick them with some sort of corresponding distribution.

Last edited by anonimnystefy (2014-09-11 01:17:12)


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#89 2014-09-11 02:20:16

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Markov chains

That idea does not get the job done.

There are other ways to compute that matrix too.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#90 2014-09-11 02:22:33

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: Markov chains

Which matrix?


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#91 2014-09-11 02:23:51

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Markov chains

The big one or the smaller.

Can you say what your labels mean?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#92 2014-09-11 02:29:17

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: Markov chains

Of course. For the big one, the letters stand for prisoners that are still in the game and the asterisks mark the prisoner whose turn it is. B+C stands for any state in which A is no longer in the game and that state is the goal.

For the ssecond one:
ABC - all three are left, A is speaking
AB - A and B left, A is speaking
AC -A and C left, C is speaking
A and B+C the same as in the big one.

Last edited by anonimnystefy (2014-09-11 02:33:54)


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#93 2014-09-11 02:31:18

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Markov chains

AC is all three are left, C is speaking ?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#94 2014-09-11 02:34:12

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: Markov chains

Sorry, fixed.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#95 2014-09-11 02:35:52

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Markov chains

C is speaking?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#96 2014-09-11 02:37:28

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: Markov chains

Yep. It's like that because of what hapens when B tells the truth. You go from the first state to the third state and C is speaking.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Offline

#97 2014-09-11 02:40:37

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Markov chains

No wonder I did not get it. By the way it does not require any advanced math to answer the question at all.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#98 2014-09-11 02:41:15

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
Website

Re: Markov chains

What math does it require, then?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

#99 2014-09-11 02:45:51

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Markov chains

Case work and simple use of fractions.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#100 2014-09-11 03:11:33

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: Markov chains

That would be some mighty casework.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Offline

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