Monte Carlo method - Revision history

DavidB4-bot: /* top */Spelling/Grammar Check, typos fixed: be be → be

2016-07-28T12:43:24Z

top: Spelling/Grammar Check, typos fixed: be be → be

DavidB4-bot: clean up & uniformity

2016-07-13T16:14:25Z

clean up & uniformity

Jazzman831: dewiki dates

2007-08-15T02:09:57Z

dewiki dates

Ed Poor: category:Probability and Statistics

2007-04-06T15:06:19Z

category:Probability and Statistics

Etaroced at 23:44, April 3, 2007

2007-04-03T23:44:41Z

Jaques at 21:08, April 3, 2007

2007-04-03T21:08:04Z

Etaroced at 21:06, April 3, 2007

2007-04-03T21:06:27Z

Jaques at 20:59, April 3, 2007

2007-04-03T20:59:39Z

Etaroced: New page: '''Monte Carlo method''' is a non-deterministic numerical algorithm used in computer programming to solve problems that do not lend themselves to analytic or step-wise computation....

2007-04-03T20:58:24Z

New page: '''Monte Carlo method''' is a non-deterministic numerical algorithm used in computer programming to solve problems that do not lend themselves to analytic or step-wise computation....

New page

'''Monte Carlo method''' is a non-[[deterministic]] [[numerical algorithm]] used in computer programming to solve problems that do not lend themselves to analytic or step-wise computation. Solutions to the problem are generated with the aid of some [[random]] or [[pseudo-random]] factor and then the appropriateness of the randomly generated solution is assessed. This process is repeated multiple times, however, the size of the jump to a new solution is controlled by how good the solution is. So when a solution that is a poor fit is selected, the next random jump is much more likely to be be big, when it is a good solution then the next random jump is more likely to be small. This essentially favors those solutions which are a better fit to the problem.

Monte Carlo methods are used mostly for problems with a large number of variables and dimensions. For example, [[Bayesian statistics]] often involve calculating dozens of variables each of which can exist along a continuation of hundreds of thousands or millions of values. In order to find the best solution each value of each variable would have to be integrated. This is an intractable problem even for advanced computers to solve. The development of Monte Carlo methods has allowed Bayesian solutions to large scale problems to be calculated.

==References==
* Bernd A. Berg, ''Markov Chain Monte Carlo Simulations and Their Statistical Analysis (With Web-Based Fortran Code)'', World Scientific [[2004]], ISBN 981-238-935-0.

← Older revision		Revision as of 12:43, July 28, 2016
Line 1:		Line 1:
−	'''Monte Carlo method''' is a non-[[deterministic]] [[numerical algorithm]] used in computer programming to solve problems that do not lend themselves to analytic or step-wise computation. Solutions to the problem are generated with the aid of some [[random]] or [[pseudo-random]] factor and then the appropriateness of the randomly generated solution is assessed. This process is repeated multiple times, however, the size of the jump to a new solution is controlled by how good the solution is. So when a solution that is a poor fit is selected, the next random jump is much more likely to be be big, when it is a good solution then the next random jump is more likely to be small. This essentially favors those solutions which are a better fit to the problem.	+	'''Monte Carlo method''' is a non-[[deterministic]] [[numerical algorithm]] used in computer programming to solve problems that do not lend themselves to analytic or step-wise computation. Solutions to the problem are generated with the aid of some [[random]] or [[pseudo-random]] factor and then the appropriateness of the randomly generated solution is assessed. This process is repeated multiple times, however, the size of the jump to a new solution is controlled by how good the solution is. So when a solution that is a poor fit is selected, the next random jump is much more likely to be big, when it is a good solution then the next random jump is more likely to be small. This essentially favors those solutions which are a better fit to the problem.

	Monte Carlo methods are used mostly for problems with a large number of variables and dimensions. For example, [[Bayesian statistics]] often involve calculating dozens of variables each of which can exist along a continuation of hundreds of thousands or millions of values. In order to find the best solution each value of each variable would have to be integrated. This is an intractable problem even for advanced computers to solve. The development of Monte Carlo methods has allowed Bayesian solutions to large scale problems to be calculated.		Monte Carlo methods are used mostly for problems with a large number of variables and dimensions. For example, [[Bayesian statistics]] often involve calculating dozens of variables each of which can exist along a continuation of hundreds of thousands or millions of values. In order to find the best solution each value of each variable would have to be integrated. This is an intractable problem even for advanced computers to solve. The development of Monte Carlo methods has allowed Bayesian solutions to large scale problems to be calculated.

@@ Line 3: / Line 3: @@
 Monte Carlo methods are used mostly for problems with a large number of variables and dimensions. For example, [[Bayesian statistics]] often involve calculating dozens of variables each of which can exist along a continuation of hundreds of thousands or millions of values. In order to find the best solution each value of each variable would have to be integrated. This is an intractable problem even for advanced computers to solve. The development of Monte Carlo methods has allowed Bayesian solutions to large scale problems to be calculated.
-==See Also==
+==See also==
 [[Genetic algorithm]]
@@ Line 13: / Line 13: @@
 ==References==
 * Bernd A. Berg, ''Markov Chain Monte Carlo Simulations and Their Statistical Analysis (With Web-Based Fortran Code)'', World Scientific 2004, ISBN 981-238-935-0.
-[[category:Probability and Statistics]]
+[[Category:Probability and Statistics]]

@@ Line 12: / Line 12: @@
 ==References==
-* Bernd A. Berg, ''Markov Chain Monte Carlo Simulations and Their Statistical Analysis (With Web-Based Fortran Code)'', World Scientific [[2004]], ISBN 981-238-935-0.
+* Bernd A. Berg, ''Markov Chain Monte Carlo Simulations and Their Statistical Analysis (With Web-Based Fortran Code)'', World Scientific 2004, ISBN 981-238-935-0.
 [[category:Probability and Statistics]]

@@ Line 13: / Line 13: @@
 ==References==
 * Bernd A. Berg, ''Markov Chain Monte Carlo Simulations and Their Statistical Analysis (With Web-Based Fortran Code)'', World Scientific [[2004]], ISBN 981-238-935-0.
-[[category:Mathematics]]
+[[category:Probability and Statistics]]

@@ Line 3: / Line 3: @@
 Monte Carlo methods are used mostly for problems with a large number of variables and dimensions. For example, [[Bayesian statistics]] often involve calculating dozens of variables each of which can exist along a continuation of hundreds of thousands or millions of values. In order to find the best solution each value of each variable would have to be integrated. This is an intractable problem even for advanced computers to solve. The development of Monte Carlo methods has allowed Bayesian solutions to large scale problems to be calculated.
-Other stochastic numerical methods include: [[Genetic algorithms | genetic and evolutionary algorithms]], [[Gaussian elimination]], [[Random boolean networks]] and [[Neural networks]].
+==See Also==
 ==References==
 * Bernd A. Berg, ''Markov Chain Monte Carlo Simulations and Their Statistical Analysis (With Web-Based Fortran Code)'', World Scientific [[2004]], ISBN 981-238-935-0.
 [[category:Mathematics]]

← Older revision		Revision as of 20:59, April 3, 2007
Line 5:		Line 5:
	==References==		==References==
	* Bernd A. Berg, ''Markov Chain Monte Carlo Simulations and Their Statistical Analysis (With Web-Based Fortran Code)'', World Scientific [[2004]], ISBN 981-238-935-0.		* Bernd A. Berg, ''Markov Chain Monte Carlo Simulations and Their Statistical Analysis (With Web-Based Fortran Code)'', World Scientific [[2004]], ISBN 981-238-935-0.
		+	[[category:science]]