MonteCarloMethod - Revision history

Yaua00 at 16:27, 23 January 2018

2018-01-23T16:27:33Z

Yaua00: /* How Monte Carlo simulation works. */

2018-01-23T16:27:01Z

‎How Monte Carlo simulation works.

Yaua00 at 16:26, 23 January 2018

2018-01-23T16:26:31Z

Yaua00: /* 3. How Monte Carlo simulation works. */

2018-01-23T16:06:21Z

‎3. How Monte Carlo simulation works.

Yaua00: /* 3. How Monte Carlo simulation works. */

2018-01-23T16:06:07Z

‎3. How Monte Carlo simulation works.

Yaua00: /* 4. Summary */

2018-01-23T16:05:55Z

‎4. Summary

Yaua00 at 16:05, 23 January 2018

2018-01-23T16:05:45Z

Yaua00: /* 3. How Monte Carlo simulation works. */

2018-01-23T16:03:59Z

‎3. How Monte Carlo simulation works.

Yaua00: /* 3. How Monte Carlo simulation works. */

2018-01-23T16:03:41Z

‎3. How Monte Carlo simulation works.

Yaua00: /* 4. Summary */

2018-01-23T16:01:24Z

‎4. Summary

@@ Line 36: / Line 36: @@
 Monte Carlo Simulation is used for obtaining a distribution of possible numerical outcome values for a given problem. It performs analysis by building models of possible results by substituting a range of values — a probability distribution — for any factor that has inherent uncertainty. It then calculates results over and over, each time using a different set of random values from the probability functions. Depending upon the number of uncertainties and the ranges specified for them, a Monte Carlo simulation could involve thousands of recalculations before it is complete. Monte Carlo simulation produces distributions of possible outcome values.
-'''Monte Carlo Simulation has 3 basic elements''':
+*'''Monte Carlo Simulation has 3 basic elements''':
 '''1.''' A mathematical formula that represents how inputs turn into an output.
@@ Line 62: / Line 62: @@
 During a Monte Carlo simulation, values are sampled at random from the input probability distributions.  Each set of samples is called an iteration, and the resulting outcome from that sample is recorded.  Monte Carlo simulation does this hundreds or thousands of times, and the result is a probability distribution of possible outcomes.  In this way, Monte Carlo simulation provides a much more comprehensive view of what may happen. It tells you not only what could happen, but how likely it is to happen.
-'''Monte Carlo simulation provides a number of advantages over deterministic analysis:'''
+*'''Monte Carlo simulation provides a number of advantages over deterministic analysis:'''
 '''Probabilistic Results.''' Results show not only what could happen, but how likely each outcome is.

@@ Line 36: / Line 36: @@
 Monte Carlo Simulation is used for obtaining a distribution of possible numerical outcome values for a given problem. It performs analysis by building models of possible results by substituting a range of values — a probability distribution — for any factor that has inherent uncertainty. It then calculates results over and over, each time using a different set of random values from the probability functions. Depending upon the number of uncertainties and the ranges specified for them, a Monte Carlo simulation could involve thousands of recalculations before it is complete. Monte Carlo simulation produces distributions of possible outcome values.
-*'''Monte Carlo Simulation has 3 basic elements''':
+'''Monte Carlo Simulation has 3 basic elements''':
 '''1.''' A mathematical formula that represents how inputs turn into an output.
@@ Line 62: / Line 62: @@
 During a Monte Carlo simulation, values are sampled at random from the input probability distributions.  Each set of samples is called an iteration, and the resulting outcome from that sample is recorded.  Monte Carlo simulation does this hundreds or thousands of times, and the result is a probability distribution of possible outcomes.  In this way, Monte Carlo simulation provides a much more comprehensive view of what may happen. It tells you not only what could happen, but how likely it is to happen.
-*'''Monte Carlo simulation provides a number of advantages over deterministic analysis:'''
+'''Monte Carlo simulation provides a number of advantages over deterministic analysis:'''
 '''Probabilistic Results.''' Results show not only what could happen, but how likely each outcome is.

@@ Line 5: / Line 5: @@
 *'''Author''': Bc. Yauheniya Andreyuk
-=1. Introduction=
+=Introduction=
 <div>
 Monte Carlo method is an algorithm that rely on repeated random sampling to obtain numerical results. Essential idea of Monte Carlo is using randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration, and generating draws from a probability distribution. <ref> Monte Carlo method. Wikipedia.org [online]. Available at: https://en.wikipedia.org/wiki/Monte_Carlo_method</ref> Monte Carlo simulation is a technique that allows to see all the possible outcomes of the decisions and assess the impact of risk, allowing better decision making under uncertainty. The technique is used by professionals in such fields as finance, project management, energy, manufacturing, engineering, research and development, insurance, oil & gas, transportation, and the environment. The simulation furnishes the decision-maker with a range of possible outcomes and the probabilities they will occur for any choice of action. It shows the extreme possibilities — the outcomes of going for broke and for the most conservative decision — along with all possible consequences for middle-of-the-road decisions.
 </div>
-=2. History=
+=History=
 <div>
 Principles of Monte Carlo Simulations the way we know it today were developed at the beginning of the 18th century. The history of Monte Carlo started with the work of a French scientist Georges Louis LeClerc, Comte de Buffon (1707-1788), who created “Buffon’s Needle.” <ref> Buffon's needle. Wikipedia.org [online]. Available at: https://en.wikipedia.org/wiki/Buffon%27s_needle</ref> In his work he used a method of dropping random needles on a lined background to estimate π.  He proved that for a needle the same length as the distance between the lines the probability that each time a needle would intersect a line was 2/ π. He tested his theory by throwing baguettes over his shoulder on to a tile floor.
@@ Line 31: / Line 31: @@
 </div>
-=3. How Monte Carlo simulation works.=
+=How Monte Carlo simulation works.=
 <div>

@@ Line 38: / Line 38: @@
 *'''Monte Carlo Simulation has 3 basic elements''':
-'''1.''' A mathematical formula that represents how inputs turn into an output
+'''1.''' A mathematical formula that represents how inputs turn into an output.
 '''2.''' A reasonable estimation of the variation of each input.

@@ Line 38: / Line 38: @@
 *'''Monte Carlo Simulation has 3 basic elements''':
-'''1.''' A mathematical formula that represents how inputs turn into an output (Probability Density Functions)
+'''1.''' A mathematical formula that represents how inputs turn into an output
 '''2.''' A reasonable estimation of the variation of each input.

@@ Line 74: / Line 74: @@
 '''Correlation of Inputs.''' In Monte Carlo simulation, it’s possible to model interdependent relationships between input variables.  It’s important for accuracy to represent how, in reality, when some factors goes up, others go up or down accordingly.
 </div>
 ==References==

@@ Line 62: / Line 62: @@
 During a Monte Carlo simulation, values are sampled at random from the input probability distributions.  Each set of samples is called an iteration, and the resulting outcome from that sample is recorded.  Monte Carlo simulation does this hundreds or thousands of times, and the result is a probability distribution of possible outcomes.  In this way, Monte Carlo simulation provides a much more comprehensive view of what may happen. It tells you not only what could happen, but how likely it is to happen.
-*'''Monte Carlo simulation provides a number of advantages over deterministic, or “single-point estimate” analysis:'''
+*'''Monte Carlo simulation provides a number of advantages over deterministic analysis:'''
 '''Probabilistic Results.''' Results show not only what could happen, but how likely each outcome is.
-'''Graphical Results.''' Because of the data a Monte Carlo simulation generates, it’s easy to create graphs of different outcomes and their chances of occurrence.  This is important for communicating findings to other stakeholders.
+'''Graphical Results.''' Because of the data a Monte Carlo simulation generates, it’s easy to create graphs of different outcomes and their chances of occurrence.
 '''Sensitivity Analysis.''' With just a few cases, deterministic analysis makes it difficult to see which variables impact the outcome the most.  In Monte Carlo simulation, it’s easy to see which inputs had the biggest effect on bottom-line results.
-'''Scenario Analysis:''' In deterministic models, it’s very difficult to model different combinations of values for different inputs to see the effects of truly different scenarios.  Using Monte Carlo simulation, analysts can see exactly which inputs had which values together when certain outcomes occurred.  This is invaluable for pursuing further analysis.
+'''Scenario Analysis:''' In deterministic models, it’s very difficult to model different combinations of values for different inputs to see the effects of truly different scenarios.  Using Monte Carlo simulation, analysts can see exactly which inputs had which values together when certain outcomes occurred.
 '''Correlation of Inputs.''' In Monte Carlo simulation, it’s possible to model interdependent relationships between input variables.  It’s important for accuracy to represent how, in reality, when some factors goes up, others go up or down accordingly.

@@ Line 78: / Line 78: @@
 =4. Summary=
 <div>
-Monte Carlo simulation is a key tool for studying analytically intractable problems. Its history dates back to the eighteenth century, but it came into its modern form in the push to develop nuclear weapons during World War II.
+Monte Carlo simulation is a key tool for studying analytically intractable problems. Often a single ‘event’ in a simulation will require sampling from many different Probability Density Functions, some many times, and be tallied in many ways. Each sample will require one or more random numbers, and may require converting a uniform random number into a sample from another distribution using the inversion or acceptance-rejection methods.
 </div>
 ==References==