What is Monte carlo: Definition and 128 Discussions

Monte Carlo (; Italian: [ˈmonte ˈkarlo]; French: Monte-Carlo [mɔ̃te kaʁlo], or colloquially Monte-Carl [mɔ̃te kaʁl]; Monégasque: Munte Carlu; lit. '"Mount Charles"') is officially an administrative area of the Principality of Monaco, specifically the ward of Monte Carlo/Spélugues, where the Monte Carlo Casino is located. Informally, the name also refers to a larger district, the Monte Carlo Quarter (corresponding to the former municipality of Monte Carlo), which besides Monte Carlo/Spélugues also includes the wards of La Rousse/Saint Roman, Larvotto/Bas Moulins and Saint Michel. The permanent population of the ward of Monte Carlo is about 3,500, while that of the quarter is about 15,000. Monaco has four traditional quarters. From west to east they are: Fontvieille (the newest), Monaco-Ville (the oldest), La Condamine, and Monte Carlo.
Monte Carlo is situated on a prominent escarpment at the base of the Maritime Alps along the French Riviera. Near the quarter's western end is the world-famous Place du Casino, the gambling center which has made Monte Carlo "an international byword for the extravagant display and reckless dispersal of wealth". It is also the location of the Hôtel de Paris, Café de Paris and Salle Garnier (the casino theatre which is the home of the Opéra de Monte-Carlo). The quarter's eastern part includes the community of Larvotto with Monaco's only public beach, as well as its new convention center (the Grimaldi Forum), and the Monte-Carlo Bay Hotel & Resort. At the quarter's eastern border, one crosses into the French town of Beausoleil (sometimes referred to as Monte-Carlo-Supérieur), and 8 kilometres (5 mi) to its east is the western border of Italy.

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  1. K

    I How to implement proper error estimation using MC

    Hello! I have a situation of the following form. I have a function ##f = xy##. In my experiment ##y## is fixed, but it has some noise to it, such that at each measurement it is basically sampled from a Gaussian with the mean given by the fixed value and the standard deviation given by the known...
  2. UFSJ

    Help with Monte Carlo Wang-Landau JDoS

    Hi, guys. I have tried to write a Wang-Landau JDoS algorithm to describe a magnetic perovskite with exchange interactions J1 = 1.66 and J2 = -1.16. Then, I have a simple question: in the WL algorithm, the obtained joint density of states must have all possible E x M microstates? Since the...
  3. F

    Monte Carlo Simulation vs ML Models

    Hello, I have become familiar with ML and a number of ML models (supervised and unsupervised). I would like to now learn about Monte Carlo simulations since they are so ubiquitous in many fields. When would we choose to do a Monte Carlo simulation instead of building a ML model (supervised...
  4. K

    I Monte Carlo for uncertainty estimation

    Hello! This is tangentially also a follow up to this post. I have the following equation: $$A = \frac{0.2\frac{W}{\Delta}}{\left(\frac{W}{\Delta}\right)^2+0.1^2}$$ where ##\Delta## is an experimental parameter, ##A## is obtained by some measurements and it depends on ##\Delta## and the...
  5. K

    I Confused about using Monte Carlo for error estimation

    Hello! I have 2 probabilities ##p_1## and ##p_2## which governs the probability of measuring some events. I measure event 1 N times and get ##N_1## counts and event 2 N times and get ##N_2## counts. Then I need to build the function ##A = \frac{N_1-N_2}{N_1+N_2}##. I am trying to estimate the...
  6. WMDhamnekar

    MHB Approximating the Double Integral using Monte Carlo Method

    Write a program that uses the Monte Carlo method to approximate the double integral $\displaystyle\iint\limits_R e^{xy}dA$ where $R = [-1,1] \times [0, x^2]$. Show the program output for N = 10, 100, 1000, 10000, 100000 and 1000000 random points. My correct answer: My Java program...
  7. mark_bose

    I want to write my own Monte Carlo code for Neutron transport

    Hi, i would like to write my own MC code in order to simulate the transport of Neutrons in Nuclear reactors. I know the basics of MC and i have already written a code for homogeneus reactors, my problem is the generalization to more complex geometries made of different materials, such as fuel...
  8. A

    How to create a conical source (mamography) in Vgate

    I am new in Vgate software. I've tried a lot of things, but nothing works. I need to create a conical source that is 4 cm in radius and 16 cm in length. Example in photo attached
  9. Arman777

    Fİnding best mpi parameters for the MCMC (Markov-Chain Monte Carlo)

    I am using WSL2/Ubuntu 20.04 on Windows 10 to run a specific cosmological parameter estimation program called Cobaya. (It only runs on Linux and Mac) Here are my specs. Architecture: x86_64 CPU op-mode(s): 32-bit, 64-bit Byte Order...
  10. fluidistic

    A Monte Carlo to compute uncertainties, why report the mean and SD?

    I am learning about the use of Monte Carlo to calculate/estimate uncertainties. If I take the example of a single measurement (i.e. I measure several quantities required to get an estimate of some physical property, but I do this only once), I can use Monte Carlo and some common sense for the...
  11. fluidistic

    Puzzled about the non-teaching of Monte Carlo method(s) for error analysis

    Say you have measured several quantities and you can calculate the value of a physical quantity as a sum/product of the several measured quantities, and you are interested to calculate the uncertainty of that physical quantity. I have just learned about the Monte Carlo method applied to error...
  12. IreneFerri

    Problems with Landau Wang algorithm in fortran

    I have been struggling for over a month now with a problem I cannot fix. I would really appreciate any comment or guidance. Thank you! I am considering an Ising-like model with N agents that han hold one of the following 3 states, represented by vectors: state + : vector (1 0) state 0 : vector...
  13. IreneFerri

    New Ph.D candidate in Statistical Physics on networks, Hello

    My name is Irene and I've just started my PhD. at the University of Barcelona (October, 2020). I have a Physics degree and a Master in Computational Modelling. I work in a research group named ClabB (complexity lab Barcelona) where I develop a large scale opinion model using Monte-Carlo...
  14. S

    I Understanding different Monte Carlo approximation notations

    Currently working on a project involving Monte Carlo integrals. I haven't had any prior studies of this method, so hence the following question. Consider the following expectation: $$E[f(X)]=\int_A f(x)g(x)dx.$$ Let ##X## be a random variable taking values in ##A\subseteq\mathbb{R}^n##. Let...
  15. Arman777

    Python What is the Winning Probability in Monte Carlo Spinner Game?

    Problem: Here’s a little Monte Carlo challenge problem, Consider the following game, which uses the two spinner disks. Suppose a player spins one or the other of the pointers on the disks according to the following rules: (1) if the player spins pointer ##i## and it stops in the region with area...
  16. BryanCasanelli

    A Dissociative ionization Monte Carlo simulations

    Hi, I'm wondering if there any exists a Monte Carlo free code that can simulate dissociative ionization, per example a beam of protons on water, and then track the fragments (from water) and their energy. Thanks in advance!
  17. A

    Troubleshooting Geometry Cutting with Vised X_225 and MCNPX 2.7

    Could someone tell me why this happens when I cut geometry? The program that i used is Vised X_225 and my mcnpx version is 2.7 Sorry for my posts, I'm really in trouble.
  18. I

    Comp Sci Why Is My Java Monte Carlo Simulation Not Approximating Pi Accurately?

    Homework Statement There is a square and a circle is inscribed inside. Simulate an experiment where raindrops drop on this surface. Some raindrops can drop in or on the border of the circle. Some can drop outside the circle. The area of the square divided by the area of the circle gives you pi...
  19. PI emerging from collisions

    PI emerging from collisions

    One of the weirdest ways to calculate pi. Personally think it is weirder than Monte Carlo.
  20. diegzumillo

    I Bootstrap in Monte Carlo and the number of samples

    I am analyzing a lot of data from Montecarlo simulations and trying to use bootstrap to estimate the standard deviation. what I'm finding however is very, very little variation with each iteration of bootstrap, and I don't know why. Two reasons come to mind. Given the complexity of the analysis...
  21. H

    I Monte Carlo financial simulation

    Let's say I want to simulate a 30-year investment return scenario by running n simulations (e.g. n = 1000) using a normal distribution with mean x% and standard deviation y%. My first approach was to generate exactly n sets of 30 samples from N~(x,y) but I realized that for any given set of 30...
  22. G

    A Phase Space and Its Use in Monte Carlo Simulations of Radiation Beams

    In the field of medical physics, specifically in monte carlo simulation of radiation beams produced by electron accelerators, people call ‘phase space’ to a file that contains the data of a large number of particles when they traverse a reference surface in the machine (usually a plane), i.e...
  23. UFSJ

    Thermodynamic limit in Monte Carlo simulation

    Hi guys. I'm using the Monte Carlo method to simulate a spin lattice. If I have a square lattice, L x L, I can plot the phase transition temperature by the inverse of the lattice length (1/L) to find the phase transition temperature in the thermodynamic limit (extrapolating the curve for 1/L =...
  24. SchroedingersLion

    Setting up an FCC lattice in a simulation

    Greetings, for a Monte Carlo simulation of N hard spheres, I want to set up the initial configuration as a fcc lattice. I am thinking about how to do it most efficiently. Here is the lattice structure: The 3 lattice vectors, each one pointing to a different type of the 12 nearest neighbors...
  25. UFSJ

    A question about an expression definition in Monte Carlo

    Hi, my question is about the correct means of the expression "computer experiment" in a Monte Carlo simulation. What specifically is an "experiment" in a Monte Carlo simulation? Is the same of "Monte Carlo path" or is the whole process adopted to found a magnetization curve, for example? If the...
  26. Eva Eva Eva

    MCNP diagnostic X-ray tube simulation

    Dear all, I would like to simulate X-ray tube and check the dose rate in the room. My problem is when I simulate 80kV electrons bombard to the tungsten target, there is just a few photons coming out from the tube window. And the dose rate at 1m from the tube is nearly zero which is impossible...
  27. Ramil

    QFT on the lattice and Green's functions

    Homework Statement [/B] I'm trying to write a program for caclulating Green's function using Monte Carlo method (Metropolis algorithm) in scalar field theory with a potential λφ4 in 4D. I'm writing it in python. N_t, N_x, N_y, N_z - total number of lattice sites in each directions. Field...
  28. E

    Why Does Multiplying by 20 Correct My Monte Carlo Integration Result?

    Homework Statement $$f(x)=NormalPDF(x,2,1)+NormalPDF(x,2,(1/2)^2)$$. where NormalPDF(a,b) is the PDF for a normal distribution with mean a and variance b. Use Monte Carlo Integratoion to find: $$\int_{-10}^{10}f(x)dx$$ Homework Equations The solution to this integration is 2. I use the method...
  29. M

    If statement for Monte Carlo integration

    Hello, I am writing a program on Fortran to calculate the integral of sin^4(x) between x = 0 and x = π/2. I believe I know how to write the correct code, but I am unsure what the if statement should be for whether or not a point is inside the desired area. Any thoughts? Thanks.
  30. ChrisVer

    A Question about data & Monte Carlo statistical uncertainties

    Hi I was wondering the following/feeling uneasy about it: Does it make sense to separate the statistical uncertainties of data and Monte Carlo? For example assume infinite statistics in your MC (uncertainty-->0) while your data is finite : so they come with some "uncertainty" (if that makes...
  31. Chromatic_Universe

    C/C++ Need Help with Monte Carlo Algorithms in C++?

    I would like to discuss code for hit and miss monte carlo methods, and also monte carlo with veto algorithm in C++. Since I am coding in C++ after a long time, I am messed up with syntax too. I have a specific set of problems to work with. If interested we can start working on it here.
  32. X

    Numpy correlate, Monte Carlo

    I'm creating a Monte Carlo simulation of the 2D Ising Model for a graduate course in computational materials science. Part of the assignment is to calculate the uncertainty in the calculation of the average magnetization per spin. To do so, we are told to find the correlation time for our data...
  33. Leonardo Machado

    A Convergence of lattice Ising model

    Hello everyone. I'm working on a program to solve 2D Ising model of magnetic materials, using a system with 10x10 spins for simplicity at a temperature of 1E-8 K. I'm using this parameters to get a faster result of m=1 and guarantee it is correct. but... For now i already pass 300 Monte Carlo's...
  34. C

    A Monte Carlo script to simulate the activation and decay of cobalt

    Homework Statement A sample of cobalt was previously measured in a neutron scattering experiment. As a result, the sample has become activated. Write a Monte Carlo script to simulate the activation and decay of a Co sample during and after a neutron scattering experiment. It is recommended to...
  35. D

    MCNP VisEd Plot tracks :Error->File xsdir not available

    Hello, I use free VisEd and I want to plot the collision, the particle's transport and the particle in tally but I have an error. For the source the plot is ok. How can I solve this problem freely? Someone can help me? My input :C Cellules30 50 -1 (-1 3 19 ):(-2 3 ):(-4 3 -6 5 -7 1 2 ) imp:p=1...
  36. FallenApple

    MATLAB Sample Code for Monte Carlo estimation of pi

    Below is the partial code to plot the rejection/accept regions using monte carlo sampling. The context is to estimate pi and plotting is just one part of it. I'm not sure how the ~ symbol can work. scatter(samples(1,~reject),samples(2,~reject),'b.')...
  37. Shahed

    Monte Carlo using MCNP on a Mac

    Hi! Are there any experts out there using MCNP on a Mac? I could do with a little help setting up, I am new to it. Here's hoping! Shahed.
  38. F

    Monte Carlo Simulation, Ising model in 2D

    Homework Statement Lo,Im stuck on how to retrieve the specific heat capacity from an MC simulation, with the metropolis algorithm. I want my graph to look something like this: https://i.stack.imgur.com/NXeXs.png Homework Equations C_v = ((<E^2>-<E>^2)/T^2 The Attempt at a Solution My code is...
  39. T

    What's Wrong with My Monte Carlo Calculation of π Using Fortran?

    Hi guys, I am having trouble seeing where I have actually gone wrong with my code. If I run the code I am getting approximation of 12 as my lowest is way to big. But I am really struggling to find where I have gone wrong. Any advice would be appreciated. PROGRAM assign_10_1 IMPLICIT NONE...
  40. N

    I Why Monte Carlo Simulations? What do they tell us?

    I am an undergraduate working in my university's high energy physics lab. I'm still new to particle physics, so I have to learn/understand a bunch of things on the fly. We are currently searching for a new state theorized to occur in a specific decay process. I know we have to work with data...
  41. A

    I Understanding autocorrelations in 2D Ising model

    I wasn't sure where to post this, I hope this was the right section. I've been struggling quite a bit with implementing an autocorrelation code into my current project. The autocorrelation as it is now, is increasing exponentially from 1 at the start of my MC run, and hitting 2 halfway through...
  42. L

    A Understanding Markov Chains in Metropolis Monte Carlo Ising Simulation

    I do not understand where are Markov chains in Monte Carlo Ising simulation. Going randomly from lattice site to lattice site one flip one spin calculates energy and goes ahaid. But where are Markov chain there? Could you please explain me this. Thanks a lot.
  43. S

    I Efficient Monte Carlo Fitting with Python Package Emcee and MCMC Analysis

    Hello I use a python package called emcee to fit a function to some data points. The fit looks great, but when I want to plot the value of each parameter at each step I get the plot.png below. In their example (with a different function and data points) they get the plot1.png image. Why is my...
  44. K

    A Question about LQCD and parallelization

    Hi there, I'm currently working on a relatively simple code to do some lattice simulations. I have access to a computing cluster at school and have been learning how to use OpenMP to parallelize my code (each node has 16 cores). I'm currently not planning to use MPI. My main question is...
  45. D

    Using Monte Carlo simulation to calculate Value At Risk

    Homework Statement Calculate 5-day 1% Value at Risk of a portfolio using Monte Carlo simulation. Homework EquationsThe Attempt at a Solution I've found an article explaining how to perform Monte Carlo simulation on portfolio returns therefore calculating the Value At Risk (pdf attachment)...
  46. C

    A Where to start with path integral Monte Carlo?

    Trying to accomplish a monte carlo simulation on the condensed state of 4He, yet I am in my sophomore year and know only a bit of quantum statistical physics. Is there any documentations recommended for beginners to the algorithm applied to 4He? I've found some but they are not friendly to...
  47. zm1046838471

    A question about Monte Carlo calculations

    This is my first question here. I tried my best to work out it by myself but it didn't work. I'm reading Computational Methods in Physics and Engineering by Samuel S M Wong recently. I don't know how to deduce Eq.(7-2) on page 299 of this book. There are some paragraphs on this page as...
  48. Raptor112

    A Monte Carlo Wavefunction Methods

    From the Theory of Open Quantum Systems; the Euler scheme is given by: ##\psi_{k+1} = \psi_{k} + D_1(\psi_k)\Delta t + D_2(\psi_k) \Delta W_k## and is a scheme of order 1. What does the order of convergence mean? From my understanding higher order schemes require fewer interations to give a...
  49. A

    Monte Carlo error calculation PYTHON

    I am using the monte carlo method to calculate the integral of cos^2(x). This is done using N random numbers. In my case I am doing it for 10^i random numbers when i ranges from 1-6. I want to calculate the error on the integral for each value of i used. I know for each value of N I want to...
  50. P

    Monte Carlo methods for solving Maxwell's equations?

    Maxwell's equations are frequently solved numerically using deterministic methods such as finite difference time domain (FDTD) methods (https://en.wikipedia.org/wiki/Finite-difference_time-domain_method). The problem is that FDTD methods are known to be very computationally intensive. I'm...