Using (pseudo-)random numbers and the Law of Large Numbers to simulate the random behavior of a real system.

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Evaluating two sets of random samples

Let $p$ be a probability distribution that can be computed tractably for any given point. I use two MCMC methods to generate samples from the distributions. For each MCMC method, I run 1000 Markov ...
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19 views

Is there a survey that explores all the available Markov chain Monte Carlo methods?

I am interested in exploring the efficacy of various Monte Carlo methods. I am aware of the Metropolis acceptance criterion, Hamiltonian Markov chains, Gibbs sampling, importance sampling, slice ...
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20 views

Friedman's test or Monte Carlo?

I have two time-series data sets of the same five experiments. That makes two 5 X 7 matrices where the row is the experiment and the column is the day, and each matrix comes from a different ...
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1answer
12 views

Models for nonnegative (incl. zero) positively skewed multivariate time series (trade volumes)

I want to build a Monte Carlo simulation that is based in part on share amounts that are traded in the market for a set of stocks. I need to be able to take into account the co-dependence of trade ...
2
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31 views

Population Monte Carlo Algorithm

I am trying to wrap my head around the Population Monte Carlo Algorithm. I want to implement it for a mixture model, but I am uncertain on how to proceed. I am mostly looking for references or ...
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29 views

Monte Carlo integration with density unknown

If I want to find the integral $\int f(x)dx$, I want to use the Monte Carlo method to calculate it. What I have is the data $x_1, \cdots, x_n$ follows $p(x)$. (In my application, $f$ is some function ...
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1answer
29 views

Estimating normalization constant with Monte Carlo integration

Be $f(x)$ a function. Suppose that $f(x)$ integrates to a finite value $k$: $$\int_{-\infty}^{\infty}f(x)dx=k$$ The normalization constant of $f(x)$ is $1/k$. Monte Carlo integration can give an ...
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12 views

Use Monte Carlo to find monthly premium on a Credit Default Swap

You are holding a 10-year 100 million bond newly issued by Risky Corp (A rated). You wish to insure against the possibility of default by entering into a credit default swap with me. Our contract ...
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16 views

Efficiently sampling from Markov Chain with low-probability transitions

I need to sample a large number of paths from a Markov Chain with known state transition matrix $T$, where some of the state transitions are low probability (~0.01%). For example, I might have a large ...
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2answers
35 views

Can I use the Bhattacharyya distance as an acceptance criterion for Approximate Bayesian Computation?

I am researching the spread of a disease through a population and want to capture the behavior of this disease with a model. I already have a model and patient data. The data is a value per patient ...
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34 views

Monte Carlo Methods

_I've tried using sqrt p(1-p)/n to get the standard error and then calculate the t test but for all parts I get a very large number of t so this means ...
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1answer
58 views

Estimate integral value using Monte Carlo Importance Sampling method

I have to estimate the value of this integral: $\int_{0}^{0.5713107589} e^{-3.9365491x}dx$ using Monte Carlo Importance Sampling method. If I understood the method correctly, to estimate the value ...
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1answer
48 views

Proposal distribution - Metropolis Hastings MCMC

In Metropolis-Hastings Markov chain Monte Carlo, the proposal distribution can be anything including the Gaussian (according to the Wikipedia). Q: What's the motivation for using anything other than ...
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1answer
43 views

Question about accuracy in Monte Carlo integration

Suppose that we want to estimate the integral: $$\psi=\int_{a}^{b}h(x)dx.$$ Let $\hat{\psi}$ be the Monte Carlo estimator. As far as I know, if we desire an accuracy up to the fourth decimal, we need ...
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15 views

MCMC for Maximum Entropy?

Is there a way to sample from a discrete probability distribution, whose distribution itself is the solution to a Maximum Entropy problem with known linear constraints, without needing to solve for ...
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0answers
24 views

Standard Error for Proportion of Successes in Monte Carlo Simulation

First note, this is for an assignment. I've been through all our notes, researched online and still unsure on this. We are asked to run a stochastic simulation where, at the end of each run, there is ...
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1answer
20 views

How to interpret Monte Carlo samples of the ratio of two variables?

My aim is to find the 95% confidence interval of the ratio of two variables for which I have summary statistics. More specifically, I have the prevalence of mothers drinking during their pregnancy ...
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1answer
67 views

monte carlo simulation using exponential distributions

I'm trying to simulate a stochastic model of deterministic exponential population growth, where $dN/dt = rN$ where $N$ is population size and $r$ is rate ($t$ time). I'm assuming there's no carrying ...
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1answer
39 views

Dirac Delta function Notation

I am trying to understand the delta function notation used to be express a monte carlo approximation of a probability distribution. The notation used in this (p10) is $\pi(x_{1:n}) = ...
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1answer
64 views

Suspiciously small p-values from randomization (Fisher-Pittman) test

How are p-values calculated when using a Monte-Carlo approximation of the Fisher-Pittman test? I was under the impression[1] that $p$-values generated by randomization tests should always be of the ...
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1answer
36 views

Multiple-Try Metropolis question

I read Multiple-Try Metropolis from Wikipedia and I do not understand some points. Suppose the current state is $\mathbf{x}$. The MTM algorithm is as follows: Draw ''k'' independent ...
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3answers
80 views

How to generate the transition matrix of Markov Chain needed for Markov Chain Monte Carlo simulation?

I'm conducting a sensitivity analysis of a model using MCMC approaches. By reading the code of the sensitivity test procedure, I find the steps in Markov Chain is quite similar to random walk. Also, ...
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18 views

Calculating distribution minimum and maximum values from known p5/mode/p95 values

I am defining triangular and Beta-Pert distributions in MATLAB to produce random samples for Monte Carlo analysis. This is a trivial task if the minimum, maximum and mode are known using: ...
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22 views

Popular (single) imputation methods for ordinal variable

I am setting up a monte carlo simulation study in R for a comparison between several imputation methods for ordinal variables. So far, I am planning to use the following imputation methods: Multiple ...
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36 views

How can I use Monte Carlo to find a monthly premium?

The credit swap is as follows: I own a 100 million bond with an A rating. If that bond rating drops to a new low (during the ten years), I receive 20 million. I pay \$x a month for the arrangement. ...
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2answers
52 views

Number of Markov chain Monte Carlo Samples

There is a lot of literature out there about Markov chain Monte Carlo (MCMC) convergence diagnostics, including the most popular Gelman-Rubin diagnostic. However, all of these assess the convergence ...
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42 views

Convergence of Monte Carlo - Why square root n for rate?

Let $\theta_n = \frac{1}{n} \sum_{i=1}^n X_i$ be the Monte Carlo estimator for $E(X)$. Letting $\sigma^2 = \operatorname{Var}(X)$, by the CLT, $$ \sqrt{n}(\theta_n - E(X)) \xrightarrow d ...
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25 views

Monte Carlo Simulations: Can I Use Real Data as Universe?

In Monte Carlo simulations, it is a commonly used procedure to generate synthetic data based on a large survey (e.g. a microcensus) first. These synthetic data is then used as universe/population for ...
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51 views

How can we simulate from a geometric mixture?

If $f_1,\ldots,f_k$ are known densities from which I can simulate, i.e., for which an algorithm is available. and if the product $$\prod_{i=1}^k f_i(x)^{\alpha_i}\qquad \alpha_1,\ldots,\alpha_k>0$$ ...
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1answer
44 views

Calculating acceptance rate in Monte Carlo Markov Chain while doing Bayesian analyis

I am doing Bayesian analysis using a Monte Carlo Markov Chain of length 10000 and burn-in length 1000. I consider my chain as converged when the acceptance rate is equal to 23% and the chain mixing ...
7
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1answer
243 views

What's rollout policy in AlphaGo's paper?

The paper is here. The rollout policy ... is a linear softmax policy based on fast, incrementally computed, local pattern-based features ... I don't understand what rollout policy is, and how ...
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1answer
53 views

MCMC convergence, analytic derivations, Monte Carlo error

I'm trying to figure out some convergence statements on an MCMC example. The setup is: I'm generating data samples as observations from a (known) deterministic parameter, say $s$ (using a forward ...
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2answers
59 views

sensitivity analysis on given data [closed]

Is there any efficient method to do global parameter sensitivity analysis based on given data, without generating new cases to simulate (very expensive in my case). thanks for example, after monte ...
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43 views

uncertainties from Monte Carlo simulation and error propagation are different

Inspired by this post Is Monte Carlo uncertainty estimation equivalent to analytical error propagation?, I try to check it myself using a simple function f=A/B, where A is 10 with uncertainty 1 and B ...
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2answers
40 views

Probability distribution for proportions

I'm trying to build a Monte Carlo simulation of a production process, and one of my random variables is team productivity. Team productivity is defined as the ratio of the finished requests over the ...
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8 views

Generating a sample vector from sets of overlapping items

Given several finite sets of items, $X_1,...,X_N$, I want to sample a single element from each set to generate a vector $(x_1,...,x_n)$, where each $x_i \in X_i$, and all elements in the vector are ...
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27 views

Modeling bias in reviews of conference papers

An article in Science Magazine claims that A little bias in peer review scores can translate into big money, simulation finds . The paper referred to there is paywalled, though. Can anyone point me to ...
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19 views

Horse race odds to probability

We are given a set of horses, along with their odds as given below: Horse-A (Odds 7-1) Horse-B (Odds 5-1) Horse-C (Odds 9-1) I am trying to use Monte Carlo Simulation to predict which horse wins. ...
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39 views

Is Monte Carlo uncertainty estimation equivalent to analytical error propagation?

If I have a deterministic, analytic model, $y=f(x)$, I can analytically calculate the uncertainty in $y$ from a known uncertainty in $x$, $\sigma$. Or I can do a Monte Carlo integration: sample from ...
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14 views

Swendsen–Wang algortihm for Monte Caro Simulation in Potts Model

I am trying to implement the SPC (superparamagnetic clustering) algorithm based on this paper: http://arxiv.org/pdf/cond-mat/9702072.pdf I have few questions: 1- When I implement the algorithm does ...
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21 views

Monte Carlo Simulation for Sale Executives [closed]

I'm trying to simulate the sales process for a Service Company. The core of the process goes this way on a time period: A team of sales executives go visit possible clients.If the visit is ...
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1answer
17 views

mixture importance sampling

I have to integrate a 2 dimensional function between a range which has two peaks. I am trying to combine two Gaussian functions to get a distribution which is close to the function so as to use ...
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2answers
67 views

Metropolis, simulated annealing and proposal distributions

I'm trying to understand the physical meaning of the proposal step generating function in Metropolis algorithm. In the original paper, and most derivations I found, it seems that it's not much ...
3
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1answer
90 views

State-of-the-art sampling methods for different information about target density

I was wondering what are the current state-of-the-art methods (i.e., your favourite methods, if you are an expert) for Monte Carlo sampling from a target density function $f(x)$ with $x \in ...
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10 views

What is the relationship between sequential Monte Carlo (SMC) and sequential importance sampling (SIS)?

The papers which develop SMC (eg. [1]) often begin by describing SIS. The two terms, SMC and SIS, don't seem to be synonyms. But neither does SIS seem to be just one "type" of SMC method. So how ...
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2answers
250 views

How to generate two groups of $n$ random numbers in $U(0,1)$ such that sum of these two groups equal?

I want to have two groups of $n$ random numbers $u_i$ and $v_i$ in $U(0,1)$, such that $\sum u_i = \sum v_i$ What I tried is: I can firstly get $u_i$ by $U\sim U(0,1)$, make $s=\sum u_i$. Then I ...
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817 views

Approximate $e$ using Monte Carlo Simulation

I've been looking at Monte Carlo simulation recently, and have been using it to approximate constants such as $\pi$ (circle inside a rectangle, proportionate area). However, I'm unable to think of a ...
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29 views

Estimate number of unique items by number of duplicates in a sample

We have a v. large (1e6) population with unknown number of types of items. We draw a small sample (~100) of a certain size, and find that exactly one item was duplicated. The question is to estimate ...
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19 views

Absolute error or RMSE when you know the exact value?

I'm testing the $k$ neighbour correlation of a uniform random sequence $x_i$ in $[0,1)$. I know its exact expected value to be $1/4$ and I want to show that the error decreases with $\sqrt{N}$ where ...
2
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2answers
62 views

Monte Carlo Simulation of Complex Dynamical System

Assume that $\vec{z}(t)$, the state at time $t$ of a particle in a two-dimensional space, can be fully described by its position and velocity: $\vec{z}(t) = [r_x(t)\ r_y(t)\ v_x(t)\ v_y(t)]$. ...