Questions tagged [monte-carlo]

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

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Dealing with Problem of Small Sample Size with Monte Carlo in ARIMA

I am looking for a way one can use Monte-Carlo technology as a way out of small sample size. If I am restricted to a ...
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Simulating exponential Vasicek/Ornstein-Uhlenbeck

I am trying to simulate commodity prices using the exponential Vasicek/Ornstein-Uhlenbeck model from Schwartz 1997 p. 926 Equation (1). I am using the closed form solution from Vega 2018 p. 5 Equation ...
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How to calculate Spearman's coefficient in a NPV simulation?

I did a Monte Carlo simulation on the net present value (NPV) of an investment. The input variables are: initial investment cost ($I_0$) output volume of year $t$ ($Q_t$) output price of year $t$ ($...
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Building Confidence Intervals From Monte Carlo Simulations

I have a discrete Markov process that I am running Monte Carlo simulations to estimate the distribution parameters, with the ultimate goal of producing a mean-time-to-failure (MTTF) estimate within a ...
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Monte-Carlo Estimation of conditional expectation term

I want to ask if my approach to estimation of the following quantity is correct: I have $n$ i.i.d. draws $\{(X_i,Z_i) \}_{i=1}^n$ and I want to estimate for a fixed $(i,j)$ pair the quantity: $$ \...
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Estimating rewards for coin flip game, given the bias of the coin but not the outcome of the flip

I perform a series of $N$ coin flips, indexed $i = 1, \ldots, N$. I do not get to see the outcome of the coin flips, but for each one I know the probability of the coin being heads, $p_i(H)$. This ...
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Monte Carlo simulation for grouped averages [duplicate]

Assume we have $N$ random variables $X_1, \ldots, X_N$. As an example, assume that these random variables describe test scores of $N$ students. I am interested in finding the distribution of average ...
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Expected value of subset of variables in Bayesian setting

Assume we have $N$ random variables $X_1, \ldots, X_N$ with known (posterior) distributions that are easy to sample from. For simplicity, assume that I am interested in the expected value of the ten ...
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What is difference between epsilon greedy and epsilon soft policies?

I found that epsilon soft policies are the policies which give a probability of e/|A(s)| for a non greedy action and a probability of 1-e for a greedy action. Heree sum of probablities is equals to ...
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For the confidence interval of median using the binomial distribution why is it called exact and how does it differ from the naive loop-based method?

When I searched across documentation of various statistical packages, I noticed that the confidence interval for median based on either the binomial or beta distribution is called exact. For example: <...
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Approximate marginal posterior distribution via sampling

I'm a beginner in Bayesian inference and I have some confusion about posterior distributions, in particular sampling from it vs. approximating its value at some given point. Suppose I have a model ...
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Reinforcement Learning: SGD sampling and the independence of samples in sequences

I am taking a course in RL and many times, learning policy parameters of value function weights essentially boils down to using Stochastic Gradient Descent (SGD). The agent is represented as having a ...
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Is there any benefit to Monte Carlo simulation when probability can be directly calculated? [duplicate]

Is there any reason why an MC simulation may still be preferred? In particular is there any benefits for posterior inference?
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Making a continuous distribution from a discrete histogram

I was handed a discrete histogram of a random variable $x$. How do I generate 2,000 continuous samples from the histogram which represent the original random variable $x$? My first thought is to fit a ...
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Why is my quasibinomial GLM estimator biased - Monte Carlo simulation

I'm playing with some Monte Carlo simulations to get an idea of the properties of some linear and non-linear models. The linear OLS model in my case is specified as: $Y_t = \beta_0 + \beta_1x+ \...
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Why is the ideal exploration parameter in the UCT algorithm $\sqrt{2}$?

From Wikipedia In the Monte-Carlo Tree Search algorithm, You should choose the node that maximizes the value: ${\displaystyle {\frac {w_{i}}{n_{i}}}+c{\sqrt {\frac {\ln N_{i}}{n_{i}}}}}$ Where: ${w_{i}...
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book suggestion about statistical tests comparison with R

Is there any book with examples on how to compare two statistical tests in R? For example, I'd like to see the possible differences in significance level and power between the chi-square test and the ...
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Numerically validating rates of convergence of approximations of expectations?

In applied mathematics it is standard practise to often validate theoretical approximations using numerical simulations. Since these simulations typically use numerical methods that convergence very ...
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Monte-Carlo Simulation for Quantile Regression

I am trying to perform a Monte-Carlo simulation using R. Currently I am getting stuck simulating the data. In a usual regression setting I would draw a random sample of the independent data and then ...
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Using monte carlo standard error to determine the ideal number of trials?

I am doing a simulation study that involves estimating the parameter $\theta$ under a specific experimental design. $\theta$ is the parameter that take on the value 1 if algorithm A is better than ...
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What is the equation for action-value Q(s,a) in Monte Carlo Off-policy Prediction problem?

This is a question (Exercise 5.6) from Page 108 in Sutton's RL book (2nd edition). In Chapter 5, the authors mentioned that the state value function after importance-scaling is given by the following: ...
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Bayesian: Exponential Prior and Poisson Likelihood: Posterior Calculation

I am needing assistance in a particular question and need confirmation of my understanding. The belief is that absences in a company follow a Poisson(λ) distribution. It is believed additionally that ...
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Model that takes two percentiles as input - what is the percentile of the output value

For some analysis I have two input variables with some (unknown) probabilities distributions. Of both the input variables I know the (assumed) 10th, 50th and 90th percentile. I have some simple model ...
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Crude Monte Carlo Integration Variance

Suppose we want to evaluate the integral: $$I = \int_a^b f(x)dx\ $$ where f(x) is a smooth function defined on the interval [a, b]. In the "crude"-MC method, the integral is approximated as $...
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Real-life example in which Markov chain Monte Carlo is desirable? [duplicate]

A typical introduction to the Metropolis--Hastings algorithm, and hence to Markov chain Monte Carlo techniques in general, starts with the following assumptions on some probability distribution $P(x)$ ...
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Optimally stratifying training, validation and testing samples using simulated targets

I'm fitting a large-scale (both in size of sample and input vector) single hidden-layer feedforward neural network on simulated targets, $\tilde{t}_{\tilde{n}} \in \{\tilde{t}_1,\cdots,\tilde{t}_\...
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Why doesn’t two ways of calculating stationary distribution result in the same answer?

I use matpow=function(M,n){ ans=M for(i in 1:(n-1)){ ans=ans%*%M } ans } to set the matpow function. then I enter the transition matrix ...
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Using Monte Carlo to solve a system of non-linear equations

I'd like to use Monte Carlo (if it's useful to know, the Numpy Monte Carlo tools) to solve (arbitrary) nonlinear systems of equations where a solution might ...
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Predicting next value using monte carlo

I'm new to monte carlo simulations and have attempted to implement the simplest model in order to validate my current understanding. Generate some price data and plot it: ...
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Monte Carlo integration with Control Variate not giving any variance reduction

Given $I=\int_{3}^{+\infty}\dfrac{1}{\sqrt{2\pi}}e^{-x^2/2} \, dx$, I want to use a Control variate function to reduce the variance of a simple Monte Carlo simulation to compute this integral. In ...
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Metropolis Hastings for BART: Calculation of Tree Prior and Transition Kernel

I am trying to understand the details of BART (Bayesian Additive Regression Trees). In particular, I would like to know how the Metropolis Hastings acceptance probability is calculated for BART. My ...
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Calculating power for a simple mediation model - Can I enter values observed from my own dataset into a Monte Carlo simulation covariance matrix?

I am going to conduct secondary data analysis. I need to figure out if the dataset has enough power for a simple mediation model. Each variable is observed and continuous from a cross-sectional study....
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Is sequential reduction approximation of likelihood/importance sampling more accurate than adaptive gaussian quadrature or monte-carlo?

https://cran.r-project.org/web/packages/glmmsr/vignettes/glmmsr-vignette.pdf Is the approximation of the likelihood in glmm by sequential reduction approximation or importance sampling more accurate ...
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Comparing the overall mean of Monte Carlo simulation runs involving multiple observations

I have a set of n spatial points distributed across the landscape. I have hypothesised that the location of these points is determined by a property of the ...
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One small confusion on $\epsilon$-Greedy policy improvement based on Monte Carlo

I'm working on the RL book of Barto and Sutton, the author has provided the proof based on the policy improvement theorem, I can fully understand the inequality, but for the first equality, it really ...
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What is the limiting distribution of the Monte Carlo estimate of a log-mixed-normal distribution?

Assume $x \sim N(\mu_x,\sigma_x^2)$, $y \sim N(\mu_y,\sigma_y^2)$, and \begin{equation*} z= \begin{cases} x & \text{with probability } \alpha \\ y &\text{otherwise} \end{...
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Training/test splits (Monte Carlo sensitivity analysis) or Cross-validation

I am using SVM in Matlab (fitcsvm function) to train a classifier for a problem with two classes. Further, I have three features, e.g. A1, A2 and A3, available for each observation composing my full ...
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In a Galton–Watson process, obtain the observation report and simulation table, estimate the $E(Z_n)$ and $Var(Z_n)$ by using Monte Carlo method

The following is mathematical formulation of Galton–Watson process, which is from the wikipedia, I have two questions about this branching process. 1. How to obtain the observation report and ...
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Estimating integral by Monte Carlo method

I'm trying to solve the following problem Use Monte-Carlo methods to find a $95 \%$ confidence interval for the following integral: $$\int_{-\infty}^{\infty}\int_{-\infty}^{\infty} \exp\left( \frac{1}...
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MonteCarlo function to Simulate and Analyse ARIMA Several Times

Here is the algorithm of what I want to do with R: Simulate 10 time series data set from ARIMA model through ...
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How can I write the analytic gradient for my maximum likelihood estimation for Weibull Distribution using Monte Carlo Simulation in R?

I'm using the two parameter Weibull distribution, generating samples and estimating the loglikelihood. The Weibull density function I'm using is this: The Weibull log likelihood I'm using is this one:...
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Sampling from a distribution which results in heteroskedasticity

I have a pretty basic model whereby using a monte carlo approach I am seeking to recreate the monthly stock market returns over the last 30 years. Using the actual monthly returns of an index, I have ...
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Difference between with and without exploring starts in Monte Carlo RL algorithm

Let's assume our reinforcement learning environment is a mock financial 60-second time series representing the fluctuations of a stock, where 1 timestep = 1 second, such as the image below. Let's ...
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Search depth of Alpha Go and Alpha Go Zero [closed]

I cannot find reliable sources but someone says it is 40 moves and someone says it is 50+ moves. I read their papers and they use value function (NN) and policy function to trim the tree so more ...
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Sampling the hitting time of a Brownian motion with drift

Consider a Brownian motion with drift $\mu > 0$ and variance parameter $\sigma^2$. Then the pdf of the first hitting time to the value $a > 0$ is $$ f(t) = \frac{a}{\sigma\sqrt{2\pi t^3}}\exp\...
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Can divergent transitions signify that I am trying to fit too complex of a model / overfitting?

Divergent transitions are explained here (1) in the stan docs. They occur when the posterior has curvature that is varying too much. My thought was that maybe the posterior would vary a lot in regions ...
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Monte Carlo standard error for a sum

Suppose that I want to compute $E[X+Y]$ using Monte Carlo simulation and compute the standard error. (Note: $X,Y$ are not necessarily independent) The standard way to do this is to Consider the ...
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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(...
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Any known approximations of summing quantiles from joint (bernoulli / lognormal) distributions

This is my first post to this site! For an insurance-like scenario, I have several independent risks which I want to sum together and find a 95% percentile. Currently I do this by Monte Carlo but I ...
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While simulating the value of a double integral , why do we need to draw different samples everytime?

Suppose I want to simulate the value of the integral $\int_{0}^{1} \int_{2}^{3} 2xy \ dx dy$ using Monte Carlo methods. So, now, I draw a random sample from $U_1,U_2,...,U_n$ from $U(0,1)$ and for ...

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