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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Uses of MCMC samplers outside of Bayesian Inference? [duplicate]

I'm curious if there are applications of MCMC outside of Bayesian Inference? this conversation started when discussing Monte Carlo methods vs Markov Chain Monte Carlo methods with a coworker. He asked ...
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Do Particle Filters actually approximate the posterior distribution?

Im reading a tutorial paper about particle filters (Link) in which it is stated that as the number of samples tends to infinity the approximated posterior density given by $p(x_k|z_{1:k}) \approx \...
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How to compute standard errors of an estimator with antithetic variates?

I'm pricing American options using Longstaff and Schwartz Least square method. When using the following Python code, I obtain nearly the same prices and standard errors as in the Valuing American ...
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Compute a Monte Carlo estimate. Which of the variances (of $\hat{\theta}$ and $\hat{\theta}^{*}$) is smaller, and why?

Compute a Monte Carlo estimate $\hat{\theta}$ of $$ \theta = \int_{0}^{0.5} e^{-x} dx $$ by sampling from Uniform$(0, 0.5)$, and estimate the variance of $\hat{\theta}$. Find another Monte Carlo ...
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How to invert a random walk [closed]

I have a random walk dynamic parameterized in a function let's say $f(x)$ e given a $x_0$ I can retrieve a curve of this initial value after several simulations. But I need to "invert" this ...
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23 views

How does AlphaZero guarantee it could make consistent improvement?

I know the detail of AlphaZero. And in detail, I know it is improving by "policy iteration" mechanism. I found an answer that prove it can finally converge to optimal. But... Is it still ...
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Question on the transition analysis and if they happen by chance (R)

I am wondering if somebody could suggest there I can find a tutorial or a book how to write the code in for following problem. As the title sad I have a transition matrix , and I need to know id the ...
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How to ensure that chains in an ensemble MCMC sampler are “well-mixed”?

I am using an ensemble MCMC sampler in which I run many (e.g. >20) chains simultaneously to sample the posterior distribtuion for Bayesian inference. I find that some (or most) of the chains end up ...
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What are examples of statistical experiments that allow the calculation of the golden ratio?

There are some very simple experiences that can be done by a kid at home, whose result allows one to statistically approach famous numbers such as $\pi$ or $e$. An example where $\pi$ shows up is ...
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Simulating critical values using standard Brownian motion

Using R, I am replicating the Table 1 results of this paper https://www.tandfonline.com/doi/abs/10.1080/03610926.2014.985841. I wrote the following ...
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1answer
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Numerically integrate gaussian pdf

Suppose I want to numerically integrate the function $g(\mathbf{x}) = \exp\bigg(-\frac12 \mathbf{x}^\mathsf{T}\mathbf{\Lambda} \mathbf{x}\,\bigg)$ to obtain the normalization constant $$\int_{\mathcal{...
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Probability of acceptance for Rejection Sampling

I wondered if someone could confirm if this is correct. The probability of accepting a sample from the proposal distribution $q(z)$ is given by the ratio $\frac{\tilde {p}(z)}{kq(z)}$ where $\tilde {p}...
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1answer
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Controlling variance in survival analysis simulations?

For no practical reasons whatsoever, I designed a simple Monte Carlo simulation in python. ...
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Calculating confidence interval from a simulation

I run a simulation 10,000 times, and in each iteration I produce an estimate of the mean of some parameter X. At the end of the simulation I have 10,000 estimated means recorded. $$ \textbf{m} = (x_1, ...
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1answer
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MCMC: Rejecting samples outside the prior support?

I wish to implement a MCMC procedure for a posterior density which has non-trivial prior support. To clarify, this means that the parameter space has certain regions (i.e., combinations of parameters) ...
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Uncertainty analysis with Monte Carlo, why is the mean and SD relevant? Median and 68.3 CL wouldn't be better?

I am reading about using the Monte Carlo method for uncertainty analysis of physical experiments. In the GUM's supplement 1, page 29 (section 7.6, https://www.bipm.org/utils/common/documents/jcgm/...
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Monte Carlo sampling ( accept/reject) for geographic dataset

I have a dataset consisting of latitude and longitude and I'm confused on which approach to use to determine the distribution of points so I can apply the monte Carlo accept/reject for sampling. this ...
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Seeking more information on this Bayesian inference method

I came across an algorithm for performing Bayesian inference, see section 3.2 of this paper. Their approach is outlined as (where the "belief state" is a distribution on a discrete set of ...
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1answer
103 views

Monte Carlo Methods: [closed]

Can someone explain to me the following statement from “Introducing Monte Carlo methods with R!” By Robert Christian. “If the exploration mechanism has enough energy to reach as far as the boundaries ...
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Comparing dependent probabilities from multiple Monte Carlo Simulations vs a single Monte Carlo

I am working on predicting developing project completion timelines using a historical distribution of dev team throughput. In my initial run I ran one simulation to determine how long a given number ...
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Does this Monte Carlo method evidence the consistency of an estimator?

The Statistic Let $\hat{\theta}(x)$ be a statistical estimator of population parameter $\theta$ whose exact distribution is unknown. Let $\hat{\theta}_n(x)$ be the estimator calculate from a sample of ...
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2answers
569 views

Why a sample of skewed normal distribution is not normal?

I was under the impression that if I randomly sample from a skewed normal distribution, the distribution of my sample would be normal based on central limit theorem, but the graph clearly shows that ...
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Is there a multivariate analogue of the Discrete Inverse Transform Sampling?

Context : I have been tasked for an assignment with the implementation of a Metropolis-Hastings algorithm to simulate the Ising model. In short, this model consists - in the case I'm considering - in ...
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19 views

Testing that skewness of two distributions is different

I would like test how statistically different moments between two time series. In particular, imagine we want to test for skewness (but we think generally of a moment $s$) and we do not assume that ...
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16 views

Plotting a random walk on R [closed]

I've run a Gibbs sampler and obtained a sample for $X_1$ and $X_2$. I'm trying to recreate a plot like this one: How do I recreate the walk part on R?
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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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24 views

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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1answer
56 views

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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27 views

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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1answer
42 views

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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1answer
32 views

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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1answer
34 views

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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1answer
39 views

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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1answer
115 views

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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16 views

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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32 views

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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2answers
106 views

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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1answer
27 views

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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1answer
29 views

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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1answer
38 views

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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2answers
65 views

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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1answer
34 views

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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3answers
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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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