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

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1answer
44 views

What distribution describes this process?

I have three clinics that are testing for Zika virus. We know the proportion of positives aggregated across all clinics, i.e., the first clinic has identified 20% of all positives across the three ...
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0answers
21 views

Why does epsilon greedy policy improvement works? [on hold]

A simple, well explained proof will do the work. Thanks.
1
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0answers
13 views

Picking tuples from a list with low discrepancy

Given a list of m items, I am looking for a way to repeatedly pick a tuple of n distinct items from this list with low discrepancy. For example, suppose I have a list of 3d points, and I want to ...
1
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0answers
20 views

Sample dependency in Neural Net Training cross-validation

I've created a Monte Carlo simulation that randomly divides my data into "test" and "training"-Samples and then trains a neural network. The ratio of 0 and 1 (19.62%) Category is stabilized on ...
4
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0answers
53 views

How to Validate a Monte Carlo Simulation

I have historical data of a production process, and I've being asked to build a simulation model to predict its performance in the future. Using the historical data, I've being able to obtain the ...
1
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0answers
18 views

Order of generation in the VEGAS algorithm

The VEGAS algorithm is a way of efficiently generating Monte Carlo events. In the first iteration, it generates an n-dimensional (n can be configured) set of uniformly distributed random numbers ...
1
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0answers
24 views

Optimizing a function available only through (monte-carlo) stochastic approximation

I am working on a problem where I want to estimate the maximum of a density that I can, in practice, evaluate (pointwisely) using a Monte-Carlo approach (because of intractable integrals). Obviously, ...
1
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0answers
26 views

Bayesian MCMC Fitting

I am doing a Bayesian MCMC fit using emcee in python. I first maximize the log of the likelihood and use the results as initial parameter starting points in my MCMC. I am using a uniform prior and ...
0
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0answers
29 views

Nuisance Parameter in Bayesian MCMC

I am doing a Bayesian MCMC fit to some data using a simple model and I want to understand how to handle nuisance parameters. I am looking at this tutorial. The model is a line: $$y = m x + b$$. The ...
8
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0answers
60 views

Show estimate converges to percentile through order statistics

Let $X_1, X_2, \ldots, X_{3n}$ be a sequence of iid random variables sampled from an alpha stable distribution, with parameters $\alpha = 1.5, \; \beta = 0, \; c = 1.0, \; \mu = 1.0$. Now consider ...
1
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0answers
9 views

MCMC diagnostics for EMC or SMC

Are diagnostics developed for MCMC (e.g. Gelman-Rubin, Geweke) suitable for output from Evolutionary Monte Carlo (EMC) or Sequential Monte Carlo (SMC)?
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0answers
31 views

Monte Carlo conditional pdf

I have a question which as been bothering me. It's best explained by way of a dumb example: Suppose one wants to compute the value of pi by sampling within the unit square (i.e. https://en.wikipedia....
2
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0answers
40 views

What is the difference between the Monte Carlo Method in R package 'DMwR' and a normal Monte Carlo Method?

I am trying to estimate the performance of a machine learning model on time series data. I saw the example of model evaluation using Monte Carlo Estimates from the book "Data Mining With R Learning ...
1
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0answers
30 views

Markov chain Monte Carlo sampling using CDFs instead of PDFs

I wonder if there is any MCMC sampling method which uses the definition of the target CDF instead of the target PDF; however, I may use a proposal PDF. I would like to use Metropolis-Hastings but it ...
1
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0answers
16 views

How to relate distributions?

I have 100 objects. Each object has 10 (highly correlated) attributes that I can measure. For each object, I obtain 10000 samples of that object's attributes. I now want to relate the attributes ...
4
votes
1answer
46 views

Sampling from marginal distribution using conditional distribution?

I want to sample from a univariate density $f_X$ but I only know the relationship: $$f_X(x) = \int f_{X\vert Y}(x\vert y)f_Y(y) dy.$$ I want to avoid the use of MCMC (directly on the integral ...
1
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0answers
22 views

How is the Fermiac machine (Monte Carlo trolley) working?

There is a cool website showing the Markov chain with a machine. But nobody is explaining how it's working or showing a video of it's functioning. This is explaining the Markov chain monte carlo ...
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0answers
34 views

Monte Carlo vs simulation in GARCH (package “rugarch” in R)

What is the difference between a GARCH simulation and a GARCH Monte Carlo simulation? I look in the vingette for the "rugarch" package in R, Introduction to Rugarch. In section 6 Simulation on page ...
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0answers
141 views

How to extract distribution information from descriptive statistics?

In my thesis, I am trying to perform a Monte Carlo simulation with a set of parameters, where I take a random value from a known distribution to calculate a singe run of the simulation. However, for ...
3
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0answers
29 views

Indirect solution for maximum entropy through sampling?

Is there a way to sample from a finite set $\{A,B,C,D\}$ such that the limiting empirical proportions converges to the maximum entropy solution of their probabilities consistent with known constraints?...
-1
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1answer
173 views

Why is the intercept of linear regression biased?

Out of curiosity, I conducted the following simulation (code below). Why is it that when the variance of the error term is large coefficient associated with the intercept is biased? Can you recommend ...
0
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0answers
13 views

Generating correlated uniform random variables [duplicate]

How can I generate two Uniform $(0,1)$ variables $U, V$ with correlation approximately .25?
2
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0answers
64 views

Convergence of the distribution of 0.05 quantiles through Monte-Carlo simulation

I am trying to get admitted to a masters in quantitative finance (I come from a computer science background), so next week I will have 3h to solve an exam in statistical computing using my favourite ...
3
votes
1answer
35 views

Effective sample size for MCMC with multimodal target

I am trying to evaluate an adaptive MCMC algorithm on a multimodal target density. Among other performance measures, I would like to evaluate the sampler in terms of Effective Sample Size (ESS). The ...
2
votes
1answer
40 views

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 ...
2
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0answers
36 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 ...
0
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0answers
23 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 treatment....
1
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1answer
19 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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0answers
44 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 ...
3
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0answers
31 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 ...
1
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1answer
33 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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0answers
16 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 ...
0
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0answers
18 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 ...
3
votes
2answers
36 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 ...
1
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0answers
50 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 ...
3
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1answer
68 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 ...
3
votes
1answer
97 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 ...
4
votes
1answer
44 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 ...
1
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0answers
19 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 ...
1
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0answers
30 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 ...
0
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1answer
25 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 (...
5
votes
1answer
73 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 ...
2
votes
1answer
45 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}) = \frac{1}{N}\sum^...
2
votes
1answer
80 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 ...
2
votes
1answer
40 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 ...
4
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3answers
151 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, ...
1
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0answers
28 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: makedist('...
0
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1answer
37 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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0answers
38 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. ...
4
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2answers
65 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 ...