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# 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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### Estimate at which point a linear model hits a certain value (including probabilities)

I have a simple 1D set of datapoints with a trend, I want to estimate at which point $X_t$ (i.e., at which point in the future) the model will hit a certain threshold $Y_t$: I can fit a trendline to ...
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1 vote
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### Monte Carlo Gradient Estimation in Auto-encoding Variational Bayes

I am currently reading paper Auto-encoding Variational Bayes and I am not being able to understand the highlighted part in the screenshot below: I am not understanding why there is f(z) and what is ...
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### Use of Monte Carlo Tree Search

I was talking with someone much more experienced in stats than I am and they suggested the use of Monte Carlo Tree Search for a problem I am facing. Problem Statement: I am collecting jitter ...
1 vote
48 views

### Figure of merit for multiple simulations of point patterns

I am having problems understanding how I can evaluate a set of (Monte Carlo) simulations based on randomly distributed points. Assume you simulate a random point pattern in a square and you plot the ...
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1 vote
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### Can we find an asymptotically consistent Metropolis-Hastings estimator based on this proposal scheme?

I'm running the Metropolis-Hastings algorithm for a target distribution $\hat\mu$ (see below for the formal setup including the definition of $\hat\mu$) on a product space $I\times E'$. I'm using the ...
• 109
1 vote
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### How to generate data with given correlation, one distribution counting intergers, the other normal?

I would like to do a Monte Carlo simulation related to this post: How to predict the degree to which an extraneous variable will attenuate a correlation? I need to generate a dataset with a Pearson r ...
• 3,126
1 vote
42 views

### Confusion in Sampling using the IP algorithm (Bishop PRML)

I'm reading Bishop's PRML p. 537 and I don't understand one piece of the IP (data augmentation) algorithm. Namely, the part that says "we use the samples $\{\mathbf{Z}^{(l)}\}$ obtained in the I step ...
1 vote
169 views

### Why the Monte Carlo Control algorithm is written this way?

I am having trouble to understand this algorithm, since this is not how I would have written it. To me, we should first start to fix a policy. Then, we evaluate the Q values associated with this ...
1 vote
113 views

### Stratified sampling to generate random numbers (eg. for Monte-Carlo applications)

I am using a Monte-Carlo method to compute a value of interest $y$ from some input parameters $x_{i}$, that I use to draw statistical sets from simple distribution laws. In my case, for a single Monte-...
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1 vote
66 views

### Robust sum of non-independent random variables

What approach could be used to sum non-independent variables? I have probability distributions of stock prices and want to calculate the probability distribution of the portfolio price (sum of some ...
• 447
1 vote
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### ABC SMC: How do weights scale proportionally with number of parameters

Having some problems with the ABC SMC algorithm. I'm trying to implement the methods taken from here: Simulation-based model selection for dynamical systems in systems and population biology How do ...
• 11
1 vote
42 views

### How to use Hamiltonian Monte Carlo when some parameters result in ill-defined likelihoods?

I want to use Hamiltonian Monte Carlo for an estimation problem where, for some parameters, the solution does not "make sense," so I cannot compute the log likelihood or its gradient. In addition, I ...
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1 vote
19 views

### Probability that output is result of the same process?

I've developed a simple Monte-Carlo simulation. Output of this simulation is a histogram. This histogram is possibly a log-normal distribution, but I don't want to assume that. But I do know that the ...
• 111
1 vote
I have a statistical model given by $$y_t\sim p(y_t|x_t, \theta)\\ x_t\sim p(x_t|x_{t-1},\theta)\\ \theta\sim p(\theta)$$ where $y$ is the only observed component. Using a sequential Monte Carlo ...