# Questions tagged [numerical-integration]

A class of algorithms to approximate definite integrals.

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### Convergence of Diffusion Process Monte-Carlo

Let $X_t$ be a $d$-dimensional diffusion process initialized at $x \in \mathbb{R}^d$; given as the strong solution to the SDE $$X_t = x + \int_0^t a(t,X_t)dt + \int_0^t b(t,X_t)dW_t;$$ where $a$ and ...
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### How to approximate expectation and variance of an integral from a discrete Time series financial dataset?

I have discrete time series financial data, with time($u$), price($S$) and someVariable($q$) which looks something like this. ...
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### How to perform MCMC integration when no prior over the integrated function is available? [closed]

As far as I can tell, MCMC integration (e.g. VEGAS) is performed by sampling from a distribution proportional to $f(x)$ using MCMC, then building a density estimator $g(x)$ using these samples (for ...
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### Evaluating problematic function when cdf is close to one?

Let $F(x;\theta)$ be a cumulative distribution function and $\beta>0$. I need to evaluate $$\rho=\frac{F(x;\theta)^\beta}{F(x;\theta)-F(x;\theta)^{\beta+1}},$$ but, for some values of $\theta$, R ...
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### Calculating Integral Using MCMC

Consider the integral $\int_{\Theta}f(\theta|\mathbf{x}) \Pi(\theta)d\theta$,where $\theta$ is a univariate parameter and $\Theta$ is the support of $\Pi(\theta)$. I need to evaluate the value of this ...
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### Issues with qbeta and pbeta [closed]

I'm trying to get samples from truncated beta. I have written the following function based on inverse transform sampling method to do so, however, it seems that when CDF converges to 1 fast, pbeta ...
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### MCMC combined with numerical integration towards more efficient Bayesian inference

I am quite new to Bayesian statistics so the question can be a bit naive. My question is on how to deal with a model with individual coefficients. Simple versions of a task and a model I deal with is ...
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### Calculating expected loss of posterior distribution

I'm working with 2 posterior distributions from AB tests. For the sake of simplicity let's assume: $$A\sim Beta(10, 20)$$ $$B\sim Beta(5, 25)$$ I want to calculate the posterior expected loss of ...
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### What is the difference between monte carlo integration and gibbs sampling?

I am aware that both are methods of sampling from the posterior. MC integration replaces the integral by a sample MC sample. Is this sample independent? Gibbs sampling is a class of MCMC ...
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### Approximate a CDF

Suppose we have $n$ equations with an integral of the form $\int_0^{x_i} F(z)dz = c_i,\ i=1,\ldots,n$ where $F(y)=\mathbb{P}(X \le y)$ is an unknown cumulative distribution function of a non-negative ...
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### Numerical methods for one-dimensional Bayesian inference

I am doing inference using a Bayesian model that has only one variable, which boils down to computing a (one-dimensional) cumulative distribution and a quantile function given the log of a probability ...
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### Maximum likelihood estimation using a random number generator

Imagine that I have a random number generator $X$ where it is impossible (or mathematicaly intractable) to calculate its probability density function - this can happen when we compose several simpler ...
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### Having integration in Bayesian model: what package to use?

I have a bit experience on Bayesian analysis and am a JAGS user. Recently I have to run a more complicated model that contains integration (I use adaptIntegrate from cubature package in the original ...
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### I have three probabilities of a value falling within the following ranges +/- 5%, +/- 10% and +/- 20% of the mean value

I have the mean value and my question is: is it possible to calculate the standard deviation assuming a normal distribution? Looking at previous questions which have been asked, this question is ...
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### The median of the absolute value of the difference of two dependent log normal random variables

Assume X and Y have a bivariate lognormal distribution (x,y>0) that is: $f_{X,Y}(x,y)$=\frac{1}{2p\sqrt{1-r^2}xy\sigma_1\sigma_2}exp\{\frac{-1}{2(1-r^2)}[(\frac{ln(x)-\mu_1}{\sigma_1})^2-2r(\frac{...
I have encountered a problem that the literature suggests linear regression is able to solve, but I am at a loss. I have a function $F$ that I want to estimate. This function obeys $N$ equations of ...