Questions tagged [approximate-bayesian-computation]

Approximate Bayesian Computation (ABC) is used in problems when the likelihood function is intractable by producing datasets that are sufficiently similar to the observed dataset

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ABC (Approximate Bayesian Computation) Sampling, Simulating data from Complex models

In ABC sampling methods, Rejection, MCMC and SMC, when we sample potential parameter values from the prior/proposal, we then use those parameters on our model and simulate data values. This can be ...
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Estimating parameters for a set of related random variables

Suppose I have some random variables $$X_i \sim Dist(\theta_i)$$ for $i = 1, ..., n$ where $Dist$ is some known probability distribution family and $\theta_i$ are some parameters which may vary ...
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Hyperparameter optimisation for approximate Bayesian computation

I have a simulation model with an intractable likelihood function and would like to use approximate Bayesian computation (ABC) to obtain the posterior density for the simulator's parameters. In ...
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Understanding the set of latent variables $Z$ in variational inference

I have been trying to understand variational inference (in a Bayesian context) where we’re trying to approximate $p(Z|X)$ where $Z$ is the set of latent variables and $X$ is the set of observable ...
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ABC approximation Bias

In Approximate Bayesian Computation, we approximate the (true) likelihood of our model, $f(x_{obs}|\theta)$, with the following integral $$f_{ABC}(y_{obs}|\theta)=\int K_{h}(x-x_{obs})f(x|\theta)dx$$ ...
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Maximum Value of Kernel Function in ABC

Are there cases where a kernel function, must have 1 as the maximum value ?? The definition of a Kernel can be found in the following link, https://en.wikipedia.org/wiki/Kernel_(statistics)#In_non-...
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Understanding the Bayesian Grid Approximation Probabilities

I am working through the survivability analysis shown here. My specific question is regarding the grid approximation method, implemented in the following R code: <...
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ABC Pseudo Marginal

Suppose, that we have observed data denoted as $y_{obs}$, a likelihood function $l(y|\theta)$ where the parameter $\theta$ follows a prior distribution $\pi(\theta)$. The posterior in the usual ...
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Choice of Smoothing Kernel in ABC

In Approximate Bayesian Computation, one approximates an intractable likelihood by convolving it with some smoothing kernel $K$ as \begin{align} \ell^{\text{ABC}} ( x | \theta ) = \int \ell ( z | \...
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Model comparison with intractable likelihood using approximate Bayesian Computation

I have some models based on stochastic differential equations (SDEs). Because of the definition of these models, I can simulate data, but I cannot compute the likelihood function / distribution ...
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Metrics in comparing the rank orders of elements from 2 vectors

I am working on sampling a posterior distribution for parameters in my model using approximate Bayesian computation (ABC). I would like to come up with a summary statistic to compare the similarity/...
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distance for abc - nonparametric likelihood

When fitting models using abc, data is simulated using parameters drawn from the prior. The distance between the simulated data and the observed data is calculated, and typically if less than a ...
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Calculating the weights in ABC SMC (2 parameters and more)

Im trying to implement ABC SMC for ODE model which has 2 parameters to estimate. I stopped in the step when calculating the weights as it appear in this answer. My question is should I calculate the ...
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Approximate Bayesian computation for comparing parameters affect on a response variable [closed]

I'm not sure I understand this method perfectly so please correct me if I'm wrong. From my understanding Approximate Bayesian Computation allows you to perform likelihood free inference by re-...
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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 ...
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Reducing dataset size in likelihood-free inference

What difference does it make working with a big or small dataset in ABC? Do we get any computational benefits by reducing a very big dataset when doing inference using ABC methods? My understanding is ...
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How to use Approximate Bayesian computation to estimate the parameters of a function?

I am new in bayesian analysis and I want to use Approximate Bayesian computation in order to convert an odd giving to me by a bookmaker to a probability that the event occurs. Here is the Python code ...
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Population Monte Carlo Algorithm using L2 Distance Measure/ Likelihood Distribution

I am currently struggling with some concepts of the Population Monte Carlo Framework. Initially, I came across this set of algorithms as I am currently trying to infer parameters from a 7D ...
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Does Approximate Bayesian Computation (ABC) follow the Likelihood Principle?

I know that ABC is commonly used when the likelihood is intractable, so likelihood principle is not an interest in that case. But, I am curious whether the ABC satisfies the likelihood principle when ...
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Bayesian Statistics -Prior and Posterior distributions

Please is it ever possible for the prior distribution to contain more information about parameter(s) than the posterior distribution? If yes, when can that occur? Is it the same concept as the ...
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ABC, compute Bayes factor from posteriors

I am pretty new to ABC stuff so I may be saying dumb things. My question is: I ran an ABC with two models $M_1$ and $M_2$ and now I have an approximation of the posterior distribution for both model. ...
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Likelihood-free inference - what does it mean?

Recently I have become aware of 'likelihood-free' methods being bandied about in literature. However I am not clear on what it means for an inference or optimization method to be likelihood-free. In ...
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