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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Deriving the results in "The Variational Gaussian Approximation Revisited (Opper and Archambeau, 2009)"
I am trying to derive the results in Opper and Archambeau, 2009. In the paper, they show that the variational free energy is the following (Eq. 3.2)
$$
\mathcal{F} = \sum_n \langle -\ln \left[p(y_n|...
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Temperature scaling a bayesian neural network?
I am trying to calibrate a Bayesian neural network. I have already approximated the posterior density for its weights. In order to make predictions the Bayesian way, I am taking samples from the ...
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How to mitigate large sample number for multimodal posteriors in Approximate Bayesian Computation-Sequential Monte Carlo (ABC-SMC)?
I want to do Bayesian inference for a model function for which the likelihood cannot be explicitly computed, which is why I turned to Approximate Bayesian Computation (ABC). In particular, I am using ...
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Model, Likelihood & ABC
I'm struggling to understand what likelihood free means in ABC, since ABC is using a model as simulator to produce $y_{simulated}$. However, to me is not clear the difference between model/simulator ...
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How to solve for an unkown probability distribution within a hierarchical model?
The Problem
Given probability distributions $P(\theta)$ and $P(X)$, and given an inverse function $Y=f^{-1}(X,\theta)$ that returns a unique $Y$. How can one estimate the unkown distribution $P(Y)$ in ...
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Rejection ABC: Connection with Rejection Sampling?
I am trying to understand the link between (rejection) ABC and rejection sampling. For example, this paper states:
Approximate Bayesian Computation (ABC, Sisson et al., 2018) is centered
around the ...
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ABC model selection from posterior samples
I would like to know if there is a general scheme to do model selection based on the posterior samples from a set of ABC (Approximate Bayesian Computation) runs for a given set of models.
Particularly ...
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Robustness of Posterior distribution wrt likelihood function
Suppose we have
$$
X_1, \ldots, X_n \mid \theta \, \mathop{\sim}^{iid} \, L(\cdot \mid \theta), \quad \theta \sim \pi
$$
By Bayes' theorem, the corresponding posterior distribution is
$$
\pi_n(\mathrm ...
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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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Choice of approximate posterior in variational inference with positive support
I have a simple probabilistic graphical model: $z \longrightarrow x$ where $z_i \sim Exp\left(\lambda_i\right)$ where subscript $i$ denotes the $i$th dimension and $x|z \sim \mathcal{N}\left(f\left(z\...
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ABC, make tolerance threshold $\epsilon$ adaptive
Briefly the Approximate Bayesian Computation instead of using the exact likelihood function $L(\theta;x)$ tries to approximate this function with the use of the observed summary statistics $s(x_{obs})$...
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Difference between Bayesian Information Criteria and Approximate Bayesian Computation as model selection
My question is not very technical and more like a discussion but I will be happy to have a technical input for the comparison b/w BIC and ABC.
I am trying to understand and use the best model ...
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Bayesian Coresets
From the paper "Campbell and Broderick (2019), Automated Scalable Bayesian Inference via Hilbert Coresets":
We want to create a Bayesian Coreset which is a small weighted subset of our full ...
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Sampling for Approximate Bayesian Computation without Simulation
I am trying to use ABC for a physical black box phenomenon. Both the input space and output space are 3D, and there is a proper distance function for the performance space (CIEL*A*B* ΔE). It is not ...
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