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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 ...
AlexS123's user avatar
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1 answer
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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|...
ItsKalvik's user avatar
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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 ...
Randomdude's user avatar
1 vote
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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 ...
lm1909's user avatar
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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 ...
ellabella's user avatar
1 vote
1 answer
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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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1 answer
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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 ...
user1747134's user avatar
1 vote
1 answer
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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\...
isle_of_gods's user avatar
2 votes
1 answer
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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 ...
Usman YousafZai's user avatar
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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 ...
SorushN's user avatar
3 votes
1 answer
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Model selection: comparing Bayesian models with likelihood vs likelihood-free (Approximate Bayesian Computation)

I have two families of models that can possibly explain the data at hand. One family is rather process-based, using fairly complicated simulations and Approximate Bayesian Computation to estimate the ...
WaterFox's user avatar
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2 answers
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Calculating mean follow up from ONLY sample size and range

I have several observational studies (mostly historical, prior to 1950s) that are looking at relapse rate across several years of follow up period for depression. I only have MINIMUM and MAXIMUM ...
Mutahira Q's user avatar
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106 views

ABC-SMC, how to obtain summary statistics

I'm using the package pyABC which implements the ABC-SMC algorithm. My model is described by fewer than 10 parameters. I run the code with $N=50$ particles and stop the process after a maximum run ...
Gabriel's user avatar
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The Role of Summary Statistics

I am reading about this algorithm called "ABC" (Approximate Bayesian Computation). https://cran.r-project.org/web/packages/abc/vignettes/abcvignette.pdf (page 3) Over here, it makes mention ...
stats_noob's user avatar
1 vote
3 answers
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How can we assume the models are exhaustive in Bayesian Model Averaging?

Bayesian model averaging is justified using the law of total probability which requires the the set of models that we average over to be exhaustive. Shouldn’t we prove that the set of models are ...
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3 votes
1 answer
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Handling a big number of Summary Statistics in ABC

I went through a big amount of literature in $ABC$, in how it is possible to handle a large number of (many cases sufficient) summary statistics. Like a large number, I consider $K>>200$, where $...
Fiodor1234's user avatar
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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 ...
joelnmdyer's user avatar
3 votes
1 answer
1k views

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 ...
Nick's user avatar
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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 $$f_{ABC}(y_{obs}|\theta)=\int K_{h}(x-x_{obs})f(x|\theta)dx $$ ...
Fiodor1234's user avatar
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4 votes
2 answers
332 views

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-...
Fiodor1234's user avatar
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3 votes
3 answers
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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: <...
coolhand's user avatar
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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 ...
Fiodor1234's user avatar
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2 votes
0 answers
80 views

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 | \...
πr8's user avatar
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6 votes
1 answer
194 views

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 ...
LiKao's user avatar
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1 vote
2 answers
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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/...
tiantianchen's user avatar
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2 votes
0 answers
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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 ...
hugh's user avatar
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1 vote
0 answers
210 views

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 ...
Sarah's user avatar
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1 vote
0 answers
11 views

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-...
Jin's user avatar
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1 vote
0 answers
139 views

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 ...
Behzad's user avatar
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2 votes
1 answer
98 views

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 ...
Dion's user avatar
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3 votes
0 answers
267 views

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 ...
Pierre's user avatar
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1 vote
0 answers
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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 ...
NewKidAround's user avatar
7 votes
1 answer
291 views

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 ...
Minsuk Shin's user avatar
2 votes
2 answers
1k views

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 ...
emma's user avatar
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2 votes
1 answer
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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. ...
Simon C.'s user avatar
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21 votes
4 answers
8k views

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 ...
piccolo's user avatar
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7 votes
1 answer
674 views

Proof of Approximate / Exact Bayesian Computation

The ABC algorithm is given as Draw $\theta \sim \pi(\theta)$ Simulate data $X \sim \pi(x | \theta)$ Accept $\theta$ if $\rho(X, D) < \varepsilon$ where $\pi(\theta)$ is the prior, $\pi(x | \...
user-2147482565's user avatar
2 votes
0 answers
129 views

Approximate bayesian computation: model selection on nested models

For model selection within an ABC framework when the models are nested, say model 1 is equal to model 2 on some subset of the parameter space, is it better to try and do parameter inference or use a ...
Michael's user avatar
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3 votes
1 answer
430 views

ABC: Population Monte Carlo (PMC) convergence statistics?

I'm using the abcpmc code: Approximate Bayesian Computing (ABC) Population Monte Carlo (PMC) implementation based on Sequential Monte Carlo (SMC) with Particle Filtering techniques. described in ...
Gabriel's user avatar
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6 votes
1 answer
951 views

ABC: Population Monte Carlo (PMC) vs Sequential Monte Carlo (SMC)?

I'm reading about the Approximate Bayesian Computation (ABC) method, and I came across two rather popular approaches: Sequential Monte Carlo (SMC) methodology to sample sequentially from a ...
Gabriel's user avatar
  • 4,342
2 votes
1 answer
129 views

Why is Bayesian data analysis done if we already know the distribution of the parameters?

I am trying to learn Bayesian data analysis, so what I see is that most computations are carried out using MCMC simulations. So far as I understand, for simulating MCMC we need to know the ...
Siddharth Shakya's user avatar
2 votes
1 answer
230 views

Approximate Bayesian Computation for parameters estimation in ODE-based model

I am simulating a system of ODEs by using parameters taking from the literature. The next step would be to use ABC in order to estimate them (I have experimental data about all the curves of the model)...
wrong_path's user avatar
3 votes
2 answers
457 views

ABC with non-uniform prior

I had asked some similar questions in the past, but I never got either the answers or the discussion I was hopping for. So I will rephrase the problem to see if I can understand it myself. I'm trying ...
Diogo Santos's user avatar
3 votes
1 answer
375 views

Is it possible to do posterior predictive checks when using Random Forest for Bayesian parameter inference?

Random Forest algorithm has been recently proposed for estimating parameter values within the context of Approximate Bayesian Computation (Raynal et al 2017). The idea consists of training regression ...
SimonLL's user avatar
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1 vote
0 answers
69 views

Using constrained regression model to get closer to the true posterior when doing Approximate Bayesian Computation

I'm using rejection sampling algorithm to generate a reference table ($\theta$,SS). Where $\theta$ are parameter values of model M1 and SS the summary statistics extracted from the pseudo-data ...
SimonLL's user avatar
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