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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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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Likelihood computation in Approximate Gaussian Process binary classification using DTC

I was reading a paper on Variational Bayesian Unlearning and one of their experiments involves training a binary classifier on a synthetic moon dataset using sparse Gaussian Process. Let $\chi$ be the ...
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To obtain the BPM should the BMA model be worked out?

In section 8.4 of this book: An Introduction to Bayesian Thinking, I learned the Bayesian Model Averaging(BMA) model and the Best Predictive Model(BPM). The Bayesian Model Averaging Model is obtained ...
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Joint realizations of the ELBO

The ELBO for the VAE is given by $$\mathcal{L}(\phi, \theta) = \frac{1}{N}\sum_{n=1}^N\left[\mathbb{E}_{q_\phi(z|x)} [\log p_\theta(x_n|z_n)] - KL (q_\phi(z_n|x_n) || p(z_n))\right].$$ Suppose we view ...
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1answer
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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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111 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-...
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Understanding the Bayesian Grid Approximation Probabilities

I am working through the survivability analysis shown here: https://www.r-bloggers.com/2020/01/survival-analysis-fitting-weibull-models-for-improving-device-reliability-in-r/ My specific question is ...
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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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Likelihood-free inference: what is a tractable prior distribution of parameters?

I am reading the normalizing flows review article by Deepmind and came across a sentence that I don't understand in section 6.2.4 Likelihood-Free Inference regarding use of normalizing flows to ...
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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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19 views

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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63 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 ...
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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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1answer
79 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 ...
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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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1answer
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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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2answers
686 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 ...
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1answer
167 views

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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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 | \...
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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 ...
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1answer
186 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 ...
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373 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 ...
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1answer
91 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 ...
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1answer
145 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)...
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2answers
311 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 ...
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1answer
248 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 ...
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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 ...
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2answers
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How do I calculate the weights in ABC-SMC

I have been reading through the Tutorial on ABC rejection and ABC SMC for parameter estimation and model selection by Tina Toni and Michael P. H. Stumpf. I can't work out how to calculate the weights ...
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57 views

Parameter values fall outside the prior range after post-hoc adjustments in the context of Approximate Bayesian Computation?

I'm doing simple rejection sampling within the Approximate Bayesian Computation framework, and I use regression adjustments (i.e., non-parametric multiple linear regression) to get closer to the true ...
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1answer
83 views

Using maximum Likelihood regression to get closer to the true posterior when doing Approximate Bayesian Computation : contradiction?

Post-hoc adjustments are used to get closer to the true posterior distribution when doing Approximate Bayesian Computation. This is particularly important when using a rough algorithm like rejection/...
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1answer
80 views

Model choice using approximate Bayesian computation using different sets of summary statistics

I would like to know if it is possible to do a model-selection under the approximate Bayesian computation paradigm and using particular sets of summary statistics (e.g., S1 and S2) that differ for ...
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1answer
207 views

How to use ABC for a quadratic regression model [closed]

Edit: I have solved this. I was incorrectly simulating values for the dependent variable and not using a good summary statistic. I have changed my algorithm to: Simulate y value using simulated B0, ...
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1answer
103 views

Infer parameters with ABC with non-uniform prior

Edit (thanks to Xi'an) : My data consists of $n$ realization of a specific experiment with $t$ time points and $2$ types of data measured in each time point. I summarized this data by computing the ...
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What defines a “low” predictive error

Using an Approximate Bayesian Computation (ABC) approach I have estimated a parameter from my observed data. Now, following this vignette from the R package abc (https://cran.r-project.org/web/...
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1answer
63 views

Weighting prior proposals based on distance function in approximate Bayesian computation

The typical approach in approximate Bayesian computation (ABC) is to propose parameters from the prior, simulate data $\chi'_\text{sim}$ and then accept data that minimises the data misfit $\lambda$ ...
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2answers
105 views

An approach to analyse error in ABC posterior

I trying to understand approximate Bayesian computation (ABC) better so please evaluate my idea to analyse the error in the ABC posterior: Choose arbitrary constant values $\theta_0$ for model ...
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1answer
112 views

An approach to adaptive Bayesian computation where the acceptance rate is a Bernoulli process

I am considering an approach to adaptive approximate Bayesian computation technique (ABC). The acceptance rejection algorithm is used wherein proposals from the prior are accepted if the simulated ...
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1answer
504 views

In what situations would one use Approximate Bayesian Computation instead of Bayesian inference?

I'm not sure why one would use ABC/Likelihood-free inference methods instead of standard Bayesian inference methods. Is this fundamentally a conceptual problem of mine? Are there any concrete ...
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1answer
784 views

Simple linear regression using Approximate Bayesian Computation (ABC)

To understand how ABC works, I like to use it in a simple linear regression model. I am using EasyABC package in R. My problem is that the results I get are not ...
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3answers
559 views

Approximate Bayesian computation: where to start from? [duplicate]

I am about to start a project in ABC methods and I need to first of all study ABC since I know nothing about it. I spent quite a bit looking for on-line tutorials and notes but I found nothing apart ...
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1answer
704 views

Two algorithms are given for rejection sampling. I can not relate these two algorithms

Algorithm 1) Step 1:Obtain a sample $y$ from distribution $Y$ and a sample $u$ from $(0,1)$ Step 2: Check whether or not $u < f(y)/ M.g(y)$ if true accept $...
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Estimating the posterior predictive distribution post regression adjustment when doing Approximate Bayesian Computation

I'm currently correcting the parameter values of the posterior distribution estimated with Approximate Bayesian Computation. The correction is obtained using a multiple weighted linear regression ...
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1answer
366 views

Distance metric for Approximate Bayesian Computation (ABC) regression

I am working on Approximate Bayesian Computation for a simple regression model. Currently, I am not sure how a distance metric in the setting of regression analysis should look like. Imagine a ...
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238 views

Parameter Estimation for intractable Likelihoods / Alternatives to approximate Bayesian computation

Suppose that I have a stochastic model with some parameters that I want to fit to some observed data. Let's assume the Likelihood intractable, i.e. for some reason I cannot work with the analytical ...