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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19
votes
2answers
3k views

What would be an example of a really simple model with an intractable likelihood?

Approximate Bayesian computation is a really cool technique for fitting basically any stochastic model, intended for models where the likelihood is intractable (say, you can sample from the model if ...
15
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4answers
4k 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 ...
11
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1answer
1k views

ABC model selection

It has been shown that ABC model choice using Bayes factors is not to be recommended due to the presence of an error coming from the use of summary statistics. The conclusion in this paper relies on ...
8
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1answer
738 views

Posterior predictive check following ABC inference for multiple parameters

I am relatively new to Bayesian statistics so please be gentle. I have just performed Approximate Bayesian Computation (ABC) for the inference of a multi-parameter model. Now I am looking to perform ...
8
votes
1answer
406 views

Inferring parameters for a regression with features of both multivariate probit and ordinal regression?

Based on my data generated by a complex process and the problem below detailed, I have tried various approaches, to no avail. I am trying to answer one or more of the following questions: a) Has ...
7
votes
1answer
500 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 | \...
7
votes
1answer
730 views

How is ABC more computationally efficient than exact Bayesian Computation for parameter estimation in dynamical systems (ODE) models?

Approximate Bayesian Computation has been suggested as an approach to parameter estimation for computationally intensive simulations, most commonly in population genetics, but also in dynamical ...
7
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0answers
2k views

Modeling prior probability as a delta function [closed]

I'm using approximate Bayesian computation to find the true value of a parameter. My prior distribution is uniform over $(0, 1)$. I was watching this video on Bayesian learning and the lecturer ...
6
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2answers
223 views

ABC: Why not use the distance measure as a pseudo-likelihood instead?

I've read about the ABC rejection algorithm when not being able to calculate the likelihood directly, and my question is: if we have to introduce a distance measure $\rho(D,D')$ anyways, why not use ...
6
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1answer
268 views

ABC. How can it avoid the likelihood function?

According to the Wikipedia article, we have the scenario shown below, but how can ABC generate simulation datasets from samples of $\theta$ without knowing or evaluating the likelihood function? For ...
6
votes
1answer
206 views

How to choose the scaling matrix in ABC (without cheating!)?

I am doing a numerical experiment involving comparing Approximate Bayesian Computation (ABC) with other methods. I am simulating data $\boldsymbol{y}$ from a model and I'm using ABC to get a sample ...
6
votes
1answer
214 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 ...
5
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2answers
267 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 ...
5
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1answer
523 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 ...
5
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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/...
4
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3answers
588 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 ...
4
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1answer
732 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 $...
4
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2answers
1k views

How to choose the tolerance parameter for ABC?

I have the following sorted data (sampling from parametric space [1,5]) with respect to their distances of parameter Theta. i.e., Let say N = 1000, Theta : 1.1, 1.7, 1.9, 2.4, 2.8, . . . , 4.9 ...
4
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1answer
309 views

ABC with Lotka-Volterra (or any dynamical system)

I have set out to implement a simple ABC rejection sampling algorithm in order to approximate the posterior distribution of parameters for Lotka-Volterra system and I have a few questions: 1) What ...
4
votes
1answer
85 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 ...
3
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2answers
129 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-...
3
votes
1answer
454 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 ...
3
votes
1answer
838 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 ...
3
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1answer
171 views

Does a metric in ABC need be a true metric

I am considering a number of experiments using Approximate Bayesian Computation. In most of the literature I see reference to a metric function to calculate distance between observed and simulated ...
3
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1answer
115 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 ...
3
votes
1answer
299 views

How to approximate Bayes Factor?

I am searching for a computationally simple way to approximate a Bayes Factor. Currently, I'm using an approach which seems pretty logical to me but I would still be interested to know if this is ...
3
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0answers
157 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 ...
3
votes
1answer
277 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 ...
2
votes
2answers
807 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 ...
2
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1answer
2k views

Combining multiple posterior distributions

I am new to Bayesian statistics, and thus have problems to come up with a solution for the following problem: Using Approximate Bayesian Computation (ABC), I generate a posterior distribution from ...
2
votes
1answer
124 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 ...
2
votes
1answer
202 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 ...
2
votes
2answers
335 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 ...
2
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1answer
110 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 ...
2
votes
1answer
31 views

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 $...
2
votes
1answer
192 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. ...
2
votes
1answer
160 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)...
2
votes
1answer
86 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 ...
2
votes
1answer
395 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 ...
2
votes
0answers
18 views

ABC approximation Bias

In Approximate Bayesian Computation, we approximate the (true) likelihood of our model, $f(x_{obs}|\theta)$, with the following integral $$f_{ABC}(y_{obs}|\theta)=\int K_{h}(x-x_{obs})f(x|\theta)dx $$ ...
2
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0answers
27 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 | \...
2
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0answers
38 views

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 ...
2
votes
0answers
87 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 ...
2
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0answers
124 views

Should I trust logistic regression in ABC model selection with more statistics than retained simulations?

I am using multinomial logistic regression to aid model selection in approximate Bayesian computation. However, I just realize at the preferred tolerance, the number of retained simulations is ...
2
votes
0answers
110 views

Building artificial state space model from noise-less data

I have a discrete time stochastic process, where at each time the state of the system $X_t$ is given by: $$ X_t = f_\theta(X_{t-1},\epsilon_t), \; \; \text{for} \; t = 1,\dots,T $$ and, for example, ...
1
vote
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 ...
1
vote
2answers
273 views

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 ...
1
vote
3answers
75 views

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 ...
1
vote
1answer
81 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 ...
1
vote
0answers
43 views

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 ...