Questions tagged [abc]

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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1answer
13 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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0answers
30 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 ...
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0answers
39 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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0answers
7 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-...
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0answers
42 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 ...
1
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1answer
74 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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0answers
90 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 ...
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0answers
61 views

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 ...
6
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1answer
192 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 ...
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2answers
501 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
141 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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4answers
2k 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 ...
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1answer
460 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 | \...
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0answers
69 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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1answer
165 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 ...
3
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1answer
308 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
89 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
125 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
273 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 ...
3
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1answer
199 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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0answers
34 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 ...
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2answers
729 views

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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0answers
49 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 ...
5
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1answer
80 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/...
2
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1answer
78 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 ...
1
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1answer
168 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, ...
2
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1answer
96 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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0answers
23 views

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
51 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
102 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 ...
3
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1answer
106 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 ...
5
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1answer
471 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 ...
3
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1answer
703 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 ...
4
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3answers
523 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
655 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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0answers
141 views

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 ...
2
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1answer
344 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 ...
5
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2answers
198 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 ...
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0answers
133 views

weight updating scheme in ABC SMC

I am trying to develop some intuition about how weights are updated in ABC PMC. The multiple sources suggest: $ w_t^{(i)}=\frac{\pi(x_t^{(i)})}{\sum_j^N w_{t-1}^{(j)}K_t(x_{t-1}^{(j)},x_t^{(i)})} $ ...
3
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1answer
156 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 ...
4
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1answer
275 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 ...
2
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0answers
115 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
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1answer
252 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 ...
7
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1answer
624 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 ...
18
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2answers
2k 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 ...
8
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1answer
634 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 ...
5
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2answers
198 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 ...
8
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1answer
391 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 ...
6
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1answer
244 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 ...
7
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0answers
1k 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 ...