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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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0answers
37 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
174 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
127 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
63 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. ...
9
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4answers
411 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 ...
5
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1answer
398 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
50 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 ...
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0answers
21 views

Why in ABC algorithms, when likelihood is intractable, we can draw observations from $p(y|\theta)$? [duplicate]

One of the main reasons for using the Approximate Bayesian Computation(ABC) algorithm is when we have a situation where direct computation of $p(y_{obs}|\theta)$ is numerically intractable. However, ...
2
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1answer
90 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
159 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 ...
1
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1answer
64 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
58 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
187 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
127 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
22 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
351 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
42 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
76 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
64 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
113 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
85 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
22 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
35 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
93 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
94 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
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1answer
340 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
505 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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3answers
425 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
510 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
120 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
votes
1answer
256 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 ...
4
votes
2answers
156 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
95 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
109 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
232 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
94 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
1answer
199 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 ...
6
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1answer
547 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 ...
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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
565 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
votes
2answers
176 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 ...
7
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1answer
376 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
votes
1answer
220 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 ...
6
votes
1answer
189 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 ...
2
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0answers
105 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, ...
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 ...
2
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1answer
1k 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 ...
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2answers
728 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 ...