# 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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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/...
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 ...
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 ...
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-...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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. ...
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 ...
460 views

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 ...
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 ...
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 ...
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: $w_t^{(i)}=\frac{\pi(x_t^{(i)})}{\sum_j^N w_{t-1}^{(j)}K_t(x_{t-1}^{(j)},x_t^{(i)})}$ ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...