All Questions
Tagged with abc or approximate-bayesian-computation
83 questions
0
votes
2
answers
2k
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 ...
- 129
0
votes
0
answers
77
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 ...
- 135
5
votes
1
answer
93
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/...
- 135
2
votes
1
answer
104
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 ...
- 135
1
vote
1
answer
387
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, ...
- 11
3
votes
1
answer
155
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 ...
- 787
1
vote
0
answers
28
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/...
1
vote
1
answer
111
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 $\lambda$ ...
- 1,235
1
vote
2
answers
150
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 ...
- 1,235
3
votes
1
answer
180
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 ...
- 1,235
7
votes
1
answer
617
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 ...
- 703
4
votes
1
answer
1k
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 ...
- 1,704
4
votes
3
answers
646
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 ...
- 729
4
votes
1
answer
793
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 $...
- 63
1
vote
0
answers
203
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 ...
- 135
3
votes
1
answer
538
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 ...
- 741
5
votes
2
answers
430
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 ...
- 173
1
vote
0
answers
243
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)})}
$
...
- 259
3
votes
1
answer
203
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 ...
- 133
5
votes
1
answer
413
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 ...
- 259
2
votes
0
answers
158
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 ...
- 21
7
votes
1
answer
830
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 ...
- 2,724
22
votes
2
answers
4k
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 ...
- 6,880
8
votes
1
answer
868
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 ...
- 83
6
votes
2
answers
270
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 ...
- 163
8
votes
1
answer
444
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 ...
- 1,014
6
votes
1
answer
337
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 ...
- 19.7k
7
votes
0
answers
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 ...
- 189
6
votes
1
answer
249
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 ...
- 3,284
2
votes
0
answers
112
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, ...
- 21
11
votes
1
answer
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 ...
user10525
4
votes
1
answer
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 ...
- 143
6
votes
2
answers
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
...
- 1,284