All Questions
Tagged with abc or approximate-bayesian-computation
83 questions
5
votes
1
answer
50
views
ABC (Approximate Bayesian Computation) Sampling, Simulating data from Complex models
In ABC sampling methods, Rejection, MCMC and SMC, when we sample potential parameter values from the prior/proposal, we then use those parameters on our model and simulate data values. This can be ...
- 63
0
votes
1
answer
54
views
Deriving the results in "The Variational Gaussian Approximation Revisited (Opper and Archambeau, 2009)"
I am trying to derive the results in Opper and Archambeau, 2009. In the paper, they show that the variational free energy is the following (Eq. 3.2)
$$
\mathcal{F} = \sum_n \langle -\ln \left[p(y_n|...
- 51
1
vote
0
answers
56
views
Temperature scaling a bayesian neural network?
I am trying to calibrate a Bayesian neural network. I have already approximated the posterior density for its weights. In order to make predictions the Bayesian way, I am taking samples from the ...
- 11
1
vote
0
answers
42
views
How to mitigate large sample number for multimodal posteriors in Approximate Bayesian Computation-Sequential Monte Carlo (ABC-SMC)?
I want to do Bayesian inference for a model function for which the likelihood cannot be explicitly computed, which is why I turned to Approximate Bayesian Computation (ABC). In particular, I am using ...
- 11
1
vote
1
answer
52
views
Model, Likelihood & ABC
I'm struggling to understand what likelihood free means in ABC, since ABC is using a model as simulator to produce $y_{simulated}$. However, to me is not clear the difference between model/simulator ...
- 518
1
vote
0
answers
44
views
How to solve for an unkown probability distribution within a hierarchical model?
The Problem
Given probability distributions $P(\theta)$ and $P(X)$, and given an inverse function $Y=f^{-1}(X,\theta)$ that returns a unique $Y$. How can one estimate the unkown distribution $P(Y)$ in ...
- 11
1
vote
1
answer
65
views
Rejection ABC: Connection with Rejection Sampling?
I am trying to understand the link between (rejection) ABC and rejection sampling. For example, this paper states:
Approximate Bayesian Computation (ABC, Sisson et al., 2018) is centered
around the ...
- 145
2
votes
1
answer
202
views
ABC model selection from posterior samples
I would like to know if there is a general scheme to do model selection based on the posterior samples from a set of ABC (Approximate Bayesian Computation) runs for a given set of models.
Particularly ...
- 23
3
votes
1
answer
64
views
Robustness of Posterior distribution wrt likelihood function
Suppose we have
$$
X_1, \ldots, X_n \mid \theta \, \mathop{\sim}^{iid} \, L(\cdot \mid \theta), \quad \theta \sim \pi
$$
By Bayes' theorem, the corresponding posterior distribution is
$$
\pi_n(\mathrm ...
- 550
2
votes
0
answers
36
views
Estimating parameters for a set of related random variables
Suppose I have some random variables
$$X_i \sim Dist(\theta_i)$$
for $i = 1, ..., n$ where $Dist$ is some known probability distribution family and $\theta_i$ are some parameters which may vary ...
- 203
1
vote
1
answer
185
views
Choice of approximate posterior in variational inference with positive support
I have a simple probabilistic graphical model: $z \longrightarrow x$ where $z_i \sim Exp\left(\lambda_i\right)$ where subscript $i$ denotes the $i$th dimension and $x|z \sim \mathcal{N}\left(f\left(z\...
- 141
2
votes
1
answer
518
views
ABC, make tolerance threshold $\epsilon$ adaptive
Briefly the Approximate Bayesian Computation instead of using the exact likelihood function $L(\theta;x)$ tries to approximate this function with the use of the observed summary statistics $s(x_{obs})$...
- 2,286
0
votes
0
answers
60
views
Difference between Bayesian Information Criteria and Approximate Bayesian Computation as model selection
My question is not very technical and more like a discussion but I will be happy to have a technical input for the comparison b/w BIC and ABC.
I am trying to understand and use the best model ...
- 141
0
votes
0
answers
37
views
Bayesian Coresets
From the paper "Campbell and Broderick (2019), Automated Scalable Bayesian Inference via Hilbert Coresets":
We want to create a Bayesian Coreset which is a small weighted subset of our full ...
- 21
0
votes
0
answers
32
views
Sampling for Approximate Bayesian Computation without Simulation
I am trying to use ABC for a physical black box phenomenon. Both the input space and output space are 3D, and there is a proper distance function for the performance space (CIEL*A*B* ΔE). It is not ...
- 1
3
votes
1
answer
109
views
Model selection: comparing Bayesian models with likelihood vs likelihood-free (Approximate Bayesian Computation)
I have two families of models that can possibly explain the data at hand.
One family is rather process-based, using fairly complicated simulations and Approximate Bayesian Computation to estimate the ...
- 131
3
votes
2
answers
191
views
Calculating mean follow up from ONLY sample size and range
I have several observational studies (mostly historical, prior to 1950s) that are looking at relapse rate across several years of follow up period for depression. I only have MINIMUM and MAXIMUM ...
- 51
0
votes
0
answers
117
views
ABC-SMC, how to obtain summary statistics
I'm using the package pyABC which implements the ABC-SMC algorithm. My model is described by fewer than 10 parameters.
I run the code with $N=50$ particles and stop the process after a maximum run ...
- 4,362
0
votes
0
answers
47
views
The Role of Summary Statistics
I am reading about this algorithm called "ABC" (Approximate Bayesian Computation).
https://cran.r-project.org/web/packages/abc/vignettes/abcvignette.pdf (page 3)
Over here, it makes mention ...
1
vote
3
answers
108
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 ...
user297721
3
votes
1
answer
105
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 $...
- 2,286
1
vote
0
answers
46
views
Hyperparameter optimisation for approximate Bayesian computation
I have a simulation model with an intractable likelihood function and would like to use approximate Bayesian computation (ABC) to obtain the posterior density for the simulator's parameters.
In ...
- 11
4
votes
1
answer
1k
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 ...
- 43
2
votes
0
answers
37
views
ABC approximation Bias
In Approximate Bayesian Computation, we approximate the (true) likelihood of our model, $f(x_{obs}|\theta)$, with the following integral
$$f_{ABC}(y_{obs}|\theta)=\int K_{h}(x-x_{obs})f(x|\theta)dx $$
...
- 2,286
4
votes
2
answers
346
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-...
- 2,286
3
votes
3
answers
1k
views
Understanding the Bayesian Grid Approximation Probabilities
I am working through the survivability analysis shown here. My specific question is regarding the grid approximation method, implemented in the following R code:
<...
- 199
2
votes
0
answers
70
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 ...
- 2,286
2
votes
0
answers
91
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 | \...
- 1,356
6
votes
1
answer
199
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 ...
- 2,671
1
vote
2
answers
503
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/...
- 2,131
2
votes
0
answers
82
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 ...
- 33
1
vote
0
answers
216
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 ...
- 11
1
vote
0
answers
12
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-...
- 576
1
vote
0
answers
143
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 ...
- 11
2
votes
1
answer
98
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 ...
- 964
3
votes
0
answers
268
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 ...
- 422
1
vote
0
answers
100
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 ...
- 11
7
votes
1
answer
293
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 ...
- 111
2
votes
2
answers
1k
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 ...
- 21
2
votes
1
answer
300
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.
...
- 123
22
votes
4
answers
8k
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 ...
- 967
7
votes
1
answer
687
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 | \...
- 173
2
votes
0
answers
131
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 ...
- 220
3
votes
1
answer
446
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 ...
- 4,362
6
votes
1
answer
1k
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 ...
- 4,362
2
votes
1
answer
133
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 ...
- 738
2
votes
1
answer
236
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)...
- 729
3
votes
2
answers
474
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 ...
- 787
3
votes
1
answer
379
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 ...
- 135
1
vote
0
answers
71
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 ...
- 135