# Questions tagged [laplace-approximation]

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### Laplace approximation for small number of data

When a large number of data points is available, according to the central limit theorem, Laplace method can give an efficient, good approximation of posterior as a Gaussian distribution centered at ...
210 views

### How are PQL, REML, ML, Laplace, Gauss-Hermite related to each other?

While learning about the Generalized Linear Mixed Models, I often see the above terms. Sometimes it seems to me these are separate methods of estimation of (fixed? random? both?) effects, but when I ...
75 views

### What is the difference between approximate bayesian computation vs approximate bayesian inference?

What are the main differences between approximate bayesian computation vs approximate bayesian inference? Are they essentially the same? Do they refer to the same of different family of models? My ...
23 views

### Can Laplace Approximation be used when Gaussian Process is only a part of bigger model?

I felt in love with Gaussian Process models in Species Distribution Modelling, especially with the Laplace Approximation (LA), which is able to compute these models very fast. This way, I am able to ...
57 views

### Why does this improper prior = constant?

MacKay has an exercise on using Laplace's method for a Poisson model: $$p(r \mid \lambda ) = \frac{e^{-\lambda} \lambda^r}{r!}, \qquad p(\lambda) = \frac{1}{\lambda}$$ And he asks the reader to ...
65 views

### Approximating the Kullback-Leibler Divergence with a Laplace approximation

Suppose I wish to compute the (asymptotic) Kullback-Leibler Divergence (KLD) between the exact Bayesian posterior $$q_{n}(\theta|x_{1:n}) \propto \pi(\theta)\prod_{i=1}^n p(x_i|\theta)$$ and the ...
99 views

### Equation (3.23) GP for ML book

This is the computation of the variance when we do Laplace Approximation for inference in binary classification. I do not understand why the variance is decomposed into these two terms.
353 views

### Bayesian inverse modeling with non-identifiable parameters?

If I have a physical model \begin{equation} y = \frac{1}{\beta_0} (\beta_1 x_1 + \beta_2 x_2) \end{equation} and want to estimate coefficients $\beta_0$, $\beta_1$, and $\beta_2$ from given data ...
129 views

### Lower-bound on covariance estimated via Laplace approximation?

I think when a posterior is approximated to be multivariate normal as in Laplace approximation, the covariance matrix is taken to be the negative inverse Hessian evaluated at the log-posterior maximum,...
78 views

168 views

### Calculating variance using Laplace approximation for GP classification

I'm having some trouble implementing Algorithm 3.2 from Rasmussen and Williams. Namely, sometimes when I evaluate step 6, I obtain a negative variance, which I believe is impossible (and makes line ...
992 views

### Marginalization of GP regression hyperparameters with Laplace approximation

I am using Gaussian Processes (GP) for regression (via the gpml package for MATLAB). So far, I was optimizing the hyper-parameters by maximizing the log likelihood, but I would like to try a more ...
548 views

### Laplace approximation for binomial distribution in matlab

i using bionrnd() function to generate a random vector and Laplace approximation formula to approximate the binomial distribution. but Laplace histogram dose not ...