# Posts Tagged ‘ Bayesian ’

## Shaping up Laplace Approximation using Importance Sampling

December 2, 2013
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In the last post I showed how to use Laplace approximation to quickly (but dirtily) approximate the posterior distribution of a Bayesian model coded in R. This is just a short follow up where I show how to use importance sampling as an easy method to...

## Not only verbs but also believes can be conjugated

November 26, 2013
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Following on from last week, where I presented a simple example of a Bayesian network with discrete probabilities to predict the number of claims for a motor insurance customer, I will look at continuos probability distributions today. Here I follow ex...

## Easy Laplace Approximation of Bayesian Models in R

November 22, 2013
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Thank you for tuning in! In this post, a continuation of Three Ways to Run Bayesian Models in R, I will: Handwave an explanation of the Laplace Approximation, a fast and (hopefully not too) dirty method to approximate the posterior of a Bayesian mo...

## Convenient and innocuous priors

November 21, 2013
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Andrew Gelman has some interesting comments on non-informative priors this morning. Rather than thinking of the prior as a static thing, think of it as a way to prime the pump. … a non-informative prior is a placeholder: you can…Read more ›

## Predicting claims with a Bayesian network

November 19, 2013
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Here is a little Bayesian Network to predict the claims for two different types of drivers over the next year, see also example 16.15 in [1]. Let's assume there are good and bad drivers. The probabilities that a good driver will have 0, 1 or 2 claims i...

## The Uncertainty of Predictions

October 2, 2013
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There are many kinds of intervals in statistics.  To name a few of the common intervals: confidence intervals, prediction intervals, credible intervals, and tolerance intervals. Each are useful and serve their own purpose. I’ve been recently working on a couple of projects that involve making predictions from a regression model and I’ve been doing some […]

## Marginal likelihood from tempered Bayesian posteriors

October 1, 2013
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$Marginal likelihood from tempered Bayesian posteriors$

Introduction In the previous post I showed that it is possible to couple parallel tempered MCMC chains in order to improve mixing. Such methods can be used when the target of interest is a Bayesian posterior distribution that is difficult to sample. There are (at least) a couple of obvious ways that one can temper […]

## The Beta Prior, Likelihood, and Posterior

September 5, 2013
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The Beta distribution (and more generally the Dirichlet) are probably my favorite distributions.  However, sometimes only limited information is available when trying set up the distribution.  For example maybe you only know the lowest likely value, the highest likely value and the median, as a measure of center.  That information is sufficient to construct a […]

## Summary stats for ABC

September 1, 2013
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$Summary stats for ABC$

Introduction In the previous post I gave a very brief introduction to ABC, including a simple example for inferring the parameters of a Markov process given some time series observations. Towards the end of the post I observed that there were (at least!) two potential problems with scaling up the simple approach described, one relating […]

## Bayesian Estimation of Correlation – Now Robust!

August 28, 2013
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So in the last post I showed how to run the Bayesian counterpart of Pearson’s correlation test by estimating the parameters of a bivariate normal distribution. A problem with assuming normality is that the normal distribution isn’t robust against...