Posts Tagged ‘ Bayesian ’

Posterior predictive output with Stan

May 19, 2015
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Posterior predictive output with Stan

I continue my Stan experiments with another insurance example. Here I am particular interested in the posterior predictive distribution from only three data points. Or, to put it differently I have a customer of three years and I'd like to predict the ...

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Hello Stan!

May 12, 2015
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Hello Stan!

In my previous post I discussed how Longley-Cook, an actuary at an insurance company in the 1950's, used Bayesian reasoning to estimate the probability for a mid-air collision of two planes.Here I will use the same model to get started with Stan/RStan,...

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Predicting events, when they haven’t happened yet

May 5, 2015
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Predicting events, when they haven’t happened yet

Suppose you have to predict the probabilities of events which haven't happened yet. How do you do this?Here is an example from the 1950s when Longley-Cook, an actuary at an insurance company, was asked to price the risk for a mid-air collision of two p...

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The Non-parametric Bootstrap as a Bayesian Model

April 17, 2015
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The Non-parametric Bootstrap as a Bayesian Model

The non-parametric bootstrap was my first love. I was lost in a muddy swamp of zs, ts and ps when I first saw her. Conceptually beautiful, simple to implement, easy to understand (I thought back then, at least). And when she whispered in my ear, “I...

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Bayes factors vs p-values

March 31, 2015
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Bayesian analysis and Frequentist analysis often lead to the same conclusions by different routes. But sometimes the two forms of analysis lead to starkly different conclusions. The following illustration of this difference comes from a talk by Luis Pericci last week. He attributes the example to “Bernardo (2010)” though I have not been able to find the exact […]

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Wrapping up Bayes@Lund 2015

February 12, 2015
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Wrapping up Bayes@Lund 2015

For the second year around I and Ullrika Sahlin arranged the mini-conference Bayes@Lund, with the aim of bringing together researchers in the in the south of Sweden working with Bayesian methods. This year the committee was also beefed up by Paul Cap...

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More data, less accuracy

January 27, 2015
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Statistical methods should do better with more data. That’s essentially what the technical term “consistency” means. But with improper numerical techniques, the the numerical error can increase with more data, overshadowing the decreasing statistical error. There are three ways Bayesian posterior probability calculations can degrade with more data: Polynomial approximation Missing the spike Underflow Elementary numerical integration algorithms, […]

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Extended Kalman filter example in R

January 13, 2015
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Extended Kalman filter example in R

Last week's post about the Kalman filter focused on the derivation of the algorithm. Today I will continue with the extended Kalman filter (EKF) that can deal also with nonlinearities. According to Wikipedia the EKF has been considered the de facto sta...

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Probable Points and Credible Intervals, Part 2: Decision Theory

January 7, 2015
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Probable Points and Credible Intervals, Part 2: Decision Theory

“Behind every great point estimate stands a minimized loss function.” – Me, just now This is a continuation of Probable Points and Credible Intervals, a series of posts on Bayesian point and interval estimates. In Part 1 we looked at these...

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Kalman filter example visualised with R

January 6, 2015
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Kalman filter example visualised with R

At the last Cologne R user meeting Holger Zien gave a great introduction to dynamic linear models (dlm). One special case of a dlm is the Kalman filter, which I will discuss in this post in more detail. I kind of used it earlier when I measured the tem...

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