mages' blog

The next Cologne R user group meeting is scheduled for tomorrow, 26 February 2014. We are delighted to welcome:

• Diego de Castillo: R and databases
• Kim Kuen Tang: Hands on using R and kdb+ together
• Frank Celler: ArangoDB (Lightning Talk)

Further details and the agenda are available on our KölnRUG Meetup site.

Please sign up if you would like to come along. Notes from past meetings are available here.


The organisers, Bernd Weiß and Markus Gesmann, gratefully acknowledge the sponsorship of Revolution Analytics, who support the Cologne R user group as part of their vector programme.


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Here is the poster for the 2nd R in Insurance conference on Monday 14 July 2014 at Cass Business School in London:

R in Insurance 2014 conference poster. Download PDF version

Important dead lines to keep in mind:

• Abstract submissions: 28 March 2014
• Early bird booking: 30 May 2014
• R in Insurance Conference: 14 July 2014

For all further information see: www.rininsurance.com.

The programme and the presentation files of the first R in Insurance conference have been published on GitHub.

The other day I had data that showed the development of many products over time. I grouped the products into categories and visualised the data as line graphs in lattice. But instead of adding an extensive legend to the plot I wanted to add labels to each line's latest point. How do you do that? It turns out that panel.groups is there to help again.

Here is my solution:

R code

The registration for the second conference on R in Insurance on Monday 14 July 2014 at Cass Business School in London has opened.

This one-day conference will focus again on applications in insurance and actuarial science that use R, the lingua franca for statistical computation. Topics covered may include actuarial statistics, capital modelling, pricing, reserving, reinsurance and extreme events, portfolio allocation, advanced risk tools, high-performance computing, econometrics and more. All topics will be discussed within the context of using R as a primary tool for insurance risk management, analysis and modelling.

The intended audience of the conference includes both academics and practitioners who are active or interested in the applications of R in insurance.

Invited talks will be given by:

• Arthur Charpentier, Département de mathématiques Université du Québec à Montréal
• Montserrat Guillen, Dept. Econometrics University of Barcelona together with Leo Guelman, Royal Bank of Canada (RBC Insurance division)

Attendance of the whole conference is the equivalent of 6.5 hours of CPD for members of the Actuarial Profession.

We invite you to submit a one-page abstract for consideration. Both academic and practitioner proposals related to R are encouraged. The submission deadline for abstracts is 28 March 2014.

Details about the registration and abstract submission are given on the dedicated R in Insurance page at Cass Business School.

Sponsors

The organisers, Andreas Tsanakas and Markus Gesmann, gratefully acknowledge the sponsorship of Mango Solutions, Cybaea, PwC and RStudio.



Last year's programme, abstracts and talks are available online.

What a great little device the Raspberry Pi is! After my initial setup it is time to play around with the input and output pins. The first example has to be to switch on an LED. This can also be done remotely via a web interface and better, I cannot only switch the LED off, but the whole Raspberry Pi as well.


Thanks to the work of many others, it is straightforward to control the GPIO (General-purpose input/output) pins. Gordon's Project site shows how this can be done with his wiringPi library. For testing purposes I use an LED and a small resistor on pin 17. To control the LED it is as simple as:

gpio mode 0 out
gpio write 0 1
gpio write 0 0

I can also use a browser to control the pins. The webiopi projects provides an out-of-the-box solution for this. That means, I can control the pins from any other device in the network, such as my mobile phone!


Even better, I can switch the Pi off from my phone as well. Daniel Pecos presents a little script and layout that shuts the Pi down via a physical button on pin 4. But, I can also use my phone via webiopi; with Daniel's script running in the background, I can set pin 4 to input, tap it and the Raspberry Pi will shutdown.

Recently the Guardian's Data Blog reported about the results from the third National Survey of Sexual Attitudes and Lifestyles in the UK. One of the questions asked in the survey was if the participants had sex in the last four weeks. The results - a summary is available in this info graphic - show that the British have their most sexual active period when they are in their 20s - 40s.

The article ended with the Guardian asking its readers to answer the same question over the course of a week. Last Friday they published some high level numbers in a follow-up post. Of course there are many things you may criticise about their survey, e.g. it isn't randomised. However, the data provide a nice little example to get familiar with the prop.test function in R, to test if the proportions (probabilities of success) in several groups are the same, or that they equal certain given values.

Here are the data and a first plot:



Although the numbers of responses vary a lot between age groups, the proportion of those who answered with 'Yes' look more similar:


The function prop.test allows me to test, if the proportions of those who said 'Yes' are the same between different age groups.

Running the test across all age groups shows that if the hypothesis were true, then it would be very unlikely to observe the data by chance; the p-value is less than 2.2e-16. Unlike when I compare the age groups of 25-34 and 35-44 years old. Here the p-value is 11.4% and hence I might accept that the behaviours of the two groups are similar (61% vs. 59%). Adding the next age group on the other hand suggests that the three groups are less likely to have the same proportion (p-value is 0.2%). Still, when I compare the groups of 35-44 and 45-54 years old, then I might accept again that they have a similar sexual activity (p-value 8%).


What do I make of this? Well, most will not notice a change of their sexual activity on a day to day basis. Only when they look back over the decades they will notice a significant change. No surprise there, ageing is a slow process.

Session Info

R version 3.0.2 (2013-09-25)
Platform: x86_64-apple-darwin10.8.0 (64-bit)

locale:
[1] en_GB.UTF-8/en_GB.UTF-8/en_GB.UTF-8/C/en_GB.UTF-8/en_GB.UTF-8

attached base packages:
[1] stats  graphics  grDevices  utils  datasets  methods   base     

other attached packages:
[1] latticeExtra_0.6-26 lattice_0.20-24  RColorBrewer_1.0-5 

loaded via a namespace (and not attached):
[1] grid_3.0.2  tools_3.0.2

Rasmus' post of last week on binomial testing made me think about p-values and testing again. In my head I was tossing coins, thinking about gender diversity and toast. The toast and tossing a buttered toast in particular was the most helpful thought experiment, as I didn't have a fixed opinion on the probabilities for a toast to land on either side. I have yet to carry out some real experiments.

Suppose I tossed 6 buttered toasts and observed that all but one toast landed on their buttered side.

Now I have two questions:

• Would it be reasonable to assume that there is a 50/50 chance for a toast to land on either side?
• Which probability should I assume?

If I believe the toast is fair, then the probability for landing on the buttered (B) or unbuttered (U) side is 50%.

The probability of observing one ore more B (right tail event) is:

(gt <- 1-1/2^6)
# [1] 0.984375

and the probability of observing one or fewer B (left tail event) is:

(lt <- 1/2^6*choose(6,1) + 1/2^6)
# [1] 0.109375

while the probability of either extreme event, one or fewer B (or U), is:

2*min(c(gt, lt))
# [1] 0.21875

In summary, if the toast has an equally probability to fall on either side, then there is 22% chance to observe one or fewer B (or U) in 6 tosses. That's not that unlikely and hence I would not dismiss the hypothesis that the toast is fair, despite the fact that the sample frequency is only 1/6.

Actually, the probabilities I calculated above are exactly the p-values I get from the classical binomal tests:

## Right tail event
binom.test(1, 6, alternative="greater")
## Left tail event
binom.test(1, 6, alternative="less")
## Double tail event
binom.test(1, 6, alternative="two.sided")

Additionally I can read from the tests that my assumption of a 50% probability is on the higher end of the 95 percent confidence interval. Thus, wouldn't it make sense to update my belief about the toast following my observations? In particular, I am not convinced that a 50/50 probability is a good assumption to start with. Arguably the toast is biased by the butter.

Here the concept of a conjugate prior becomes handy again. The idea is to assume that the parameter \(\theta\) of the binomial distribution is a random variable itself. Suppose I have no prior knowledge about the true probability of the toast falling on either side, then a flat prior, such as the Uniform distribution would be reasonable. However, the beta distribution with parameter \(\alpha=1\) and \(\beta=1\) has the same property and is a conjugate to the binomial distribution with parameter \(\theta\). That means there is an analytical solution, in this case the posterior distribution is beta-binomial with hyperparaemters:
\[\alpha':=\alpha + \sum_{i=1}^n x_i,\; \beta':=\beta + n - \sum_{i=1}^n x_i,\]
and the posterior predictor for one trial is given as
\[\frac{\alpha'}{\alpha' + \beta'}\]
so in my case:

alpha <- 1; beta <- 1; n <- 6; success <- 1
alpha1 <- alpha + success
beta1 <- beta + n - success
(theta <- alpha1 / ( alpha1 + beta1))
# [1] 0.25

My updated believe about the toast landing on the unbuttered side is a probability of 25%. That's lower than my prior of 50% but still higher than the sample frequency of 1/6. If I would have more toasts I could run more experiments and update my posterior predictor.

I get the same answer from Rasmus' bayes.binom.test function:

> library(BayesianFirstAid)
> bayes.binom.test(1, 6)

 Bayesian first aid binomial test

data: 1 and 6
number of successes = 1, number of trials = 6
Estimated relative frequency of success:
  0.25 
95% credible interval:
  0.014 0.527 
The relative frequency of success is more than 0.5 by a probability of 0.061 
and less than 0.5 by a probability of 0.939 

Of course I could change my view on the prior and come to a different conclusion. I could follow the Wikipedia article on buttered toast and believe that the chance of the toast landing on the buttered side is 62%. I further have to express my uncertainty, say a standard deviation of 10%, that is a variance of 1%. With that information I can update my belief of the toast landing on the unbuttered side following my observations (and transforming the variables):

x <- 0.38
v <- 0.01
alpha <- x*(x*(1-x)/v-1)
beta <- (1-x)*(x*(1-x)/v-1)
alpha1 <- alpha + success
beta1 <- beta + n - success
(theta <- alpha1 / ( alpha1 + beta1))
# [1] 0.3351821

I would conclude that for my toasts / tossing technique the portability is 34% to land on the unbuttered side.

In summary, although their is no sufficient evidence to reject the hypothesis that the 'true' probability is not 50% (at the typical 5% level), I would work with 34% until I have more data. Toast and butter please!

Session Info

R version 3.0.1 (2013-05-16)
Platform: x86_64-apple-darwin10.8.0 (64-bit)

locale:
[1] en_GB.UTF-8/en_GB.UTF-8/en_GB.UTF-8/C/en_GB.UTF-8/en_GB.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods  
[7] base     

other attached packages:
[1] BayesianFirstAid_0.1 rjags_3-12           coda_0.16-1         
[4] lattice_0.20-24     

loaded via a namespace (and not attached):
[1] grid_3.0.1  tools_3.0.1