Notes from the Kölner R meeting, 12 December 2014
Bayesian
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dlm
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Julia
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Kalman
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Koelner R User
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Kölner R Users
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R
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Introduction to Julia for R Users
 |
| Download slides |
Interestingly, as Hans Werner pointed out, Julia is by far not the only new language around the block. Indeed, over the last decade nearly every year saw the announcement of a new language. Also big tech companies such as Microsoft, Google, Mozilla and Apple are trying to push their own programming languages: F# (2005), Go (2009), Rust (2010) and Swift (2014) respectively.
Over the more recent years we notice a movement towards the use of LLVM (Low Level Virtual Machine), on which Julia is based as well and which makes it fast. The just in time compilation demands a little mind shift if you come from R, where the mantra for speed is: vectorise - remove all for-loops. Well, the opposite is true for Julia, because your code will be compiled. For-loops are much easier to understand for the underlying compiler. Hans Werner's slides provide some good examples to get you started and pointers to further resources.
Dynamic Linear Models and Kalman Filtering
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| Download slides |
Nowadays, his challenges can be very different, sometimes only a few data points from a non-stationary process are available, and yet he is still expected to predict the future.
Dynamic linear models (dlm) can provide a remedy in those situations. In their simplest version a dlm links system and observational equations in the following way:
\[
y_t = F \theta_t + \nu_t\quad\mbox{observation eq. }\\
\theta_t = G \theta_{t-1} + \omega_t\quad\mbox{system eq.}
\] with \(\nu_t, \omega_t\) mutually independent random variables. A special case of dynamic linear models is the well known Kalman filter. In the more general case \(y_t\) and \(\theta_t\) are vectors and \(F_t, G_t\) are time variant matrices.
Holger explained that a dlm can principally be used for three purposes:
- Filtering: Estimate of the current value of the state/system variable.
- Smoothing: Estimate of past values of the state/system variable, i.e., estimating at time \(t\) given measurements up to time \(t' > t\).
- Forecasting: Forecasting future observations or values of the state/system variable.
Next Kölner R meeting
The next meeting is scheduled for 6 March 2015.Please get in touch if you would like to present and share your experience, or indeed if you have a request for a topic you would like to hear more about. For more details see also our Meetup page.
Thanks again to Bernd Weiß for hosting the event and Revolution Analytics for their sponsorship.
Next Kölner R User Meeting: Friday, 12 December 2014
dlm
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Julia
,
Kalman
,
Kölner R Users
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KölnR
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News
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R
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The next Cologne R user group meeting is scheduled for this Friday, 12 December 2014.
We have an exciting agenda with two talks on Julia and Dynamic Linear Models:
Introduction to Julia for R Users
Hans Werner BorchersJulia is a high-performance dynamic programming language for scientific computing, with a syntax that is familiar to users of other technical computing environments (Matlab, Python, R, etc.). It provides a sophisticated compiler, high performance with numerical accuracy, and extensive mathematical function libraries.
Some of the highlights of Julia are an implementation of automated differentiation, an optimisation modelling language, also integrating some of the optimisation solvers available from the COIN-OR project, and user-contributed packages for time series, statistics and machine learning, or operations research.
Dynamic Linear Models and Kalman Filtering
Holger ZienOne of the problems most commonly presented to everybody working in statistics is forecasting time series. The textbook answer is to fit an ARMA model to the data and to use the model for prediction. This approach works well for long and stationary time series. However, often the actual time series one is given to analyse are more complicated. They are ridiculously short and clearly non-stationary. Dynamic Linear Models (DLM) and Kalman Filtering go one step beyond ARMA models and may be applied to these more complicated data. I will give a brief introduction into their mathematical background and will talk about my experience using them in practice.
Drinks and Networking
The event will be followed by drinks and schnitzel at the Lux.For further details visit 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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Measuring temperature with my Arduino
Last week's approach of me guessing/feeling the temperature combined with an old thermometer was perhaps too simplistic and too unreliable. This week's attempt to measure the temperature with my Arduino might be a little OTT (over the top), but at least I am using the micro-controller again.
Yet, I have to overcome similar challenges again as last week. The Arduino with the temperature sensor (TMP36) should be a better device to measure the temperature than my thermometer, but it isn't perfect either and the readings will have some uncertainty as well. But, it will be easy to make frequent measurements and with a little trick I should be able to filter out the noise and get a much better view of the 'true' temperature.
The trick is Bayesian filtering, or as it turns out, a simplified Kalman filter (univariate, no control actions, no transition matrices).
I can't observe the temperature directly, I can only try to measure it. I think of this scenario as a series of Bayesian networks (or Hidden Markov Model). The hidden or latent variable is the 'true' temperature and the observable variable is the reading of my Arduino sensor.
I start with a prior guess of the Temperature at time \(k=0\), just like last week (note, here I will use \(x_k\) instead of \(\mu_k\)). My initial prior is \(N(x_0, \sigma_0^2)\). Now I predict the state (temperature) \(\hat{x}_1\) at the next time step. I expect the temperature to be largely unchanged and therefore my prediction is just \(\hat{x}_1 = x_0 + \varepsilon_P\) with \(\varepsilon_P \sim N(0, \sigma_P^2)\) describing the additional process variance going from one time step to the next. The process variance is independent from the uncertainty of \(x_0\), hence I can add them up and thus my prior for \(x_1\) is \(N(x_0, \sigma_0^2+\sigma_P^2)\).
The measurement of the temperature should reflect the 'true' temperature with some measurement uncertainty \(\sigma_M\). My prediction of the measurement is \(\hat{z}_1 = \hat{x}_1 + \varepsilon_M\) with \(\varepsilon_M \sim N(0, \sigma_M^2)\). The best estimator for \(\hat{z}_1\) is the actual measurement \(z_1\) and therefore the likelihood distribution of \(z_1|x_1\) is \(\,N(z_1, \sigma_M)\). Applying the formulas for Bayesian conjugates again gives the hyper-parameters for the posterior normal distribution \(x_1|\,z_1, x_0\), the temperature given the measurement and my prediction from the previous time step:
\[
x_1=\left.\left(\frac{x_0}{\sigma_0^2+\sigma_P^2} + \frac{z_1}{\sigma_M^2}\right)\right/\left(\frac{1}{\sigma_0^2+\sigma_P^2} + \frac{1}{\sigma_M^2}\right) \\
\sigma_1^2=\left(\frac{1}{\sigma_0^2+\sigma_P^2} + \frac{1}{\sigma_M^2}\right)^{-1}
\]With \(K_1 := \frac{\sigma_0^2+\sigma_P^2}{\sigma_M^2+\sigma_0^2+\sigma_P^2} \) this simplifies to:
\[
x_1 = K_1\, z_1 + (1 - K_1)\, x_0\\
\sigma_1^2 = (1 - K_1) (\sigma_0^2 + \sigma_P^2)
\]
This gives the simple iterative updating procedure (or Kalman filter):
\[
K_{k+1} = \frac{\sigma_k^2+\sigma_P^2}{\sigma_M^2+\sigma_k^2+\sigma_P^2} \\
\sigma_{k+1}^2 = (1 - K_{k+1}) (\sigma_k^2 + \sigma_P^2)\\
x_{k+1} = K_{k+1}\, z_{k+1} + (1 - K_{k+1})\, x_k
\]
In my code below I set the process variance to \(\sigma_P^2=0.01\) and the measurement variance to \(\sigma_M^2=0.5\), which led to a fairly stable reading of 21.5°C.
Changing the parameters \(\sigma_P\) and \(\sigma_M\) influence how quickly the filter reacts to changes. Here is an example where I briefly touch the temperature sensor with the above parameters. The time axis in those screen shots is about 6 seconds.
I have to do a bit more reading on the Kalman filter. It appears to be an immensely powerful tool to extract the signal from the noise. Well, it helped to put a man on the moon.
Code
This is the Processing and Arduino code I used in this post. You may have to change the port number in line 28 to your own settings.
How cold is it? A Bayesian attempt to measure temperature
Luckily I found an old thermometer to check. The thermometer showed 18°C. Is it really below 20°C?
The thermometer is quite old and I'm not sure that is works properly anymore. So, what shall I do now? Perhaps I should consider that both measurements are uncertain and try to combine them.
I believe that I can sense the temperature within ±3°C, while I think that the thermometer still works within ±2°C. Assuming that both measurements follow a Gaussian (Normal) distribution, with the uncertainties given as standard deviations, I can use Bayes' theorem to combine my hypothesis with the data. The posterior distribution will be Gaussian again with conjugated hyper-parameters:
\[
\mu=\left.\left(\frac{\mu_0}{\sigma_0^2} + \frac{\sum_{i=1}^n x_i}{s^2}\right)\right/\left(\frac{1}{\sigma_0^2} + \frac{n}{s^2}\right) \\
\sigma^2=\left(\frac{1}{\sigma_0^2} + \frac{n}{s^2}\right)^{-1}
\]With \(K := \frac{n\sigma_0^2}{s^2+n\sigma_0^2} \) this simplifies to:
\[
\mu = K\, \bar{x} + (1 - K)\, \mu_0 \mbox{, with } \bar{x}=\frac{1}{n}\sum_{i=1}^n x_i\\
\sigma = s \,\sqrt{K/n}
\]In my case I have: \(n=1,\; x_1=18^{\circ}C,\; s=2^{\circ}C,\; \mu_0=20^{\circ}C,\; \sigma_0=3^{\circ}C\).
Hence, the posterior distribution has parameters \(\mu=18.6^{\circ}C\) and \(\sigma=1.7^{\circ}C\). Thus, my best guess would be that is actually a little colder than I thought. One could argue that the probability that is below 20° is 80%.
Over the last five days my perception of the temperature didn't change, neither did the weather forecast, but the measurements showed: 18°C, 19°C, 17.5°C, 18°C, 18.5°C.
With that information the parameters update to \(\mu=18.3^{\circ}C\) and \(\sigma=0.9^{\circ}C\). I can't deny it any longer it has got colder. The probability that is below 20°C is now at 97% and the heating is on.
Without any prior knowledge I may have used a t-test to check the measurements. But here I believe that I have information about the thermometer and my own temperature sensing abilities which I don't want to ignore.
R code
Session Info
R version 3.1.2 (2014-10-31)
Platform: x86_64-apple-darwin13.4.0 (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_3-14 coda_0.16-1
[4] lattice_0.20-29
loaded via a namespace (and not attached):
[1] grid_3.1.2 MASS_7.3-35 mnormt_1.5-1 stringr_0.6.2First steps with ChainLadder: Import triangle from Excel into R
Actuarial
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ChainLadder
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Insurance
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R
1 comment
Suppose you would like to use the
ChainLadder package to forecast future claims payments for a run-off triangle that you have stored in Excel.
How do you get the triangle into R and execute a reserving function, such as
MackChainLadder?Well, there are many ways to do this and the ChainLadder package vignette, as well as the R manual on Data Import/Export has all of the details, but here is a quick and dirty solution using a CSV-file.
Open a new Excel workbook and copy your triangle into cell A1, with the first column being the accident or origin period and the first row describing the development period or age. You find an example CSV-file on GitHub.
Make sure that your triangle has no formatting, such a commas to separate thousands, as Excel will save those cell as characters. Now open R and go through the following commands:
# The first command will open a window and
# ask you to select your CSV-file
myCSVfile <- file.choose()
# Read file into R
dat <- read.csv(file=myCSVfile)
# use read.csv2 if semicolons are used as a separator
# likely to be the case if you are in continental Europe
dat # to see your data
AY X1 X2 X3 X4 X5 X6 X7 X8 X9 X10
1 1981 5012 8269 10907 11805 13539 16181 18009 18608 18662 18834
2 1982 106 4285 5396 10666 13782 15599 15496 16169 16704 NA
3 1983 3410 8992 13873 16141 18735 22214 22863 23466 NA NA
4 1984 5655 11555 15766 21266 23425 26083 27067 NA NA NA
5 1985 1092 9565 15836 22169 25955 26180 NA NA NA NA
6 1986 1513 6445 11702 12935 15852 NA NA NA NA NA
7 1987 557 4020 10946 12314 NA NA NA NA NA NA
8 1988 1351 6947 13112 NA NA NA NA NA NA NA
9 1989 3133 5395 NA NA NA NA NA NA NA NA
10 1990 2063 NA NA NA NA NA NA NA NA NA
# Load the ChainLadder package
library(ChainLadder)
# Ignore first column which holds accident year information
tri <- dat[,-1]
# Convert to matrix
tri <- as.matrix(tri)
# Add dimension names
dimnames(tri) <- list(origin=dat[,1], dev=1:ncol(tri))
# Convert into a triangle class
tri <- as.triangle(tri)
tri
dev
origin 1 2 3 4 5 6 7 8 9 10
1981 5012 8269 10907 11805 13539 16181 18009 18608 18662 18834
1982 106 4285 5396 10666 13782 15599 15496 16169 16704 NA
1983 3410 8992 13873 16141 18735 22214 22863 23466 NA NA
1984 5655 11555 15766 21266 23425 26083 27067 NA NA NA
1985 1092 9565 15836 22169 25955 26180 NA NA NA NA
1986 1513 6445 11702 12935 15852 NA NA NA NA NA
1987 557 4020 10946 12314 NA NA NA NA NA NA
1988 1351 6947 13112 NA NA NA NA NA NA NA
1989 3133 5395 NA NA NA NA NA NA NA NA
1990 2063 NA NA NA NA NA NA NA NA NA
MackChainLadder function:M <- MackChainLadder(tri, est.sigma = "Mack")
M
Latest Dev.To.Date Ultimate IBNR Mack.S.E CV(IBNR)
1981 18,834 1.000 18,834 0 0 NaN
1982 16,704 0.991 16,858 154 206 1.339
1983 23,466 0.974 24,083 617 623 1.010
1984 27,067 0.943 28,703 1,636 747 0.457
1985 26,180 0.905 28,927 2,747 1,469 0.535
1986 15,852 0.813 19,501 3,649 2,002 0.549
1987 12,314 0.694 17,749 5,435 2,209 0.406
1988 13,112 0.546 24,019 10,907 5,358 0.491
1989 5,395 0.336 16,045 10,650 6,333 0.595
1990 2,063 0.112 18,402 16,339 24,566 1.503
Totals
Latest: 160,987.00
Dev: 0.76
Ultimate: 213,122.23
IBNR: 52,135.23
Mack S.E.: 26,909.01
CV(IBNR): 0.52
To copy the full triangle back into Excel you can use the clipboard:
write.table(M$FullTriangle, file="clipboard", sep="\t"). Go back to Excel and hit <Ctrl> + V on your keyboard to paste the data into R.
For more details see the package vignette and Dan's post on pasting triangles from Excel into R via the clipboard.
If you are after a thorough overview of R in insurance take a look at the book Computational Actuarial Science with R.
Finally, join the Special Interest Group on using R in actuarial science and insurance to share your questions and answers.
Session Info
R version 3.1.2 (2014-10-31)
Platform: x86_64-apple-darwin13.4.0 (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] ChainLadder_0.1.9 systemfit_1.1-14 lmtest_0.9-33
[4] zoo_1.7-11 car_2.0-21 Matrix_1.1-4
loaded via a namespace (and not attached):
[1] acepack_1.3-3.3 actuar_1.1-6 cluster_1.15.3
[4] foreign_0.8-61 Formula_1.1-2 grid_3.1.2
[7] Hmisc_3.14-5 lattice_0.20-29 latticeExtra_0.6-26
[10] MASS_7.3-35 nnet_7.3-8 plyr_1.8.1
[13] RColorBrewer_1.0-5 Rcpp_0.11.3 reshape2_1.4
[16] rpart_4.1-8 sandwich_2.3-2 splines_3.1.2
[19] statmod_1.4.20 stringr_0.6.2 survival_2.37-7
[22] tools_3.1.2 tweedie_2.2.1 Unknown pleasures
A comment on my blog post of last week suggested just that. Reason enough to explore Python a little. Learning another computer language is like learning another human language - it takes time. Often it is helpful to start by translating from the new language back into the old one.
I found a Python script by Ludwig Schwardt that creates a plot like this:
It is only a small Python script, but it illustrated how to:
- load packages
- use conditional statements
- add comments
- write functions
- deal with arrays
- write loops
- create plots
- save output into a PDF file
R code
Session Info
R version 3.1.2 (2014-10-31)
Platform: x86_64-apple-darwin13.4.0 (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] signal_0.7-4 e1071_1.6-4
loaded via a namespace (and not attached):
[1] class_7.3-11 MASS_7.3-35 tools_3.1.2
Phase plane analysis in R
Dynamical Systems
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FitzHugh-Nagumo
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phaseR
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R
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XPP
1 comment
As an example I use here the FitzHugh-Nagumo system introduced earlier:
\begin{align}
\dot{v}=&2 (w + v - \frac{1}{3}v^3) + I_0 \\
\dot{w}=&\frac{1}{2}(1 - v - w)\\
\end{align}
The FitzHugh-Nagumo system is a simplification of the Hodgkin-Huxley model of spike generation in squid giant axon. Here \(I_0\) is a bifurcation parameter. As I decrease \(I_0\) from 0 the system dynamics change (Hopf-bifurcation): a stable equilibrium solution transform into a limit cycle.
Following Michael's paper, I can use
phaseR to plot the velocity field, add nullclines and plot trajectories from different starting points.Here I plot the FitzHugh-Nagumo system for four different parameters of \(I_0\) and three different initial starting values. The blue line show the nullcline of \(w\) i.e. \(\dot{w}=0\), while the red line shows the nullcline of \(v\). For \(I_0=-2\) I can observe the limit cycle.
Yet, I was a little surprised that the paper didn't make any references to the XPPAUT software by Bard Ermentrout, which has been around for many years as tool to analyse dynamical systems.
The GUI to the software itself gives many more options to analyse dynamical systems, including an interface to the popular bifurcation program AUTO. A good tutorial with the FitzHugh-Nagumo model was given by Mathieu Desroches at the ICS summer school 2012.
Of course I could use XPPAUT as a pure integration engine from R as well:
Considering that R started as a tool for statisticians it has made a remarkable journey; here competing with more traditional engineering tools like Matlab with MatCont or special software like XPPAUT. If someday, someone would find the time and motivation to write an interface to AUTO then R would indeed be a very good environment for the analysis of dynamical systems.
Session Info
R version 3.1.2 (2014-10-31)
Platform: x86_64-apple-darwin13.4.0 (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] phaseR_1.3 deSolve_1.10-9
loaded via a namespace (and not attached):
[1] tools_3.1.2It is the small data that matters the most
Here is a little story as it happened over the weekend.
A friend of mine flew on Saturday night from Vienna to Yerevan. The plane was scheduled to leave Austria at 10:15 PM and to arrive at 4:35 AM in Armenia. However, last weekend was the weekend when the summer time or daylight saving time (DST) ended in many European countries, including Austria, but not in Armenia.
Armenia used DST in 1981-1995 and 1997-2011. This may look a little odd, but Armenia is bar far not the only region that has changed its policy over the years. Russia decided in 2011 not to switch to winter time and keep DST all year round, only to switch to permanent winter time last weekend again.
Back to my friend, she arrives early Sunday morning at the airport in Yerivan, but her friend who promised to pick her up is not there. After a little while she takes a cab to her friends house, making it just in time before he was about to leave for the airport. What happened? Well, her friend relied on his mobile phone for his wake-up call. However, his mobile phone wasn't aware of the fact that Armenia didn't have DST anymore and set his clock back by one hour, allowing him more sleep. His phone might either be a little old or getting its signal from Russia, I don't know. Yet, this little story illustrates nicely how reliant we are nowadays on our interconnected devices having access to the correct reference data.
Imagine being in an intensive care unit relying on medial devices that have to work correctly together on time signals, when they are sourced from different companies, countries and running on different systems. Try to stay healthy, particular in late March and October, would be my advise.
So, how do systems/computers actually know which timezone to use?
Most computers will use the tz reference code and database maintained by a group of volunteers until 2011 and now by IANA. Still, how do they get informed that a region or state decided to change the rules? By keeping their ears on the ground!
The following extract from the Asia file of the tz database 2014b release is quite telling:
# Armenia
# From Paul Eggert (2006-03-22):
# Shanks & Pottenger have Yerevan switching to 3:00 (with Russian DST)
# in spring 1991, then to 4:00 with no DST in fall 1995, then
# readopting Russian DST in 1997. Go with Shanks & Pottenger, even
# when they disagree with others. Edgar Der-Danieliantz
# reported (1996-05-04) that Yerevan probably wouldn't use DST
# in 1996, though it did use DST in 1995. IATA SSIM (1991/1998) reports
# that Armenia switched from 3:00 to 4:00 in 1998 and observed DST
# after 1991, but started switching at 3:00s in 1998.
# From Arthur David Olson (2011-06-15):
# While Russia abandoned DST in 2011, Armenia may choose to
# follow Russia's "old" rules.
# From Alexander Krivenyshev (2012-02-10):
# According to News Armenia, on Feb 9, 2012,
# http://newsarmenia.ru/society/20120209/42609695.html
#
# The Armenia National Assembly adopted final reading of Amendments to the
# Law "On procedure of calculation time on the territory of the Republic of
# Armenia" according to which Armenia [is] abolishing Daylight Saving Time.
# or
# (brief)
# http://www.worldtimezone.com/dst_news/dst_news_armenia03.html
# Zone NAME GMTOFF RULES FORMAT [UNTIL]
Zone Asia/Yerevan 2:58:00 - LMT 1924 May 2
3:00 - YERT 1957 Mar # Yerevan Time
4:00 RussiaAsia YER%sT 1991 Mar 31 2:00s
3:00 1:00 YERST 1991 Sep 23 # independence
3:00 RussiaAsia AM%sT 1995 Sep 24 2:00s
4:00 - AMT 1997
4:00 RussiaAsia AM%sT 2012 Mar 25 2:00s
4:00 - AMT
Does this all sounds familiar to you and the challenges in your own organisation? Well, I gave a talk on Small & Big Data recently with a colleague of mine, should you be interested to find out more about this topic.
1. or Tiny Data in Rasmus' case↩
Approximating the impact of inflation
\[ n = \frac{70}{p}\]
Here \(p\) is the inflation in percent, e.g. if the inflation rate is \(2\%\) then today's money would buy only half of today's goods and services in 35 years. You can also think of a saving account with an interest rate of \(2\%\) that would double your money in 35 years.
It is not difficult to derive this formula. The starting point is:
\[
2K = K (1 + \frac{p}{100})^n
\]
This is equivalent to:
\[
2 = (1 + \frac{p}{100})^n
\]
Taking the log gives:
\[
\log(2) = n \log(1 + \frac{p}{100})
\]
The first term of the Taylor series approximation of \(\log(1+x)\) for small \(x\) is \(x\). Hence for small \(p\) I can set:
\[
\log(2) \doteq n \, \frac{p}{100}
\]
Next I have to estimate the value for \(\log(2)\). Writing it as an integral leads to:
\[
\log(2) = \int_1^2 \frac{1}{x} \,dx
\]
Using Simpson's rule I can approximate the integral with:
\[
\int_1^2 \frac{1}{x} \,dx \doteq \frac{2-1}{6} (1+4\frac{2}{1+2}+\frac{1}{2} )
= \frac{25}{36} \doteq 0.7
\]
Thus,
\[
n \doteq \frac{70}{p}
\]
Plotting the two formulas against each other reveals that the approximation works pretty well, even for inflation rates up to 10%.
R Code
Here is the R code to reproduce the plot.curve(70/x, from=1, to=10,
xlab="Inflation rate p%",
ylab="Number of years for purchaing power to half",
main="Impact of inflation on purchasing power",
col="blue",
type="p", pch=16, cex=0.5)
curve(log(2)/(log(1+x/100)),
from=1, to=10, add=TRUE,
col="red")
legend("topright",
legend=c("70/p","log(2)/log(1+p/100)"),
bty="n",
col=c("blue", "red"),
pch=c(16,16), pt.cex=c(1,1))googleVis 0.5.6 released on CRAN
googleVis
,
Motion Chart
,
News
,
R
No comments
gvisMotionChart. Its arguments xvar, yvar, sizevar and colorvar were not always picked up correctly. Thanks to Juuso Parkkinen for reporting this issue.
Example: Love, or to love
A few years ago Martin Hilpert posted an interesting case study for motion charts. Martin is a linguist and he researched how the usage of words in American English changed over time, e.g. some words were more often used as nouns in the past and then became more popular as a verb. Do you talk about love, or do you tell someone that you love her/him? Visit his motion chart web page for more information and details!R code
Session Info
R version 3.1.1 (2014-07-10)
Platform: x86_64-apple-darwin13.1.0 (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] googleVis_0.5.6
loaded via a namespace (and not attached):
[1] RJSONIO_1.3-0 tools_3.1.1Visualising the seasonality of Atlantic windstorms
data.table
,
ggplot2
,
Hurricane
,
Insurance
,
R
2 comments
According to the Insurance Information Institute, a normal season, based on averages from 1980 to 2010, has 12 named storms, six hurricanes and three major hurricanes. The usual peak months of August and September passed without any major catastrophes this year, but the Atlantic hurricane season is not over yet.
So, let's take a look at the data again, and here I will use code from Gaston Sanchez, who looked at windstorm data earlier.
I believe, I am using the same data as Arthur, but from a different source, which allows me to download it in one file (13.9MB). Using code from Gaston my chart of all named windstorms over the period of 1989 to 2013 looks like this.
Plotting the data by months illustrates the seasonality of windstorms during the year. Note, that there are no named windstorms for the months of February and March and although the season runs until the end of November, I can clearly see that the peak months are August and September.
Perhaps there are other time components that effect the seasonality across years, such as La Niña? Plotting the years 1989 to 2013 certainly shows that there are years with more windstorm activity than others. Critical to the impact and cost of windstorms is if they make landfall or not. Hence, I add information on deaths and economic damages for major hurricanes over that period from Wikipedia.
Although 1992 doesn't show much windstorm activity, hurricane Andrew was the most expensive one to that date and changed the insurance industry significantly. Following hurricane Andrew insurance companies started to embrace catastrophe models.
The economic loss is a very poor proxy to the loss of lives. In 1998 Hurricane Mitch cost the lives of over 19,000, with most of them living in Honduras. The economic cost of $6.2bn looks small compared to the cost of Andrew six years earlier ($26.5bn).
Although over the last few years we have seen a fairly benign impact of windstorm activity, the next big event can have a much more sever impact than what we have seen historically, as the population (and economy) on the Gulf of Mexico has and is growing rapidly, 150% from 1960 to 2008 alone. A hurricane season causing damages over $200bn doesn't look unreasonable anymore.
R Code
Session Info
R version 3.1.1 (2014-07-10)
Platform: x86_64-apple-darwin13.1.0 (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] grid stats graphics grDevices utils datasets
[7] methods base
other attached packages:
[1] XML_3.98-1.1 data.table_1.9.2 ggplot2_1.0.0
[4] maps_2.3-7
loaded via a namespace (and not attached):
[1] colorspace_1.2-4 digest_0.6.4 gtable_0.1.2
[4] labeling_0.3 MASS_7.3-33 munsell_0.4.2
[7] plyr_1.8.1 proto_0.3-10 Rcpp_0.11.2
[10] reshape2_1.4 scales_0.2.4 stringr_0.6.2
[13] tools_3.1.1 Running RStudio via Docker in the Cloud
Docker
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R
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RStudio
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My aim was to rent some resources in the cloud, pull an RStudio Server container and run RStudio in a browser. It was actually surprisingly simple to get started.
I chose Digital Ocean as my cloud provider. They have many Linux systems to choose from and also a pre-built Docker system.
After about a minute I had kicked off the Docker droplet I could log into the system in a browser window and start pulling the Docker file, e.g. Dirk's container.
Once the downloads finished I could start the RStudio Server using the
docker run command and log into a RStudio session. To my surprise even my googleVis package worked out of the box. The plot command opened just another browser window to display the chart; here the output of the WorldBank demo.
All of this was done within minutes in a browser window. I didn't even use a terminal window. So, that's how you run R on an iPad. Considering that the cost for the server was $0.015 per hour, I wonder why I should buy my own server, or indeed buy a new computer.
Managing R package dependencies
CRAN
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End User Computing
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EUC
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R
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roxyPackage
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Two packages can help here: roxyPackage and miniCRAN.
I wrote about roxyPackage earlier on this blog. It allows me to create a local repository to distribute my package, while at the same time execute and control the build process from within R. But what about my package's dependencies? Here miniCRAN helps. miniCRAN is a new package by Andrie de Vries that enables me to find and download all package dependencies and store them in a local repository, e.g. the one used by roxyPackage.
For more details about roxyPackage and miniCRAN read the respective package vignettes.
Example
To create a local sub-CRAN repository for the two packages I maintain on CRAN and with all their dependencies I use:library("miniCRAN")
my.pkgs <- c("googleVis", "ChainLadder")
pkgs <- pkgDep(my.pkgs, suggests = TRUE, enhances=FALSE)
makeRepo(pkgs = pkgs, path="/Users/Shared/myCRANRepos")dg <- makeDepGraph(my.pkgs, includeBasePkgs=FALSE,
suggests=TRUE, enhances=TRUE)
set.seed(1)
plot(dg, legendPosEdge = c(-1, 1),
legendPosVertex = c(1, 1), vertex.size=20)
What a surprise! In total I end up with 42 packages from CRAN and I didn't expect any connection between the ChainLadder and googleVis package.
Bonus tip
Don't miss out on Pat Burns's insightful talk about effective risk management from EARL. His thoughts reminded me of the great Karl Popper: Good tests kill flawed theories; we remain alive to guess again.Session Info
R version 3.1.1 (2014-07-10)
Platform: x86_64-apple-darwin13.1.0 (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] miniCRAN_0.1-0
loaded via a namespace (and not attached):
[1] httr_0.5 igraph_0.7.1 stringr_0.6.2 tools_3.1.1
[5] XML_3.98-1.1Notes from the Kölner R meeting, 12 September 2014
Next Kölner R User Meeting: Friday, 12 September 2014
Kölner R Users
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KölnR
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News
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R
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The next Cologne R user group meeting is scheduled for this Friday, 12 September 2014.
We have a great agenda with international speakers:
- Maarten-Jan Kallen: Introduction to Renjin, the R interpreter for the JVM
- Jonathan Cornelissen, Martijn Theuwissen: DataCamp - An online interactive learning platform for R
Zoom, zoom, googleVis
googleVis
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interactive
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R
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zoom
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ChainLadder 0.1.8 released
ChainLadder
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Insurance
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News
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R
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reserving
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stochastic reserving
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What is claims reserving?
The insurance industry, unlike other industries, does not sell products as such but promises. An insurance policy is a promise by the insurer to the policyholder to pay for future claims for an upfront received premium.As a result insurers don't know the upfront cost for their service, but rely on historical data analysis and judgement to predict a sustainable price for their offering. In General Insurance (or Non-Life Insurance, e.g. motor, property and casualty insurance) most policies run for a period of 12 months. However, the claims payment process can take years or even decades. Therefore often not even the delivery date of their product is known to insurers. The money set aside for those future claims payments are called reserves.
googleVis 0.5.5 released
googleVis
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News
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R
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 |
| Screen shot of some of the Google Charts |
New to googleVis? Review the examples of all googleVis charts on CRAN.
Perhaps the best known example of the Google Chart API is the motion chart, popularised by Hans Rosling in his 2006 TED talk.
GrapheR: A GUI for base graphics in R
GrapheR
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graphics
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R
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tcltk
5 comments
The author, Maxime Hervé, published an article about the package [1] in the same issue of the R Journal as we did on googleVis. Yet, it took me a package update notification on CRANbeeries to look into GrapheR in more detail - 3 years later! And what a wonderful gem GrapheR is.
The package provides a graphical user interface for creating base charts in R. It is ideal for beginners in R, as the user interface is very clear and the code is written along side into a text file, allowing users to recreate the charts directly in the console.
Adding and changing legends? Messing around with the plotting window settings? It is much easier/quicker with this GUI than reading the help file and trying to understand the various parameters.
Here is a little example using the
iris data set.library(GrapheR)
data(iris)
run.GrapheR()
Thanks to R Markdown: Perhaps Word is an option after all?
I have been using R Markdown for a while now and have grown very fond of it. Although I am quite happy with PDF and HTML output for basic reports and to switch to Sweave/LaTeX for more complex documents, I was pleasantly surprised to learn that the new version of RStudio can produce MS Word files directly from R Markdown as well; thanks to the power of pandoc. Perhaps Word is an option after all?
Hit and run. Think Bayes!
Bayesian
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gRain
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R
8 comments
Bayes' theorem
Bayes' theorem states that given two events \(D\) and \(H\), the probability of \(D\) and \(H\) happening at the same time is the same as the probability of \(D\) occurring, given \(H\), weighted by the probability that \(H\) occurs; or the other way round. As a formula it can be written as:\[
P(H \cap D) = P(H|D) \, P(D) = P(D|H) \, P(H)
\]
Or if I rearrange it:
\[
P(H|D) = \dfrac{P(D|H) \, P(H)}{P(D)}
\]
Imagine \(H\) is short for hypothesis and \(D\) is short for data, or evidence. Then Bayes' theorem states that the probability of a hypothesis given data is the same as the likelihood that we observe the data given the hypothesis, weighted by the prior belief of the hypothesis, normalised by the probability that we observe the data regardless of the hypothesis.
The tricky bit in real life is often to figure out what the hypothesis and data are.
Hit and run accident
This example is taken from Daniel Kahneman's book Thinking, fast and slow [1].A cab was involved in a hit and run accident at night. Two cab companies, the Green and the Blue, operate in the city. 85% of the cabs in the city are Green and 15% are Blue. A witness identified the cab as Blue. The court tested the reliability of the witness under the same circumstances that existed on the night of the accident and concluded that the witness correctly identified each one of the two colours 80% of the time and failed 20% of the time.
What is the probability that the cab involved in the accident was Blue rather than Green knowing that this witness identified it as Blue?
What is here the data and what is here the hypothesis? Intuitively you may think that the proportion of Blue and Green cabs is the data at hand and the witness accusation that a Blue cab was involved in the accident is the hypothesis. However, after some thought I found the following assignment much more helpful, as then \(P(H|D)\) matches the above question:
\(H =\) Accident caused by Blue cab. \(D =\) Witness said the cab was Blue.
With this it is straightforward to get the probabilities of \(P(H)=15\%\) and \(P(D|H)=80\%\). But what is \(P(D)\)? Well, when would the witness say that the cab was Blue? Either, when the cab was Blue and so the witness is right, or when the cab was actually Green and the witness is incorrect. Thus, following the law of total probability:
$$\begin{align}
P(D) & = P(D|H) P(H) + P(D | \bar{H}) P(\bar{H})\\
& = 0.8 \cdot 0.15 + 0.2 \cdot 0.85 = 0.29
\end{align}$$Therefore I get \(P(H|D)=41\%\). Thus, even if the witness states that the cab involved in the accident was Blue, the probability of this being true is only \(41\%\).
An alternative way to think about this problem is via a Bayesian Network. The colour of the cab will influence the statement of the witness. In R I can specify such a network using the gRain package [2], which I discussed in an earlier post. Here I provide the distribution of the cabs and the conditional probabilities of the witness as an input. After I compile the network, I can again read off the probabilities that a Blue cab was involved, when the witness said so.
R code
Notes from the 2nd R in Insurance Conference
This one-day conference focused once more on applications in insurance and actuarial science that use R. Topics covered included reserving, pricing, loss modelling, the use of R in a production environment and more.
In the first plenary session, Montserrat Guillen (Riskcenter, University of Barcelona) and Leo Guelman (Royal Bank of Canada, RBC Insurance) spoke about the rise of uplift models. These predictive models are used for improved targeting of policyholders by marketing campaigns, through the use of experimental data. The presenters illustrated the use of their uplift package (available on CRAN), which they have developed for such applications.
Simple user interface in R to get login details
Fortunately, I found some old code in a post by Barry Rowlingson that does just that. It uses the tcltk package in R to create a little window in which the user can enter her details, without showing the password. The tcltk package is part of base R, which means the code will run on any operating system. Nice!
googleVis 0.5.3 released
googleVis
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News
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R
3 comments
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| Screen shot of some of the Google Charts |
Although this is mainly a maintenance release, I'd like to point out two changes:
- Default chart width is set to 'automatic' instead of 500 pixels.
- Intervals for columns roles have to end with the suffix ".i", with "i" being an integer. Several interval columns are allowed, see the roles demo and vignette for more details.
- The order of y-variables in core charts wasn't maintained. Thanks to John Taveras for reporting this bug.
- Width and height of googleVis charts were only accepted in pixels, although the Google Charts API uses standard HTML units (for example, '100px', '80em', '60', 'automatic'). If no units are specified the number is assumed to be pixels. This has been fixed. Thanks to Paul Murrell for reporting this issue.
Last chance to register for the R in Insurance conference
The registration for the 2nd R in Insurance conference at Cass Business School London will close this Friday, 4 July.
The programme includes talks from international practitioners and leading academics, see below. For more details and registration visit: http://www.rininsurance.com.
Generating and visualising multivariate random numbers in R
pairs.panels function of the psych package [1] that I discovered recently to visualise multivariate random numbers.Here is a little example with a Gaussian copula and normal and log-normal marginal distributions. I use
pairs.panels to illustrate the steps along the way.I start with standardised multivariate normal random numbers:
library(psych)
library(MASS)
Sig <- matrix(c(1, -0.7, -.5,
-0.7, 1, 0.6,
-0.5, 0.6, 1),
nrow=3)
X <- mvrnorm(1000, mu=rep(0,3), Sigma = Sig,
empirical = TRUE)
pairs.panels(X)
Who will win the World Cup and which prediction model?
forecast
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googleVis
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R
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World Cup
8 comments
To me the question is not only which country will win the World Cup, but also which prediction model will come closest to the actual results. Here I present three teams, FiveThirtyEight, a polling aggregation website, Groll & Schauberger, two academics from Munich and finally Lloyd's of London, the insurance market.
The guys around Nate Silver at FiveThirtyEight have used the ESPN’s Soccer Power Index to predict the outcomes of games and continue to update their model. Brazil is their clear favourite.
Andreas Groll & Gunther Schauberger from the LMU Munich developed a model, which like the approach from FiveThirtyEight aims to estimate the probability of a team winning the world cup. But unlike FiveThirtyEight, they see Germany to take the trophy home.
Lloyd's chose a different approach for predicting the World Cup final. The insurance market looked at the risk aspect of the teams and ranked the teams by their insured value. Arguably the better a team the higher their insured value. As a result Lloyd's predicts Germany to win the World Cup.
Quick reminder; what's the difference between insurance and gambling? Gambling introduces risk, where none exists. Insurance mitigates risk, where risk exists.
The joy of joining data.tables
data.table
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join
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lattice
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R
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data.table in R. Mapping old data to new data
Categories in general are never fixed, they always change at some point. And then the trouble starts with the data. For example not that long ago we didn't distinguish between smartphones and dumbphones, or video on demand and video rental shops.I would like to back track price change data for smartphones and online movie rental shops, assuming that their earlier development can be set to the categories they were formerly part of, namely mobile and video rental shops to create indices.
Here is my toy data:
I'd like to create price indices for all products and where data for the new product categories is missing, use the price changes of the old product category.
The
data.table package helps here. I start with my original data, convert it into a data.table and create mapping tables. That allows me to add the old product with its price change to the new product. The trick here is to set certain columns as key. Two data tables with the same key can easily be joined. Once I have the price changes for products and years the price index can be added. The plot illustrates the result, the R code is below.
Early bird registration for R in Insurance closes tomorrow
This one-day conference will focus once more on applications in insurance and actuarial science that use R, the lingua franca for statistical computation. Topics covered include reserving, pricing, loss modelling, the use of R in a production environment, and more. All topics are to be discussed within the context of using R as a primary tool for insurance risk management, analysis and modelling.
The conference programme consists of invited talks and contributed presentations discussing the wide range of fields in which R is used in insurance:
Attendance of the whole conference is the equivalent of 6.5 hours of CPD for members of the Actuarial Profession.
You can register directly on the conference web site www.rininsurance.com.
The organisers gratefully acknowledge the sponsorship of Mango Solutions, CYBAEA, RStudio and PwC without whom the event wouldn't be possible.
Notes from the Kölner R meeting, 23 May 2014
Taking R to the Enterprise
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| Andrie de Vries: Taking R to the Enterprise. Photo: Günter Faes |
Andrie talked about how R is finding its way into the enterprise. He argued that R has become the go-to tool for data and statistical analysis in many companies. He observed that over the years the commercial user base evolved from a small expert community with a love for the command line and cutting edge technology into a much wider audience. Although R is still used by the technical experts, who demand more and more power, out-of-memory computations on bigger data, etc. the number of casual R users is growing rapidly. Often the casual R user relies on code written by others as part of a bigger workflow and hence prefers a more standardised user interface.
Andrie illustrated how Revolution Analytics aims to satisfy both user groups. He started with the expert R users by demonstrating Revolution Analytics' RevoScaleR package that allows them to carry out analysis on bigger data. His example followed closely the airline analysis of Joseph Rickert's white paper. Andrie then showed how more complex R code and functions can be integrated (and to some extend hidden) into Alteryx and Tableau via Rserve.
googleVis overview & developments
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| Slides and code available on GitHub |
I gave a brief introduction to googleVis and presented recent developments. The googleVis package provides an interface between R and the Google Chart Tools API. It allows users to create web pages with interactive charts based on R data frames and to display them either via the local R HTTP help server or within their own sites, without uploading the data to Google. The best known example is perhaps the motion chart of fertility and life expectancy data from the World Bank as first presented by Hans Rosling. Another popular example is the chart that illustrates the performance of the famous Lloyd's insurance market.
Since version 0.5.0 of googleVis many new chart types have been added to googleVis, including annotation, sankey, calendar and timeline charts. Additionally new markdown vignettes have been included to present the examples also on CRAN. The slides and rmarkdown code are available via GitHub.
Kölsch & Schnitzel
No Kölner R meeting would be complete without a few Kölsch and Schnitzel at the Lux. We were lucky with the weather so that we could sit outside to enjoy drinks, food and networking opportunities. |
| Kölsch and Schnitzel at the Lux. Photo: Günter Faes |
Next Kölner R meeting
The next meeting is scheduled for 12 September 2014.Please get in touch if you would like to present and share your experience, or indeed if you have a request for a topic you would like to hear more about. For more details see also our Meetup page.
Thanks again to Bernd Weiß for hosting the event and Revolution Analytics for their sponsorship.
Next Kölner R User Meeting: Friday, 23 May 2014
Kölner R Users
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KölnR
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News
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R
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To celebrate our 10th meeting we welcome:
- Andrie de Vries (Revolution Analytics and Co-author of R for Dummies): Taking R to the Enterprise
- Markus Gesmann: googleVis overview and recent developments
Further details 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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