Category Archives: Non classé

October, grant proposal season

In 2012, Danielle Herbert, Adrian Barnett, Philip Clarke and Nicholas Graves published an article entitled “on the time spent preparing grant proposals: an observational study of Australian researchers“, whose conclusions had been included in Nature under a more explicit title, “Australia’s grant system wastes time” ! In this study, they included 3700 grant applications sent to the National Health and Medical Research Council, and showed that each application represented 37 working days: “Extrapolating this to all 3,727 submitted proposals gives an estimated 550 working years of researchers’ time (95% confidence interval, 513-589)“. But in these times when I have to write my funding application, I find that losing 37 days of work is huge. Because it’s become the norm! And somehow, it’s sad.

Forget about the crazy idea that I would rather, in fact, spend more time doing my research. In fact, the thought I had this morning was that it is rather sad that in the Faculty of Science, mathematicians are asked to spend a considerable amount of time, comparable to that required of physicists or chemists, for often smaller amounts of funding… And I thought it could be easily verified. We start by retrieving the discipline codes

url="http://www.nserc-crsng.gc.ca/NSERC-CRSNG/FundingDecisions-DecisionsFinancement/ResearchGrants-SubventionsDeRecherche/ResultsGSC-ResultatsCSS_eng.asp"
download.file(url,destfile = "GSC.html")
library(XML)
tables=readHTMLTable("GSC.html")
GSC=tables[[1]]$V1
GSC=as.character(GSC[-(1:2)])
namesGSC=tables[[1]]$V2
namesGSC=as.character(namesGSC[-(1:2)])

We’re going to need a small function, to remove the $ and other symbols that pollute the data (and prevent them from being treated as numbers)

library(stringr)
Correction = function(x) as.numeric(gsub('[$,]', '', x))

We will now read the 12 pages, and harvest (we will just take the 2017 data, but we could go back a few years before)

grants= function(gsc){
     url=paste("http://www.nserc-crsng.gc.ca/NSERC-CRSNG/FundingDecisions-DecisionsFinancement/ResearchGrants-SubventionsDeRecherche/ResultsGSCDetail-ResultatsCSSDetails_eng.asp?Year=2017&GSC=",gsc,sep="")
    download.file(url,destfile = "GSC.html")
    library(XML)
    tables=readHTMLTable("GSC.html")
    X=as.character(tables[[1]]$"Awarded Amount")
    A=as.numeric(Vectorize(Correction)(X))
return(c(median(A),mean(A),as.numeric(quantile(A,(1:99)/100))))
}
M=Vectorize(grants)(GSC[1:12])

The average amounts of individual grants can be compared,

barplot(M[2,])

In mathematics, the average grant amount is $24400. If we normalize by this quantity, we obtain

barplot(M[2,]/M[2,8])

In other words, the average amount of a (individual) grant in chemistry (to pay for students, conferences, etc.) is twice that in mathematics, 60% higher in physics than in maths…

We can also look at the median values (rather than the averages)

barplot(M[1,])

Here again, it is in mathematics that it is the weakest….

barplot(M[1,]/M[1,8])

in comparable proportions. If we think that the time spent writing should be proportional to the amount allocated, we should spend half as much time in math as in chemistry.

Cumulative functions can also be ploted,

plot(M[3:101,8],(1:99)/100,type="s",xlim=range(M))
lines(M[3:101,5],(1:99)/100,type="s",col="red")
lines(M[3:101,4],(1:99)/100,type="s",col="blue")

with math in black, physics in red, and chemistry in blue. What is surprising is the bottom part: a “bad” researcher in chemistry or physics will earn more than the median researcher in mathematics…

Now that my intuition is confirmed, I have to go back, writing my proposal… and explain to my coauthors that I have to postpone some research projects because, well, you know…

Tests non-paramétriques et simulations

Lors du dernier cours de statistique, nous avons présenter les tests d’ajustment de lois. Nous avions illustré ces tests à partir de la taille d’individus (déjà utilisé pour présenter l’ajustement de lois, et l’estimation de densité), correspondant à https://latex.codecogs.com/gif.latex?\boldsymbol{x}=\{x_1,\cdots,x_n\}.

> Davis=read.table(
+ "http://socserv.socsci.mcmaster.ca/jfox/Books/Applied-Regression-2E/datasets/Davis.txt")
> Davis[12,c(2,3)]=Davis[12,c(3,2)]
> X=Davis$height
> n=length(X)

On notera https://latex.codecogs.com/gif.latex?%20(x_{i:n}) la statistique d’ordre, au sens où

https://latex.codecogs.com/gif.latex?%20x_{1:n}\leq%20x_{2:n}\leq\cdots\leq%20x_{n-1:n}\leq%20x_{n:n}

Parmi les outils graphiques, nous avons vu le PP plot (graphique probabilité-probabilité) et le QQ plot (graphique quantile). Le code pour créer un PP plot peut être le suivant

> PP=function(Y,F=pnorm){
+   n=length(Y)
+   x=F(sort(Y))
+   y=seq(1/n/2,1-1/n/2,by=1/n)
+   return(data.frame(x=x,y=y))
+ }

qui représente (à un détail près) le nuage de points

https://latex.codecogs.com/gif.latex?\left\{F_0(x_{i:n}),\frac{i}{n}\right\}

et celui pour le QQ plot serait

> QQ=function(Y,Q=qnorm){
+   n=length(Y)
+   x=Q(seq(1/n/2,1-1/n/2,by=1/n))
+   y=sort(Y)
+   return(data.frame(x=x,y=y))
+ }

qui représente (toujours à un détail près) le nuage de points

https://latex.codecogs.com/gif.latex?%20\left\{F_0^{-1}\left(\frac{i}{n}\right),x_{i:n}\right\}

où https://latex.codecogs.com/gif.latex?%20F_0 est la loi que l’on cherche à tester, au sens où on a https://latex.codecogs.com/gif.latex?%20H_0:F=F_0 avec comme hypothèse alternative https://latex.codecogs.com/gif.latex?%20H_1:F\neq%20F_0.

Continue reading Tests non-paramétriques et simulations

La tarification en assurance, et la sélection à l’université

En assurance, même si les primes sont calculées ex ante, on distingue la tarification a priori et a posteriori. Dans la tarification a priori on va utiliser des variables dites explicatives pour affecter dans une classe tarifaire. Par exemple en assurance automobile, on va utiliser l’âge, le genre, le lieu d’habitation, la puissance du véhicule pour prédire, a priori, la charge sinistre pour l’année à venir. Le principe de la tarification repose sur la loi des grands nombres qui consiste à faire demande un prime égale à ce que l’on pense payer – en moyenne – par classe de risque (la compagnie est alors – en moyenne – à l’équilibre financier). Mais on peut utiliser une tarification dite a posteriori où on utilise de l’information passé (par exemple le nombre de sinistres survenus les 3 dernières années, information que l’on peut retrouver, en France, dans le mécanisme bonus-malus). Si j’oppose ici les deux, on imagine que ces deux informations sont intéressantes, et peut être complémentaires. En revanche, il n’y a pas de tarification ex post avec ce mécanisme. Il y aura éventuellement un bonus qui sera offert l’année prochaine (et non pas de manière rétroactive), mais l’assureur ne peut pas rétropédaler en disant “finalement, vu la manière dont vous conduisez, la prime que vous nous devez pour l’année en cours n’est pas de 600 euros, mais de 900 euros“. La seule possibilité est de rediscuter, au moment du renouvellement, le montant de la prime, au vu de l’expérience.

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“A 99% TVaR is generally a 99.6% VaR”

Almost 6 years ago, I posted a brief comment on a sentence I found surprising, by that time, discovered in a report claiming that

the expected shortfall […] at the 99 % level corresponds quite closely to the […] value-at-risk at a 99.6% level

which was inspired by a remark in Swiss Experience report,

expected shortfall […] on a 99% confidence level […} corresponds to approximately 99.6% to 99.8% Value at Risk

Continue reading “A 99% TVaR is generally a 99.6% VaR”

Another Interactive Map for the Cholera Dataset

Following my previous post, François (aka @FrancoisKeck) posted a comment mentionning another package I could use to get an interactive map, the rleafmap package. And the heatmap was here easy to include.

The first part is still the same, to get the data,

> require(rleafmap)
> library(sp)
> library(rgdal)
> library(maptools)
> library(KernSmooth)
> setwd("/home/arthur/Documents/")
> deaths <- readShapePoints("Cholera_Deaths")
> df_deaths <- data.frame(deaths@coords)
> coordinates(df_deaths)=~coords.x1+coords.x2
> proj4string(df_deaths)=CRS("+init=epsg:27700") 
> df_deaths = spTransform(df_deaths,CRS("+proj=longlat +datum=WGS84"))
> df=data.frame(df_deaths@coords)

To get a first visualisation, use

> stamen_bm <- basemap("stamen.toner")
> j_snow <- spLayer(df_deaths, stroke = FALSE)
> writeMap(stamen_bm, j_snow, width = 1000, height = 750, setView = c( mean(df[,1]),mean(df[,2])), setZoom = 14)

and again, using the + and the – in the top left area, we can zoom in, or out. Or we can do it manually,

> writeMap(stamen_bm, j_snow, width = 1000, height = 750, setView = c( mean(df[,1]),mean(df[,2])), setZoom = 16)

To get the heatmap, use

> library(spatstat)
> library(maptools)

> win <- owin(xrange = bbox(df_deaths)[1,] + c(-0.01,0.01), yrange = bbox(df_deaths)[2,] + c(-0.01,0.01))
> df_deaths_ppp <- ppp(coordinates(df_deaths)[,1],  coordinates(df_deaths)[,2], window = win)
> 
> df_deaths_ppp_d <- density.ppp(df_deaths_ppp, 
  sigma = min(bw.ucv(df[,1]),bw.ucv(df[,2])))
 
> df_deaths_d <- as.SpatialGridDataFrame.im(df_deaths_ppp_d)
> df_deaths_d$v[df_deaths_d$v < 10^3] <- NA

> stamen_bm <- basemap("stamen.toner")
> mapquest_bm <- basemap("mapquest.map")
 
> j_snow <- spLayer(df_deaths, stroke = FALSE)
> df_deaths_den <- spLayer(df_deaths_d, layer = "v", cells.alpha = seq(0.1, 0.8, length.out = 12))
> my_ui <- ui(layers = "topright")

> writeMap(stamen_bm, mapquest_bm, j_snow, df_deaths_den, width = 1000, height = 750, interface = my_ui, setView = c( mean(df[,1]),mean(df[,2])), setZoom = 16)

The amazing thing here are the options in the top right corner. For instance, we can remove some layers, e.g. to remove the points

or to change the background

To get an html file, instead of a standard visualisation in RStudio, use

> writeMap(stamen_bm, mapquest_bm, j_snow, df_deaths_den, width = 450, height = 350, interface = my_ui, setView = c( mean(df[,1]),mean(df[,2])), setZoom = 16, directView ="browser")

which will generate the html table (as well as some additional files actually) above. Awesome, isn’t it?

Somewhere else, part 176

yes, extreme winds  cause a waterfall (in England) to blow upward

and some more posts and articles worth reading

Continue reading Somewhere else, part 176