Sunday, July 5, 2015

More on causes of death in Netherlands over the years

Last week I had a post 'Deaths in the Netherlands by cause and age'. During creation of that post I made one plot which I had not shown. It shows something odd. There is a vertical striping. Hence mortality varies by year across age.
To examine this phenomenon further here is a plot of some underlying causes. I would say the striping is present for at least three categories; "Diseases of the circulatory system", "Diseases of the respiratory organs" and "Sympt., Abnormal clinical Observations". This is odd, since these do not seem to be contagious. I suspect therefore that something like harsh weather (heat or cold) makes life more difficult, but does not get to be the final cause in the administration.
In addition there is something which I did not realize before regarding "Mental and behavioral disorders". They are age related. But it also seems that somewhere in the nineties of last century they became acceptable to register. And suddenly they are present, across several age categories.
This plot, same data, differently organized, shows that the years with these causes are similar, especially "Diseases of the circulatory system" and "Diseases of the respiratory organs"

Can it statistically be seen?

It is very nice that I can see that, but how about measuring it? Hence for age 90 to 95, after detrending, correlation between the two most visually correlated causes of death.
Pearson's product-moment correlation

data:  xx$`Diseases of the respiratory organs` and xx$`Diseases of the circulatory system`
t = 2.4997, df = 62, p-value = 0.01509
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.06133681 0.51042863
sample estimates:
     cor 
0.302584 

Code

library(dplyr)
library(ggplot2)
txtlines <- readLines('Overledenen__doodsoo_170615161506.csv')
txtlines <- grep('Centraal',txtlines,value=TRUE,invert=TRUE) 
#txtlines[1:5]
#cat(txtlines[4])
r1 <- read.csv(sep=';',header=FALSE,
        col.names=c('Causes','Causes2','Age','year','aantal','count'),
        na.strings='-',text=txtlines[3:length(txtlines)]) %>%
    select(.,-aantal,-Causes2)
transcauses <- c(
    "Infectious and parasitic diseases",
    "Diseases of skin and subcutaneous",
    "Diseases musculoskeletal system and connective ",
    "Diseases of the genitourinary system",
    "Pregnancy, childbirth",
    "Conditions of perinatal period",
    "Congenital abnormalities",
    "Sympt., Abnormal clinical Observations",
    "External causes of death",
    "Neoplasms",
    "Illness of blood, blood-forming organs",
    "Endocrine, nutritional, metabolic illness",
    "Mental and behavioral disorders",
    "Diseases of the nervous system and sense organs",
    "Diseases of the circulatory system",
    "Diseases of the respiratory organs",
    "Diseases of the digestive organs",
    "Population",
    "Total all causes of death")
#cc <- 
cbind(transcauses,levels(r1$Causes))
options(width=100)
levels(r1$Causes) <- transcauses
levels(r1$Age) <- 
    gsub('jaar','year',levels(r1$Age)) %>%
    gsub('tot','to',.) %>%
    gsub('of ouder','+',.)
r1 <- mutate(r1,age=as.numeric(sub(' .*$','',Age)))

Deaths <- filter(r1,Causes=='Total all causes of death') %>%
    mutate(.,Total=count) %>%
    select(.,-count,-Causes) %>%
    merge(.,r1) %>%
    filter(.,Causes %in% transcauses[18]) %>%
    mutate(.,Population=count,
        Percentage=100*Total/Population,
        year = as.numeric(gsub('*','',year,fixed=TRUE))) %>%
    select(.,-Causes,-count)

png('deathall.png')
v <- ggplot(Deaths[Deaths$age>60,], aes( year,Age, fill = Percentage))
v + geom_raster() +
    scale_fill_gradientn (
        colours=c('white','black'))+
    theme(legend.position="bottom")+
    ggtitle('Total all causes of death')
dev.off()

v3 <- filter(r1,Causes %in% transcauses[18],
        age>65) %>%
    mutate(.,Population=count) %>%
    select(.,-count,-Causes) %>%
    merge(.,r1) %>%
    filter(.,Causes %in% transcauses[c(8,15,9,10,13,16)]) %>%
    mutate(.,Total=count,
        Percentage=100*Total/Population,
        year = as.numeric(gsub('*','',year,fixed=TRUE))) %>%
    select(.,-count)
png('bycause.png')
 ggplot(v3, aes( year,Age, fill = Percentage))+
  geom_raster() +
    scale_fill_gradientn (
        colours=c('white','black'))+
    theme(legend.position="bottom")+
    facet_wrap( ~ Causes,nrow=3)
dev.off()

png('byage.png')
ggplot(v3[v3$age>75,], aes( year,Causes, fill = Percentage))+
    geom_raster() +
    scale_fill_gradientn (
        colours=c('white','black'))+
    theme(legend.position="bottom")+
    facet_wrap( ~ Age,nrow=3)
dev.off()

xx <- filter(r1,Causes %in% transcauses[18],
        age==90) %>%
    mutate(.,Population=count) %>%
    select(.,-count,-Causes) %>%
    merge(.,r1) %>%
    filter(.,Causes %in% transcauses[c(8,15,9,16)]) %>%
    mutate(.,Total=count,
        Percentage=100*Total/Population,
        year = as.numeric(gsub('*','',year,fixed=TRUE)),
        Causes=factor(Causes)) %>%
    select(.,-count,-Age,-age,-Population,-Total) %>%
   reshape(.,direction='wide',timevar='Causes',idvar='year')

names(xx) <- gsub('Percentage.','',names(xx))
for (i in 2:ncol(xx)) xx[,i]<- xx[,i] - predict(loess(xx[,i] ~ year,data=xx))

cor.test(xx$`Diseases of the respiratory organs`,
    xx$`Diseases of the circulatory system`)

Sunday, June 28, 2015

Deaths in the Netherlands by cause and age

I downloaded counts of deaths by age, year and mayor cause from the Dutch statistics site. In this post I do some plots to look at causes and changes between the years.

Data 

Data from CBS. I downloaded the data in Dutch, hence the first thing to do was provide some kind of translation. The coding used seems slightly different from IDC-10 main categories (and has been alphabetically disordered compared to that). I used Google translate and IDC-10 to obtain the translations

Plots

Preparation

In the following I will be using both percentage of population and percentage of deaths by age cohort. The need for the percentage of deaths is because in some cohorts the percentages of deaths are much higher, thereby hiding anything happening in other cohorts. In addition I should mention that for visual purposes only the most important eight causes are used in the plots

Young

It seems that most of risks are associated with birth. In addition, these risks have steadily been decreasing. 
Looking at the age cohorts above 0 years, it seems accidents are most important. Most remarkable is a spike at 1953, which occurs for all four ages. After some consideration, I link this to the North Sea flood of 1953. It is remarkable that this is visible in the plot. It says a lot about how safe we are from accidents that it does. In the age category 15 to 20 there is also a relatively large bump during the 1970 to 1975. This is more difficult to explain, but I suspect traffic, especially the moped. A light motorcycle which preferably would be boosted to run much faster than the legal speed. 1975 saw the requirement to wear a helmet. It was much hated at the time, but in hindsight I can see that government felt compelled to do something and that it did have effect.
Looking at the plots, it seems the next big cause are Neoplasms. This is not because these become more deadly, it is because accidents are getting under control.

Elderly

For the elderly, diseases of the circulatory system are the main cause and decreasing quite a bit. The number of Symptoms and Abnormal Clinical Observations seems to decrease too. Since this seems to be a nice name for the 'other' category, this may be better diagnostics.
What is less visible is the increase in mental and behavioral disorders, especially after 1980 and at oldest age. It also seems that Neoplasms are getting lower very slowly.

Code

data reading

library(dplyr)
library(ggplot2)
txtlines <- readLines('Overledenen__doodsoo_170615161506.csv')
txtlines <- grep('Centraal',txtlines,value=TRUE,invert=TRUE) 
#txtlines[1:5]
#cat(txtlines[4])
r1 <- read.csv(sep=';',header=FALSE,
        col.names=c('Causes','Causes2','Age','year','aantal','count'),
        na.strings='-',text=txtlines[3:length(txtlines)]) %>%
    select(.,-aantal,-Causes2)
transcauses <- c(
    "Infectious and parasitic diseases",
    "Diseases of skin and subcutaneous",
    "Diseases musculoskeletal system and connective ",
    "Diseases of the genitourinary system",
    "Pregnancy, childbirth",
    "Conditions of perinatal period",
    "Congenital abnormalities",
    "Sympt., Abnormal clinical Observations",
    "External causes of death",
    "Neoplasms",
    "Illness of blood, blood-forming organs",
    "Endocrine, nutritional, metabolic illness",
    "Mental and behavioral disorders",
    "Diseases of the nervous system and sense organs",
    "Diseases of the circulatory system",
    "Diseases of the respiratory organs",
    "Diseases of the digestive organs",
    "Population",
    "Total all causes of death")
#cc <- cbind(transcauses,levels(r1$Causes))
#options(width=100)
levels(r1$Causes) <- transcauses
levels(r1$Age) <- 
    gsub('jaar','year',levels(r1$Age)) %>%
    gsub('tot','to',.) %>%
    gsub('of ouder','+',.) 

Preparation for plots

perc.of.death <- filter(r1,Causes=='Total all causes of death') %>%
    mutate(.,Population=count) %>%
    select(.,-count,-Causes) %>%
    merge(.,r1) %>%
    filter(.,Causes %in% transcauses[1:17]) %>%
    mutate(.,Percentage=100*count/Population,
        Causes = factor(Causes),
        year = as.numeric(gsub('*','',year,fixed=TRUE))
    )
perc.of.pop <- filter(r1,Causes=='Population') %>%
    mutate(.,Population=count) %>%
    select(.,-count,-Causes) %>%
    merge(.,r1) %>%
    filter(.,Causes %in% transcauses[1:17]) %>%
    mutate(.,Percentage=100*count/Population,
        Causes = factor(Causes),
        year = as.numeric(gsub('*','',year,fixed=TRUE))

    )

young

png('youngpop1.png')
tmp1 <- perc.of.pop %>% filter(.,Age %in% levels(perc.of.pop$Age)[c(1,2,11,3)],
        !is.na(Percentage)) %>%
    mutate(.,Age=factor(Age,levels=levels(perc.of.pop$Age)[c(1,2,11,3)]),
        Causes =factor(Causes)) 
# select 'important' causes (which somewhen got over 15%)
group_by(tmp1,Causes)%>%
    summarize(.,mp = max(Percentage)) %>%
    mutate(.,rk=rank(-mp)) %>%
    merge(.,tmp1) %>%
    filter(.,rk<=8) %>%
    ggplot(.,
        aes(y=Percentage,x=year,col=Causes)) +
    geom_line()+
    guides(col=guide_legend(ncol=2)) + 
    facet_wrap( ~Age ) +
    theme(legend.position="bottom")+
    ylab('Percentage of Cohort')
dev.off()
###
png('youngpop2.png')
tmp1 <- perc.of.pop %>% filter(.,Age %in% levels(perc.of.pop$Age)[c(2,11,3,4)],
        !is.na(Percentage)) %>%
    mutate(.,Age=factor(Age,levels=levels(perc.of.pop$Age)[c(2,11,3,4)]),
        Causes =factor(Causes)) 
# select 'important' causes (which somewhen got over 15%)
group_by(tmp1,Causes)%>%
    summarize(.,mp = max(Percentage)) %>%
    mutate(.,rk=rank(-mp)) %>%
    merge(.,tmp1) %>%
    filter(.,rk<=8) %>%
    ggplot(.,
        aes(y=Percentage,x=year,col=Causes)) +
    geom_line()+
    guides(col=guide_legend(ncol=2)) + 
    facet_wrap( ~Age ) +
    theme(legend.position="bottom")+
    ylab('Percentage of Cohort')
# https://en.wikipedia.org/wiki/North_Sea_flood_of_1953
dev.off()

old

png('oldpop.png')
tmp2 <- perc.of.pop %>% filter(.,Age %in% levels(perc.of.pop$Age)[18:21],
        !is.na(Percentage)) %>%
    mutate(.,Age=factor(Age),
        Causes =factor(Causes)) 
group_by(tmp2,Causes)%>%
    summarize(.,mp = max(Percentage)) %>%
    mutate(.,rk=rank(-mp)) %>%
    merge(.,tmp2) %>%
    filter(.,rk<=8) %>%
    ggplot(.,
        aes(y=Percentage,x=year,col=Causes)) +
    geom_line()+
    guides(col=guide_legend(ncol=2)) + 
    facet_wrap( ~Age ) +
    theme(legend.position="bottom")+
    ylab('Percentage of Cohort')
dev.off()
# rj.GD 
#     2 

png('oldpop2.png')
tmp2 <- perc.of.pop %>% 
    filter(.,
        Age %in% levels(perc.of.death$Age)[18:21],
        year>=1980,
        !is.na(Percentage)) %>%
    mutate(.,Age=factor(Age),
        Causes =factor(Causes)) 
group_by(tmp2,Causes)%>%
    summarize(.,mp = max(Percentage)) %>%
    mutate(.,rk=rank(-mp)) %>%
    merge(.,tmp2) %>%
    filter(.,rk<=8) %>%
    ggplot(.,
        aes(y=Percentage,x=year,col=Causes)) +
    geom_line()+
    guides(col=guide_legend(ncol=2)) + 
    facet_wrap( ~Age ) +
    theme(legend.position="bottom")+
    ylab('Percentage of Cohort')

dev.off()


  





Sunday, June 21, 2015

SAS PROC MCMC example 12 in R: Change point model

I restarted at working my way through the PROC MCMC examples. The SAS manual describes this example: Consider the data set from Bacon and Watts (1971), where $y_ i$ is the logarithm of the height of the stagnant surface layer and the covariate $x_ i$ is the logarithm of the flow rate of water. 
It is a simple example. It provided no problems at all for STAN and Jags. For LaplacesDemon on the other hand I had some problems. It took me quite some effort to obtain samples which seemed to be behaving. I did not try to do this in MCMCpack, but noted that the function MCMCregressChange() uses a slightly different model. The section below shows first the results, at the bottom the code is given.

Previous post in the series PROC MCMC examples programmed in R were: example 61.1: sampling from a known densityexample 61.2: Box Cox transformationexample 61.5: Poisson regressionexample 61.6: Non-Linear Poisson Regressionexample 61.7: Logistic Regression Random-Effects Model, and example 61.8: Nonlinear Poisson Regression Multilevel Random-Effects Model

Data

Data are read as below.
observed <-
'1.12  -1.39   1.12  -1.39   0.99  -1.08   1.03  -1.08
0.92  -0.94   0.90  -0.80   0.81  -0.63   0.83  -0.63
0.65  -0.25   0.67  -0.25   0.60  -0.12   0.59  -0.12
0.51   0.01   0.44   0.11   0.43   0.11   0.43   0.11
0.33   0.25   0.30   0.25   0.25   0.34   0.24   0.34
0.13   0.44  -0.01   0.59  -0.13   0.70  -0.14   0.70
-0.30   0.85  -0.33   0.85  -0.46   0.99  -0.43   0.99
-0.65   1.19'
observed <- scan(text=gsub('[[:space:]]+',' ',observed),
    what=list(y=double(),x=double()),
    sep=' ')
stagnant <- as.data.frame(observed)

LaplacesDemon

I have been playing around with LaplacesDemon. There is actually a function
LaplacesDemon.hpc which can use multiple cores. However, on my computer it seems more efficient just to use mclapply() from the parallel package and give the result class LaplacesDemon.hpc . Having said that, I had again quite some trouble to get LaplacesDemon to work well. In the end I used a combination of two calls to LaplacesDemon. The plot below shows selected samples after the first run. Not good enough, but that I do like this way of displaying the results of chains. It should be added that the labels looked correct with all parameters. However, that gave to much output for this blog. In addition, after the second call the results looked acceptable.

Call:
LaplacesDemon(Model = Model, Data = MyData, Initial.Values = apply(cc1$Posterior1,
    2, median), Covar = var(cc1$Posterior1), Iterations = 1e+05,
    Algorithm = "RWM")

Acceptance Rate: 0.2408
Algorithm: Random-Walk Metropolis
Covariance Matrix: (NOT SHOWN HERE; diagonal shown instead)
       alpha        beta1        beta2           cp           s2
4.920676e-04 2.199525e-04 3.753738e-04 8.680339e-04 6.122862e-08

Covariance (Diagonal) History: (NOT SHOWN HERE)
Deviance Information Criterion (DIC):
          All Stationary
Dbar -144.660   -144.660
pD      7.174      7.174
DIC  -137.486   -137.486
Initial Values:
        alpha         beta1         beta2            cp            s2
 0.5467048515 -0.4100040451 -1.0194586232  0.0166405998  0.0004800931

Iterations: 4e+05
Log(Marginal Likelihood): 56.92606
Minutes of run-time: 1.32
Model: (NOT SHOWN HERE)
Monitor: (NOT SHOWN HERE)
Parameters (Number of): 5
Posterior1: (NOT SHOWN HERE)
Posterior2: (NOT SHOWN HERE)
Recommended Burn-In of Thinned Samples: 0
Recommended Burn-In of Un-thinned Samples: 0
Recommended Thinning: 5
Specs: (NOT SHOWN HERE)
Status is displayed every 100 iterations
Summary1: (SHOWN BELOW)
Summary2: (SHOWN BELOW)
Thinned Samples: 40000
Thinning: 1


Summary of All Samples
                  Mean           SD         MCSE      ESS            LB
alpha     5.348239e-01 0.0244216567 2.999100e-04 11442.06  4.895229e-01
beta1    -4.196180e-01 0.0142422533 1.661658e-04 12726.60 -4.469688e-01
beta2    -1.013882e+00 0.0164892337 1.681833e-04 15191.59 -1.046349e+00
cp        2.855852e-02 0.0308177765 3.649332e-04 11945.66 -3.406306e-02
s2        4.472644e-04 0.0001429674 1.383748e-06 16571.94  2.474185e-04
Deviance -1.446602e+02 3.7879060637 4.940488e-02 10134.91 -1.496950e+02
LP        4.636511e+01 1.8939530321 2.470244e-02 10134.91  4.164313e+01
                Median            UB
alpha       0.53339024  5.842152e-01
beta1      -0.41996859 -3.903572e-01
beta2      -1.01387256 -9.815650e-01
cp          0.03110570  8.398674e-02
s2          0.00042101  8.006666e-04
Deviance -145.46896682 -1.352162e+02
LP         46.76949458  4.888251e+01


Summary of Stationary Samples
                  Mean           SD         MCSE      ESS            LB
alpha     5.348239e-01 0.0244216567 2.999100e-04 11442.06  4.895229e-01
beta1    -4.196180e-01 0.0142422533 1.661658e-04 12726.60 -4.469688e-01
beta2    -1.013882e+00 0.0164892337 1.681833e-04 15191.59 -1.046349e+00
cp        2.855852e-02 0.0308177765 3.649332e-04 11945.66 -3.406306e-02
s2        4.472644e-04 0.0001429674 1.383748e-06 16571.94  2.474185e-04
Deviance -1.446602e+02 3.7879060637 4.940488e-02 10134.91 -1.496950e+02
LP        4.636511e+01 1.8939530321 2.470244e-02 10134.91  4.164313e+01
                Median            UB
alpha       0.53339024  5.842152e-01
beta1      -0.41996859 -3.903572e-01
beta2      -1.01387256 -9.815650e-01
cp          0.03110570  8.398674e-02
s2          0.00042101  8.006666e-04
Deviance -145.46896682 -1.352162e+02
LP         46.76949458  4.888251e+01

STAN

Stan did not give much problems for this analysis.
Inference for Stan model: smodel.
4 chains, each with iter=2000; warmup=1000; thin=1;
post-warmup draws per chain=1000, total post-warmup draws=4000.

         mean se_mean   sd  2.5%   25%   50%   75% 97.5% n_eff Rhat
Beta[1] -0.42    0.00 0.01 -0.45 -0.43 -0.42 -0.41 -0.39  1017 1.00
Beta[2] -1.01    0.00 0.02 -1.05 -1.02 -1.01 -1.00 -0.98  1032 1.00
Alpha    0.54    0.00 0.03  0.49  0.52  0.53  0.55  0.59   680 1.00
s2       0.00    0.00 0.00  0.00  0.00  0.00  0.00  0.00  1361 1.00
cp       0.03    0.00 0.03 -0.04  0.00  0.03  0.05  0.09   636 1.00
lp__    90.63    0.06 1.78 86.17 89.71 91.00 91.91 93.03   935 1.01

Samples were drawn using NUTS(diag_e) at Fri Jun 19 21:17:54 2015.
For each parameter, n_eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor on split chains (at
convergence, Rhat=1).

JAGS

Again no problems for Jags.
Inference for Bugs model at "/tmp/Rtmpy4a6C5/modeld4f6e9c9055.txt", fit using jags,
 4 chains, each with 10000 iterations (first 5000 discarded), n.thin = 5
 n.sims = 4000 iterations saved
          mu.vect sd.vect     2.5%      25%      50%      75%    97.5%  Rhat
alpha       0.534   0.027    0.479    0.518    0.533    0.552    0.586 1.040
beta[1]    -0.420   0.015   -0.450   -0.429   -0.420   -0.410   -0.389 1.013
beta[2]    -1.014   0.017   -1.049   -1.024   -1.014   -1.003   -0.980 1.023
cp          0.029   0.035   -0.038    0.006    0.032    0.051    0.100 1.037
s2          0.000   0.000    0.000    0.000    0.000    0.001    0.001 1.004
deviance -144.501   3.986 -149.634 -147.378 -145.432 -142.584 -134.378 1.021
         n.eff
alpha      160
beta[1]    380
beta[2]    290
cp         160
s2         710
deviance   290

For each parameter, n.eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor (at convergence, Rhat=1).

DIC info (using the rule, pD = var(deviance)/2)
pD = 7.9 and DIC = -136.6
DIC is an estimate of expected predictive error (lower deviance is better).

CODE used

# http://support.sas.com/documentation/cdl/en/statug/67523/HTML/default/viewer.htm#statug_mcmc_examples18.htm
# Example 61.12 Change Point Models
##############
#Data                                                   
##############
observed <-
'1.12  -1.39   1.12  -1.39   0.99  -1.08   1.03  -1.08
0.92  -0.94   0.90  -0.80   0.81  -0.63   0.83  -0.63
0.65  -0.25   0.67  -0.25   0.60  -0.12   0.59  -0.12
0.51   0.01   0.44   0.11   0.43   0.11   0.43   0.11
0.33   0.25   0.30   0.25   0.25   0.34   0.24   0.34
0.13   0.44  -0.01   0.59  -0.13   0.70  -0.14   0.70
-0.30   0.85  -0.33   0.85  -0.46   0.99  -0.43   0.99
-0.65   1.19'
observed <- scan(text=gsub('[[:space:]]+',' ',observed),
    what=list(y=double(),x=double()),
    sep=' ')
stagnant <- as.data.frame(observed)
#plot(y~x,data=stagnant)
##############
#LaplacesDemon                                                   
##############
library('LaplacesDemon')
library(parallel)

mon.names <- "LP"
parm.names <- c('alpha',paste('beta',1:2,sep=''),'cp','s2')

PGF <- function(Data) {
  x <-c(rnorm(5,0,1))
  x[4] <- runif(1,-1.3,1.1)
  x[5] <- runif(1,0,2)
  x
}
MyData <- list(mon.names=mon.names,
    parm.names=parm.names,
    PGF=PGF,
    x=stagnant$x,
    y=stagnant$y)
#N<-1
Model <- function(parm, Data)
{
  alpha=parm[1]
  beta=parm[2:3]
  cp=parm[4]
  s2=parm[5]
  yhat <- alpha+(Data$x-cp)*beta[1+(Data$x>=cp)]
  LL <- sum(dnorm(Data$y,yhat,sd=sqrt(s2),log=TRUE))
  prior <- sum(dnorm(parm[1:3],0,1e3,log=TRUE))+
      dunif(cp,-1.3,1.1,log=TRUE)+
      dunif(s2,0,5,log=TRUE)
  LP=LL+prior
  Modelout <- list(LP=LP, Dev=-2*LL, Monitor=LP,
      yhat=yhat,
      parm=parm)
  return(Modelout)
}
Fit1 <- mclapply(1:4,function(i)
      LaplacesDemon(Model,
    Data=MyData,
    Iterations=100000,
    Algorithm='RWM',
    Covar=c(rep(.01,4),.00001),
    Initial.Values = c(.5,-.4,-1,.05,.001)) #Initial.Values 
)
class(Fit1) <- 'demonoid.hpc'
plot(Fit1,Data=MyData,Parms=c('alpha'))
cc1 <- Combine(Fit1,MyData)
#
Fit2 <- mclapply(1:4,function(i)
      LaplacesDemon(Model,
          Data=MyData,
          Iterations=100000,
          Algorithm='RWM',
          Covar=var(cc1$Posterior1),
          Initial.Values = apply(cc1$Posterior1,2,median)) #Initial.Values 
)
class(Fit2) <- 'demonoid.hpc'
#plot(Fit2,Data=MyData,Parms=c('alpha'))
cc2 <- Combine(Fit2,MyData)
cc2
##############
#STAN                                                   
##############
stanData <- list(
    N=nrow(stagnant),
    x=stagnant$x,
    y=stagnant$y)

library(rstan)
smodel <- '
    data {
    int <lower=1> N;
    vector[N] x;
    vector[N] y;
    }
    parameters {
    real Beta[2];
    real Alpha;
    real <lower=0> s2;
    real <lower=-1.3,upper=1.1> cp;
    }
    transformed parameters {
    vector[N] yhat;
    for (i in 1:N)
       yhat[i] <- Alpha+(x[i]-cp)*Beta[1+(x[i]>cp)];
    }
    model {
    y ~ normal(yhat,sqrt(s2));
    s2 ~ uniform(0,1e3);
    cp ~ uniform(-1.3,1.1);
    Alpha ~ normal(0,1000);
    Beta ~ normal(0,1000);
    }
    '
fstan <- stan(model_code = smodel,
    data = stanData,
    pars=c('Beta','Alpha','s2','cp'))
fstan
##############
#Jags                                                  
##############
library(R2jags)jagsdata <- list(
    N=nrow(stagnant),
    x=stagnant$x,
    y=stagnant$y)

jagsm <- function() {
  for(i in 1:N) {
    yhat[i] <- alpha+(x[i]-cp)*beta[1+(x[i]>cp)]
    y[i] ~ dnorm(yhat[i],tau)
  }
  tau <- 1/s2
  s2 ~  dunif(0,1e3)
  cp ~ dunif(-1.3,1.1)
  alpha ~ dnorm(0,0.001)
  beta[1] ~ dnorm(0,0.001)
  beta[2] ~ dnorm(0,0.001)
}
params <- c('alpha','beta','s2','cp')
myj <-jags(model=jagsm,
    data = jagsdata,
    n.chains=4,
    n.iter=10000,
    parameters=params,
)
myj

Sunday, June 14, 2015

Parallel and a new laptop

I am thinking about a new laptop. For one thing a 1366*768 resolution just seems to get impractically small. Secondly, faster comutations, more memory.
Regarding CPU speed, my current laptop has a lowly Celeron 877. From what I see at my computers activity, under R it is mostly one core which does the work. Which means that even though there are two cores the single core CPU mark of 715 (from cpubenchmark.net) is what I have available. A bit of checking shows the current batch of processors has mainly more cores. For instance, the highest rated common CPU, an Intel Core i7-4710HQ, has a CPU mark of 7935 and single core 1870. That is 2.5 times faster for one core. But it is best because there are four cores. The same is true down the line. Four cores is common. But single core speed has not improved that much. Unless I can actually use those extra cores, what is the gain? Hence I am wondering, can I do something with extra cores for real world R computations? For this I can investigate.

Easy approach, Parallel

A bit of browsing shows that the parallel package is the easy way to use multiple cores, think of using mclapply() rather than lapply. And in many situations this is easy, for instance, cross validation is easy, except for the small upfront cost of partitioning the data in chunks. Trying different settings for a machine learning problem is similar.
To give this a certain real world setting, data was taken from the UCI machine learning repository:  Physicochemical Properties of Protein Tertiary Structure Data Set which has 45730 rows and 9 variables. A bit of plotting shows this figure for 2000 random selected rows. It seems the problem is not so much which variables to use but rather interactions. This was also suggested by poor performance of linear regression.

Random forest in parallel

Even though nine variables is a bit low for random forest, I elected to use it as first technique. The main variables to tune are nodesize and number of variables to try. Hence I wrapped this in mclapply, not even using a cross validation and taking care not to nest the mclapply calls. The result was a big usage of memory. Which in hindsight may be obvious. Each of the instances gets a complete data set. The net effect is that I ran out of RAM and data was swapped. This cannot be good for performance. It may also explain comments I have read that the caret package uses too much memory. A decent set of hardware for machine learning including a four core processor would create four instances of the same data. Perhaps adding another 4 GB of memory and an SSD rather than a HDD would serve me just as well as a new laptop...
tol <- expand.grid(mtry=1:3,
    nodesize=c(3,5,10))
bomen <- mclapply(seq(1:nrow(tol)),function(i)
          randomForest(
              y=train[,1],
              x=train[,-1],
              ntree=50,
              mtry=tol$mtry[i],
              nodesize=tol$nodesize[i])
)

Final thoughts

New hardware could also bring GPU computing in the picture. But this seems not so easy. It is unclear to me if CUDA or OpenCL is preferable and neither seems particularly easy to use. Then again, I could minimize hardware usage, buy a chromebook with a decent screen do my stuff in the cloud. For now though, I will continue to investigate how extra cores can help me.