consistency property of lasso

This is about the meaning of | as in the "irrepresentable condition"  from On Model Selection Consistency of Lasso

It seems the operation is |x| = abs(sum(x)). I have never seen such a norm. But their Section "3.1 Simulation Example 1" makes me think so: 

... in two settings: (a) β1 = 2, β2 = 3 ; and (b) β1 =  2, β2 = 3. In both settings, X(1) = (X1;X2), X(2) = X3 and through (2), it is easy to get C21inv(C11)= (2/3,2/3). Therefore Strong Irrepresentable Condition fails for setting (a) and holds for setting (b).

Their Proof for Corollary 1 makes me think so:

There is a similar use here.

oracle

In "Sparse Estimators and the Oracle Property, or the Return of Hodges’ Estimator": 

Fan and Li (2001), the SCAD estimator, with appropriate choice of the regularization (tuning) parameter, possesses a sparsity property, i.e., it estimates zero components of the true parameter vector exactly as zero with probability approaching one as sample size increases while still being consistent for the non-zero components...In other words, with appropriate choice of the regularization parameter, the asymptotic distribution of the SCAD estimator based on the overall model and that of the SCAD estimator derived from the most parsimonious correct model coincide. Fan and Li (2001) have dubbed this property the “oracle property”....It is well-known for Hodges’ estimator that the maximal (scaled) mean squared error grows without bound as sample size increases (e.g., Lehmann and Casella (1998), p.442), whereas the standard maximum likelihood estimator has constant finite quadratic risk. In this note we show that a similar unbounded risk result is in fact true for any estimator possessing the sparsity property. This means that there is a substantial price to be paid for sparsity even though the oracle property (misleadingly) seems to suggest otherwise. 

In "Modern statistical estimation via oracle inequalities":

Theorem 4.1. The James–Stein estimate obeys .

In other words, the James–Stein estimator is almost as good as the ideal estimator in a mean-squared error sense.The inequality (4.2) is an oracle inequality. An oracle inequality relates the performance of a real estimator with that of an ideal estimator which relies on perfect information supplied by an oracle, and which is not available in practice.

mean, median and mode

this page explains a mean minimizes the  norm of the residual: 
a median minimizes its  norm and a mode minimizes the zero norm of the residual, namely .See the wikipedia page about median.

from here, it was further explained that

Inder Jeet Taneja’s book draft has a nice survey of the results: if you fix the upper and lower boundary, and maximize entropy, you’ll get the uniform distribution. If you fix the mean and the expected L2 norm (d^2) between the mean and the distribution, maximizing the entropy you’ll get the Gaussian. If you fix the expected L1 norm (|d|) between the mean and the distribution, maximizing the entropy you’ll get the Laplace (also referred to as Double Exponential). Moreover, log(1+d^2) norm will yield the Cauchy distribution – a special case of the standard heavy-tailed Student distribution.

check points when reviewing a genetic screening report

1. title and footnote, ensuring it describes the analysis population, the outcome variable and the class of genetic markers; 
2. eyeball examples:
• 1 example of x chr snp
• 1 example of autosomal snp with only 2 genotypes
• 1 example of top association 
• 1 example of a random association
3. use the excel output to check the value ranges for each column, pay attention to
• extreme values
• empty cells
• characters indicating missing: -,NA, 0
4. Cosmetic issues
• decimal places
• check line ends for character cut off

interaction coding

In sas: we have

Nested Effects

Nested effects are generated in the same manner as crossed effects. Hence, the design columns generated by the following statements are the same (but the ordering of the columns is different):

model y=a b(a);		(B nested within A)
model y=a a*b;		(omitted main effect for B)

merge

These should be common sense about merge for a sas programmer. I need refresh my knowledge here.
“REPEAT OF BY-VALUES"

chain information impacts summary statistics from coda

It seems chain information is not critical in mean, sd and quantiles; and not critical even for time series SE when convergence.

library(coda) 

x1 <- cbind(rnorm(100, 1, 1), rnorm(100,  1,1), rnorm(100,1 ,1 ),rnorm(100,1,1), cumsum(rnorm(100,1,1)))
x2 <- cbind(rnorm(100, 1,10), rnorm(100, 10,1), rnorm(100,10,10),rnorm(100,1,1), cumsum(rnorm(100,1,1)))
 
colnames(x1) <- colnames(x2) <- c('unequalSD','unequalMean','unequalboth','equal','autocorr')
 
o1 <- mcmc.list(mcmc(x1), mcmc(x2)) #maintain chain information. to add more chain: o1[[3]] <- mcmc(x3);
summary(o1)
 
summary(mcmc(rbind(x1,x2))) #no chain information

Created by Pretty R at inside-R.org

Quickly insert all sheet names in cells with VBA

from here:

If you want to inset all sheet names in cells, VBA macro is a good choice.
Step 1: Hold down the Alt + F11 keys in Excel, and it opens the Microsoft Visual Basic for Applications window.
Step 2: Click Insert > Module, and paste the following macro in the Module Window.
VBA for inserting all worksheets' names in cells:

Sub SheetNames()
Columns(1).Insert
For i = 1 To Sheets.Count
Cells(i, 1) = Sheets(i).Name
Next i
End Sub

seriation

Seriation, also the name for an R package 

is to arrange all objects in a set in a linear order given available data and some loss or merit function in order to reveal structural information. Together with cluster analysis and variable selection, seriation is an important problem in the field of combinatorial data analysis

This post discussed the application of seriation on plotting binary matrices, together with other clustering algorithms.

Prioritizing GWAS Results

This review paper mentioned 3 analytic methods to prioritizing GWAS results (for follow-up studies):

• Meta-analysis seeks to pool information from multiple GWAS to increase the chances of finding true positives among the false positives and provides a way to combine associations across GWAS, even when the original data are unavailable.

• Testing for epistasis within a single GWAS study can identify the stronger results that are revealed when genes interact.

• Pathway analysis of GWAS results is used to prioritize genes and pathways within a biological context. Following a GWAS, association results can be assigned to pathways and tested in aggregate with computational tools and pathway databases.

a tutorial for ggplot2, comprehensive and concise

here

The default plot function from glmnet is quite basic and plain. The following function tries to improve the plots

#this function is to achieve the same purpose of plot.glmnet()
#with the following enhancement:

# 1) show variable number instead of column number
# 2) show the value of lambda that gives smallest cross validation error with a solid line
# 3) show the largest lambda such that the error is within 1 se of the minimal cross validation error with a dashed line
 
#input variables: a glmnet object from glmnet(), a cv. glmnet object from cv.glmnet(), and a possible plot title
 

rjags conflicts with igraph

#Start a new R session with --vanilla;
 
library(igraph) # version 0.6-2
n1 <- read.graph ('network.txt', format="ncol", directed=F, name=T); 

a1 <- get.adjacency="" n1="" pre="" type="both">
if (is.connected(n1, mode="weak")){ 
    #do something 
} 
 
library(rjags) #version 3.5
data(LINE)
LINE$recompile() #example analysis included in rjags
 
#Start a new R session with --vanilla, and the following line runs smoothly;
 
library(rjags) #version 3.5
data(LINE)
LINE$recompile()

Created by Pretty R at inside-R.org

inline rjags

from here

igraph tutorial

http://horicky.blogspot.com/2012/04/basic-graph-analytics-using-igraph.html
http://igraph.sourceforge.net/igraphbook/
leaves = V(g)[degree(g, mode="out")==0]

from here:

The methods under consideration included observed case MMRM, per protocol visits MMRM, interval last observation carried forward (LOCF) MMRM, and a hybrid of the per protocol visits and interval LOCF MMRM approaches.Simulation results reveal that the method that best controls the type I error rate is the per protocol visits method.

HapMap 3: more people ~ more genetic variation

from here.
Centre d’Etude du Polymorphisme Humain collected in Utah, USA, with ancestry from northern and western Europe (CEU)
Han Chinese in Beijing, China (CHB)
Japanese in Tokyo, Japan (JPT)
Yoruba in Ibadan, Nigeria (YRI)
African ancestry in the southwestern USA (ASW)
Chinese in metropolitan Denver, Colorado, USA (CHD)
Gujarati Indians in Houston, Texas, USA (GIH)
Luhya in Webuye, Kenya (LWK)
Maasai in Kinyawa, Kenya (MKK)
Mexican ancestry in Los Angeles, California, USA (MXL)
Tuscans in Italy (Toscani in Italia, TSI)
So memorize some of those abbreviations! One particular difference across these populations is that some are parent-offspring trios, and some are not. So the CEU sample are trios, while the TSI are not.

R factor

Convert a character vector into 1:xxx

f1 <- class="st" span="span" unlist="unlist">strsplit("cabbage", split=""))

as.numeric(unclass(factor(f1))) # levels are coded 1:n according to their alphabetical order

as.numeric(unclass(factor(f1, levels=unique(f1)))) # levels are coded 1:n according to their first appearence

ggplot2 trick

• aes_string
• when facet_wrap does not work:

Here's some code from Hadley's book that assumes you've created ggplot objects a, b, and c. It puts a in the top row, with b and c in the bottom row.

grid.newpage()
pushViewport(viewport(layout=grid.layout(2,2)))
vplayout<-function(x,y){
    viewport(layout.pos.row=x,layout.pos.col=y) 

}

print(a,vp=vplayout(1,1:2))
print(b,vp=vplayout(2,1))
print(c,vp=vplayout(2,2))

Created by Pretty R at inside-R.org

• different line style from geo_smooth in different facet_wrap

p1 <- ggplot(ds2, aes(x=visit, y=change))+ geom_point(shape=1, 

aes(color=treat), position=position_jitter(width=0.4,height=0)) 

+ facet_grid(snp~race)+ opts(title = 'rsxxxx')
 
p1 <- p1 + geom_smooth(data=subset(ds2, race == 'CA'), method='lm', 

se=F, color='blue', linetype = ifelse(pValues[pValues$'dbsnprsid' 

== 'rsxxxx', 'slope1_p'] < 0.05 ,"longdash", "solid" ))
 

Created by Pretty R at inside-R.org

•  background color in the plotting area

+ theme_grey() - the default theme, with a grey background
+ theme_bw() - a theme with a white background 

Created by Pretty R at inside-R.org

inverse gamma and gamma distribution

here