I have a microarray gene expression dataset consisting of placenta samples. I want to check whether these placenta samples are mixed with maternal decidua tissue. I have marker genes for decidua samples SCARA5, PIGF, SLPI. How to check whether these genes are expressed in placenta samples? In other words, how to check if a gene is up or down regulated without control group?
You ask about which "genes are expressed" and then you mention "if a gene is up or down regulated". These are different, and given your application I think what you actually want to know if these marker genes are expressed. This is not a question of up/down-regulation relative to a control, so you do not need control samples for this.
It seems most of your datasets are Affymetrix, and there are R/Bioconductor packages that will give you the probability a gene is expressed. One such I found is frma (https://bioconductor.org/packages/release/bioc/html/frma.html), which returns an object "weight" that is "a vector of weights which roughly correspond to the probability of expression for each gene." I haven't worked with microarrays in a while, but I recall many other R/Bioconductor packages offering this functionality.
A detection p-value is calculated for Illumina array probes in Illumina's native BeadStudio software.