chang HMM to ong

README.md

@@ -11,33 +11,7 @@ sequence for the list of SNP markers.
 ![sscocaller_fig](images/sscocaller_fig.png)
 
 ## Hidden Markov Model configuration
-
-- Observations. The allele specific counts across the informative SNP markers for
-each chromosome in each sperm cell.
-
-- States. Sperm cells have haploid genomes. There are two possible hidden states (haplotypes)
-corresponding to a REF or ALT segment in the haploid genome. At each SNP site $i$, 
-there are two hidden states: $s_{i}= 0$ corresponds to ALT segment while $s_i=1$
-corresponds to REF segment.
-
-- Emission probabilities. Two binomial distributions were used for modelling the
-emission probabilities for sperm cells at each SNP marker. For each site $s_i$
-          $$ c = c_r + c_a ~,$$
-          $$c_a |_{s = 0} \sim Bin(c,\theta_{ALT} ) ~,$$
-          $$c_a |_{s = 1}\sim Bin(c,\theta_{REF} ) ~.$$
-
-- Transition Probabilities}. A distance-dependent transition probability [[1]](#1)
-was applied, which corresponded to an average of `--cmPmb` cM (centiMorgan) per 1Mb 
-(1 million base pairs):
- $$p_{ij} = 1-e^{(-d_{ij}\mathbf{x}0.5\mathbf{x}10^{-8})} ~,$$
-where $p_{ij}$ is the transition probability of transitioning to a different 
-state at SNP $j$ from SNP $i$, and $d_{ij}$ denotes the physical base-pair 
-distances between SNP $i$ and SNP $j$.
-
-- Initial probabilities. The initial probabilities for the two hidden states
-were set to be both 0.5 since they were equally likely to happen.
-
-
+![HMM_fig](images/HMM-sscocaller.PNG)
         
 ## Inputs