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@@ -1,19 +1,27 @@
 # lshmm
-This is a Python library for prototyping and testing implementations of algorithms using the Li & Stephens (2003) HMM.
+**lshmm** is a Python library for prototyping, experimenting, and testing implementations of algorithms using the Li & Stephens (2003) Hidden Markov Model.
 
 ## Usage
 
 ### Inputs
-Reference panel contains sample and/or (partial) ancestral haplotypes.
+#### Data
+* Sample and/or ancestral haplotypes comprising a reference panel.
+* Query haplotypes.
 
-### Demo
-Forwards algorithm
-Backwards algorithm
+In the haploid mode, the alleles in haplotypes can be represented by any integer value (besides `-1` and `-2`, which are special values). In the diploid mode, the genotypes (encoded as allele dosages) can be `0` (homozygous for the reference allele), `1` (heterozygous for the alternative allele), or `2` (homozygous for the alternative allele). Currently, multiallelic sites are supported only in the haploid mode, but not the diploid mode.
+
+Note that there are two special values `NONCOPY` and `MISSING`. `NONCOPY` (or `-2`) represent non-copiable states, and can only be found in partial ancestral haplotypes in the reference panel. `MISSING` (or `-1`) representing missing data, and can be found only in query haplotypes.
+
+#### Parameters
+* Per-site recombination probabilities.
+* Per-site mutation probabilities.
+
+### Algorithms
 Viterbi algorithm
 Log-likelihood evaluation of a copying path
 
 ### Features
 * Scaling of mutation rate by the number of distinct alleles per site.
-* Non-copiable allelic state in the reference panel (`NONCOPY`).
-* Missing allelic state in the query (`MISSING`).
+* Non-copiable state in the reference panel (`NONCOPY`).
+* Missing state in the query (`MISSING`).
 * Multiallelic sites.