Update

docs/userguide/dfe.md

@@ -4,12 +4,16 @@
 
 After obtaining the cache file [1KG.YRI.CEU.20.split_mig.sel.single.gamma.spectra.bpkl](https://github.com/xin-huang/dadi-cli/blob/revision/examples/results/caches/1KG.YRI.CEU.20.split_mig.sel.single.gamma.spectra.bpkl), we can fit the spectrum from nonsynonymous SNPs for DFE inference. Although our data come from two populations, we will first infer a one-dimensional DFE, which assumes that selection coefficients are equal in the two populations. An example command is below:
 
-```         
-dadi-cli InferDFE --fs examples/results/fs/1KG.YRI.CEU.20.nonsynonymous.snps.unfold.fs --cache1d examples/results/caches/1KG.YRI.CEU.20.split_mig.sel.single.gamma.spectra.bpkl --pdf1d lognormal --p0 1 1 .5 --lbounds -10 0.01 0 --ubounds 10 10 0.5 --demo-popt examples/results/demog/1KG.YRI.CEU.20.split_mig.demog.params.InferDM.bestfits --ratio 2.31 --output-prefix examples/results/dfe/1KG.YRI.CEU.20.split_mig.dfe.1D_lognormal.params --optimizations 10 --maxeval 400 --check-convergence 5 --cpus 2
+```
+dadi-cli InferDFE --fs examples/results/fs/1KG.YRI.CEU.20.non.unfolded.fs --cache1d examples/results/caches/1KG.YRI.CEU.20.split_mig.sel.single.gamma.spectra.bpkl --pdf1d lognormal --p0 1 1 .5 --lbounds -10 0.01 0 --ubounds 10 10 0.5 --demo-popt examples/results/demog/1KG.YRI.CEU.20.split_mig.demog.params.InferDM.bestfits --ratio 2.31 --output-prefix examples/results/dfe/1KG.YRI.CEU.20.split_mig.dfe.1D_lognormal --optimizations 10 --maxeval 400 --check-convergence 5 --cpus 2
 ```
 
+Many arguments are the same as those in the `InferDM` command.
+
 We define the marginal DFE as a lognormal distribution with `--pdf1d`. We use `--ratio` to specify the ratio of the nonsynonymous SNPs to the synonymous SNPs to calculate the population-scaled mutation rate of the nonsynonymous SNPs. Our parameters are `log_mu` the mean of the lognormal distribution, `log_sigma` the standard deviation of the lognormal distribution, and `misid`.
 
+## Output
+
 The result is
 
 ```         
@@ -34,9 +38,9 @@ Similar to the best fit parameters in `./examples/results/demog/1KG.YRI.CEU.spli
 |------------|-----|-------|-------------------|
 | -1389      | 5.5 | 7.6   | 0.017             |
 
-# Joint DFE inference
+## Joint DFE inference
 
-## Inferring a bivariate lognormal joint DFE
+### Inferring a bivariate lognormal joint DFE
 
 Here we will infer a joint DFE with selection potentially being different in the two populations. We define the DFE as a bivariate lognormal distribution with `--pdf2d` and pass in a cache that assumes the population-scaled selection coefficients are different in the two populations through `--cache2d`. The bivariate lognormal has an extra parameter `rho`, the correlation of the DFE between the populations. We can allow `mu_log` and `sigma_log` be different or the same in our populations. `dadi-cli` will run either the symmetric (shared `mu_log` and `sigma_log`) or asymmetric (independent `mu_log` and `sigma_log`) bivariate lognormal based on the number of parameters. For the symmetric bivariate lognormal the parameters are `log_mu`, `log_sigma`, and `rho`, the asymmetric bivariate lognormal the parameters are `log_mu1`, `log_mu2`, `log_sigma1`, `log_sigma2`, and `rho`, where 1 denotes the first population and 2 denotes the second population.
 
@@ -52,7 +56,7 @@ An example of running an asymmetrical bivariate lognormal is:
 dadi-cli InferDFE --fs ./examples/results/fs/1KG.YRI.CEU.20.nonsynonymous.snps.unfold.fs --cache2d ./examples/results/caches/1KG.YRI.CEU.20.split_mig.sel.spectra.bpkl --pdf2d biv_lognormal --p0 1 1 1 1 .5 .5 --lbounds -10 -10 0.01 0.01 0.001 0 --ubounds 10 10 10 10 0.999 0.5 --demo-popt ./examples/results/demog/1KG.YRI.CEU.20.split_mig.demog.params.InferDM.bestfits --ratio 2.31 --output ./examples/results/dfe/1KG.YRI.CEU.20.split_mig.dfe.bivariate_asym_lognormal.params --optimizations 15 --maxeval 400 --check-convergence 10
 ```
 
-## Inferring mixture model joint DFE
+### Inferring mixture model joint DFE
 
 Here, we will use a mixture of a univariate lognormal and a bivariate lognormal distribution. To make the mixture we pass in options for both 1D and 2D: `--pdf1d`, `--pdf2d`, `--cache1d`, and `--cache2d`. Because the mixture model is assuming some proportion of the DFE is lognormal and the other is bivariate, the bivariate is symmeteric. The parameters for the mixture lognormal DFE are `log_mu`, `log_sigma`, `rho`,and `w`, the proportional weight of the bivariate lognormal DFE (1-`w` would be the weight of the univariate lognormal distribution). In this example we fix `rho` of the bivariate component to 0 with the `--constants` option.
 

examples/results/dfe/1KG.YRI.CEU.20.split_mig.dfe.1D_lognormal.InferDFE.bestfits

@@ -0,0 +1,17 @@
+# /Users/user/mambaforge/envs/dadi-cli-cpu/bin/dadi-cli InferDFE --fs examples/results/fs/1KG.YRI.CEU.20.non.unfolded.fs --cache1d examples/results/caches/1KG.YRI.CEU.20.split_mig.sel.single.gamma.spectra.bpkl --pdf1d lognormal --p0 1 1 .5 --lbounds -10 0.01 0 --ubounds 10 10 0.5 --demo-popt examples/results/demog/1KG.YRI.CEU.20.split_mig.demog.params.InferDM.bestfits --ratio 2.31 --output-prefix examples/results/dfe/1KG.YRI.CEU.20.split_mig.dfe.1D_lognormal --optimizations 10 --maxeval 400 --check-convergence 5 --cpus 2
+# /Users/user/mambaforge/envs/dadi-cli-cpu/bin/dadi-cli InferDFE --fs examples/results/fs/1KG.YRI.CEU.20.non.unfolded.fs --cache1d examples/results/caches/1KG.YRI.CEU.20.split_mig.sel.single.gamma.spectra.bpkl --pdf1d lognormal --p0 1 1 .5 --lbounds -10 0.01 0 --ubounds 10 10 0.5 --demo-popt examples/results/demog/1KG.YRI.CEU.20.split_mig.demog.params.InferDM.bestfits --ratio 2.31 --output-prefix examples/results/dfe/1KG.YRI.CEU.20.split_mig.dfe.1D_lognormal --optimizations 10 --maxeval 400 --check-convergence 5 --cpus 2
+#
+# Converged results
+# Log(likelihood)	log_mu	log_sigma	misid	theta
+-1390.216558502869	5.7078081159785725	7.934694578672994	0.01647346102391192	15691.446711371886
+-1390.2206755646514	5.696866719099689	7.910257538672334	0.016549081772691945	15691.446711371886
+-1390.2321802957717	5.6985080744503795	7.915039953288335	0.01632034569197264	15691.446711371886
+#
+# Top 100 results
+# Log(likelihood)	log_mu	log_sigma	misid	theta
+-1390.216558502869	5.7078081159785725	7.934694578672994	0.01647346102391192	15691.446711371886
+-1390.2206755646514	5.696866719099689	7.910257538672334	0.016549081772691945	15691.446711371886
+-1390.2321802957717	5.6985080744503795	7.915039953288335	0.01632034569197264	15691.446711371886
+-1390.5785860284573	5.838670032124382	8.202117596248334	0.016267679223638656	15691.446711371886
+-1391.602004080164	5.883742893394162	8.301911448575662	0.015025267493752754	15691.446711371886
+-2851.693923307018	0.9456483751405087	0.2546946309528162	0.03942740949097054	15691.446711371886

examples/results/dfe/1KG.YRI.CEU.20.split_mig.dfe.1D_lognormal.InferDFE.opts.0

@@ -0,0 +1,8 @@
+# /Users/user/mambaforge/envs/dadi-cli-cpu/bin/dadi-cli InferDFE --fs examples/results/fs/1KG.YRI.CEU.20.non.unfolded.fs --cache1d examples/results/caches/1KG.YRI.CEU.20.split_mig.sel.single.gamma.spectra.bpkl --pdf1d lognormal --p0 1 1 .5 --lbounds -10 0.01 0 --ubounds 10 10 0.5 --demo-popt examples/results/demog/1KG.YRI.CEU.20.split_mig.demog.params.InferDM.bestfits --ratio 2.31 --output-prefix examples/results/dfe/1KG.YRI.CEU.20.split_mig.dfe.1D_lognormal --optimizations 10 --maxeval 400 --check-convergence 5 --cpus 2
+# Log(likelihood)	log_mu	log_sigma	misid	theta
+-1390.2206755646514	5.696866719099689	7.910257538672334	0.016549081772691945	15691.446711371886
+-2851.693923307018	0.9456483751405087	0.2546946309528162	0.03942740949097054	15691.446711371886
+-1390.2321802957717	5.6985080744503795	7.915039953288335	0.01632034569197264	15691.446711371886
+-1390.5785860284573	5.838670032124382	8.202117596248334	0.016267679223638656	15691.446711371886
+-1391.602004080164	5.883742893394162	8.301911448575662	0.015025267493752754	15691.446711371886
+-1390.216558502869	5.7078081159785725	7.934694578672994	0.01647346102391192	15691.446711371886