def plot_mean_and_variance(unit, event, ests, model):
"""ests - dict(major: major alleles, mean: means, var: variances
model - a tuple(mean model, variance model)
TODO: add error bars"""
x_axis = range(min(ests['major']), max(ests['major']) + 1)
mean_model, var_model = model
rpy.r.plot(y=[ na(x) for x in ests['mean'] ],
x=ests['major'], xlab="Major allele", ylab="Freq",
main="%s, %s: mean vs. major allele" % (unit, event))
rpy.r.lines(predict_lm(mean_model, x_axis, log), x=x_axis, col="blue")
rpy.r.plot(y=[ na(var) for var in ests['var'] ],
x=ests['major'], xlab="Major allele", ylab="Freq",
main="%s, %s: variance vs. major allele" % (unit, event))
rpy.r.lines(predict_lm(var_model, x_axis, log), x=x_axis, col="blue")
def model_mean_and_variance(meanvar_ests):
"""Regression models of mean and var as functions of major allele len.
NOTE: since alleles are already normalized to the major allele (e.g.,
allele len=0 is the major allele), we're modeling error of the means
and variances.
LATER: Use several regression formulae to see how things look and choose
the best fit? For now, the log regression seems (simply by eye) to be
the better fit."""
# Weights are just the number of observed sites for each majro allele
weights = meanvar_ests['count']
adjmean = [ na(mean) for mean in meanvar_ests['mean'] ]
adjvar = [ na(var) for var in meanvar_ests['var'] ]
lmdata = rpy.r.data_frame(major=meanvar_ests['major'], mean=adjmean, var=adjvar)
meanmodel = rpy.r.lm(rpy.r("mean ~ log(major)"), data=lmdata,
weights=weights)
varmodel = rpy.r.lm(rpy.r("var ~ log(major)"), data=lmdata,
weights=weights)
return meanmodel, varmodel
def model_mean_and_variance(binned_data):
"""Given a histogram of observed data (binned or not), estimate the mean
and variance as functions of major allele length, then use linear
regression to model the mean and variance. These fitted curves will be
used to construct PMFs for each major allele length."""
emp_values = [] # tuple(major_allele, mean, var, gmean, gvar, lmean, lvar)
for major_allele, data in binned_data.iteritems():
N_tot = sum(freq for _, freq in data.iteritems())
mean_tot = sum(freq*float(allele) for allele, freq in data.items()) / N_tot
var_tot = sum(freq*(float(allele) - mean_tot)**2 for allele, freq in data.items()) / (N_tot - 1)
gains = [ (allele, freq) for allele, freq in data.items() if allele > 0 ]
N_gain = sum(freq for _, freq in gains)
if N_gain > 1:
mean_gain = sum(freq*float(allele) for allele, freq in gains) / N_gain
var_gain = sum(freq*(float(allele) - mean_gain)**2 for allele, freq in gains) / (N_gain - 1)
else:
mean_gain = None
var_gain = None
losses = [ (allele, freq) for allele, freq in data.items() if allele < 0 ]
N_loss = sum(freq for _, freq in losses)
if N_loss > 1:
mean_loss = sum(freq*float(allele) for allele, freq in losses) / N_loss
var_loss = sum(freq*(float(allele) - mean_loss)**2 for allele, freq in losses) / (N_loss - 1)
else:
mean_loss = None
var_loss = None
emp_values.append((int(major_allele), mean_tot, var_tot, mean_gain, var_gain, mean_loss, var_loss))
# These are just for getting plot boundaries
all_means = sum([ [ tup[1], tup[3], tup[5] ] for tup in emp_values ], [])
all_means = [ x for x in all_means if x ] # drop Nones
all_vars = sum([ [ tup[2], tup[4], tup[6] ] for tup in emp_values ], [])
all_vars = [ x for x in all_vars if x ] # drop Nones
rpy.r.layout(rpy.r.matrix([1,2], ncol=1))
# Plots for visual inspection, move elsewhere
ylim_mean = [ min(all_means), max(all_means) ]
x_axis = [ tup[0] for tup in emp_values ]
# Total mean
rpy.r.plot([ na(tup[1]) for tup in emp_values ],
x=x_axis, ylim=ylim_mean,
main="Empirical mean error vs. major allele length",
xlab="Major allele length (units)",
ylab="Empirical mean error")
# Mean for gain alleles
rpy.r.lines([ na(tup[3]) for tup in emp_values ], x=x_axis, col="green")
# Mean for loss alleles
rpy.r.lines([ na(tup[5]) for tup in emp_values ], x=x_axis, col="red")
rpy.r.legend("bottomleft", horiz=True, legend=["Total", "Gain", "Loss"],
fill=["black", "green", "red"])
# Total variance
ylim_var = [ min(all_vars), max(all_vars) ]
rpy.r.plot([ na(tup[2]) for tup in emp_values ],
x=x_axis, ylim=ylim_var, log="y",
main="Empirical variance of error vs. major allele length",
xlab="Major allele length (units)",
ylab="Empirical variance of error")
# Gain variance
rpy.r.lines([ na(tup[4]) for tup in emp_values ], x=x_axis, col="green")
# Loss variance
rpy.r.lines([ na(tup[6]) for tup in emp_values ], x=x_axis, col="red")
rpy.r.legend("topleft", horiz=True, legend=["Total", "Gain", "Loss"],
fill=["black", "green", "red"])
