def ppf(self, att, uni):
if att == 0: return 0
succ = 0
cdf = dist_fit.beta_binomial(0, att, *self.ab)
while cdf < uni:
succ += 1
cdf += dist_fit.beta_binomial(succ, att, *self.ab)
return succ
def _mae(self, data, weights=None):
assert((data >= 0).all() and (data <= self.n).all())
maes = []
alphas,betas = self._get_abs(data, weights)
support = np.arange(0,self.n+1)
for d,a,b in zip(data,alphas,betas):
probs = dist_fit.beta_binomial( support, self.n, a, b )
maes.append( sum(probs*np.abs(support-d)) )
return np.array(maes)
def cdf(self, succ, att):
# CDF is the % of the mass that is *at or equal to* the value.
# these CDFs will not be flat, since most results are 0 and that's most of the way up the CDF already
# this is the definition we want, however, for analyzing the correlations
cdf = 0.
check = 0
while check <= succ:
cdf += dist_fit.beta_binomial(check, att, *self.ab)
check += 1
return cdf
def _mse(self, data, weights=None):
# lr can be used to suppress learning
# we could also apply multiplicative decay after adding, which will result in variance decay even in long careers
assert((data >= 0).all() and (data <= self.n).all())
mses = []
alphas,betas = self._get_abs(data, weights)
# domain of summation for EV computation:
support = np.arange(0,self.n+1)
for d,a,b in zip(data,alphas,betas):
# beta-binomial isn't in scipy - there is an open ticket; the CDF is difficult to implement
# it's not so bad to compute manually since the domain is finite
probs = dist_fit.beta_binomial( support, self.n, a, b )
mses.append( sum(probs*(support-d)**2) )
# log.debug('alpha, beta = {},{}'.format(alpha,beta))
return np.array(mses)
log.info(f'all: alpha = {ainc}, beta = {binc}, LL per dof = {llpdf}')
log.info(f'mean: {ainc/(ainc+binc)}')
log.info('covariance:\n%s', cov)
sns.set()
xfvals = np.linspace(-0.5, maxgames + 0.5, 128)
plt_gp = sns.distplot(data_gp_rook,
bins=range(0, maxgames + 2),
kde=False,
norm_hist=True,
hist_kws={
'log': False,
'align': 'left'
})
plt.plot(xfvals,
dist_fit.beta_binomial(xfvals, maxgames, ark, brk),
'--',
lw=2,
color='blue')
# plt.title('rookies')
plt_gp.figure.savefig('{}_{}_rookie.png'.format(gp_stat, pos))
plt_gp.figure.show()
plt_gp = sns.distplot(data_gp,
bins=range(0, maxgames + 2),
kde=False,
norm_hist=True,
hist_kws={
'log': False,
'align': 'left'
})
data_gp = posdf[gp_stat]
_,(ark,brk),cov,llpdf = dist_fit.to_beta_binomial( maxgames, data_gp_rook )
log.info('rookie: alpha = {}, beta = {}, LL per dof = {}'.format(ark, brk, llpdf))
log.info('covariance:\n' + str(cov))
_,(ainc,binc),cov,llpdf = dist_fit.to_beta_binomial( maxgames, data_gp )
log.info('all: alpha = {}, beta = {}, LL per dof = {}'.format(ainc, binc, llpdf))
log.info('covariance:\n' + str(cov))
sns.set()
xfvals = np.linspace(-0.5, maxgames+0.5, 128)
plt_gp = sns.distplot(data_gp, bins=range(0,maxgames+2),
kde=False, norm_hist=True,
hist_kws={'log':False, 'align':'left'})
plt.plot(xfvals, dist_fit.beta_binomial(xfvals, maxgames, ark, brk), '--', lw=2, color='violet')
plt.title('rookies')
plt_gp.figure.savefig('{}_{}.png'.format(gp_stat, pos))
plt_gp.figure.show()
# The bayesian update rule is:
# alpha -> alpha + (games_played)
# beta -> beta + (n - games_played)
# we can just start on the default rookie values
# for QBs we might want to adjust for year-in-league, or just filter on those which started many games
# log.info('using rookie a,b = {},{}'.format(ark,brk))
# alpha0,beta0 = ark,brk
# log.info('using inclusive a,b = {}'.format(ainc, binc)) # does a bit worse
# alpha0,beta0 = ainc,binc
# m1 = data_gp_rook.mean()