def income_increase_under_15(
person_yrs_of_coverage_for_under_5s,
person_yrs_of_coverage_for_5_to_14s,
reduction_in_prob_of_covered_child_being_infected_under_5,
reduction_in_prob_of_covered_child_being_infected_5_to_14,
increase_in_income_from_eliminating_prob_of_malaria_infection_in_youth,
replicability_adjustment_for_malaria_vs_income,
num_yrs_between_anti_malaria_program_and_long_term_benefits,
discount_rate,
duration_of_long_term_benefits,
multiplier_for_sharing_win_households,
value_of_increasing_ln_consumption_per_capita_per_annum,
):
reduction_in_num_people_infected_at_point_in_time_in_cohort_under_5 = (
person_yrs_of_coverage_for_under_5s *
reduction_in_prob_of_covered_child_being_infected_under_5)
reduction_in_num_people_infected_at_point_in_time_in_cohort_5_to_14 = (
person_yrs_of_coverage_for_5_to_14s *
reduction_in_prob_of_covered_child_being_infected_5_to_14)
adjusted_increase_in_ln_income_from_reducing_point_in_time_probability_of_malaria_infection_from_100_to_0_for_an_invidiual_between_the_ages_of_0_and_14 = (
(log(
1 +
increase_in_income_from_eliminating_prob_of_malaria_infection_in_youth
) - log(1)) * replicability_adjustment_for_malaria_vs_income)
benefit_on_one_years_income = (
adjusted_increase_in_ln_income_from_reducing_point_in_time_probability_of_malaria_infection_from_100_to_0_for_an_invidiual_between_the_ages_of_0_and_14
/ (1 + discount_rate)**
num_yrs_between_anti_malaria_program_and_long_term_benefits)
present_value_of_lifetime_benefits_from_reducing_prevalence_from_1_to_0_for_an_individual_for_one_year_between_ages_of_0_and_14 = present_value_of_annuity(
discount_rate, duration_of_long_term_benefits,
benefit_on_one_years_income) # TODO: end of period
present_value_of_benefits_from_reducing_point_in_time_probability_of_malaria_infection_from_100_to_0_for_individual_for_one_year_between_ages_of_0_and_14 = (
present_value_of_lifetime_benefits_from_reducing_prevalence_from_1_to_0_for_an_individual_for_one_year_between_ages_of_0_and_14
* multiplier_for_sharing_win_households)
total_increase_in_ln_income_under_5 = (
present_value_of_benefits_from_reducing_point_in_time_probability_of_malaria_infection_from_100_to_0_for_individual_for_one_year_between_ages_of_0_and_14
* reduction_in_num_people_infected_at_point_in_time_in_cohort_under_5)
total_increase_in_ln_income_5_to_14 = (
present_value_of_benefits_from_reducing_point_in_time_probability_of_malaria_infection_from_100_to_0_for_individual_for_one_year_between_ages_of_0_and_14
* reduction_in_num_people_infected_at_point_in_time_in_cohort_5_to_14)
value_from_development_benefits_per_million_donated = (
value_of_increasing_ln_consumption_per_capita_per_annum *
(total_increase_in_ln_income_5_to_14 +
total_increase_in_ln_income_under_5))
value_from_development_benefits_per_dollar_wout_levfun = (
value_from_development_benefits_per_million_donated /
arbitrary_donation_size)
return {
"AMF: value from development benefits per dollar w/out lev/fun":
value_from_development_benefits_per_dollar_wout_levfun
}
def Mhat(G):
#estimate mean given G
pM = np.array([-2.42043861e-05,7.07715287e-04,-8.72589408e-03,5.78173631e-02,-2.12287390e-01,3.65070722e-01,2.39311397e-02,2.39178197e-01])
tot = 0
for i in range(8):
tot += pM[i]*log(G)**(7-i)
return tot
def Vhat(G):
#estimate variance given G
pV = np.array([-2.33501964e-06,8.10258820e-05,-1.21332152e-03,1.01946967e-02,-5.21336282e-02,1.63404382e-01,-2.95110778e-01,2.50969395e-01,-3.73368931e-02])
tot = 0
for i in range(9):
tot += pV[i]*log(G)**(8-i)
return tot
def fit(self, X, B, T):
n, k = X.shape
with pymc3.Model() as m:
beta_sd = pymc3.Exponential(
'beta_sd', 1.0) # Weak prior for the regression coefficients
beta = pymc3.Normal('beta', mu=0, sd=beta_sd,
shape=(k, )) # Regression coefficients
c = sigmoid(dot(X, beta)) # Conversion rates for each example
k = pymc3.Lognormal('k', mu=0, sd=1.0) # Weak prior around k=1
lambd = pymc3.Exponential('lambd', 0.1) # Weak prior
# PDF of Weibull: k * lambda * (x * lambda)^(k-1) * exp(-(t * lambda)^k)
LL_observed = log(c) + log(k) + log(
lambd) + (k - 1) * (log(T) + log(lambd)) - (T * lambd)**k
# CDF of Weibull: 1 - exp(-(t * lambda)^k)
LL_censored = log((1 - c) + c * exp(-(T * lambd)**k))
# We need to implement the likelihood using pymc3.Potential (custom likelihood)
# https://github.com/pymc-devs/pymc3/issues/826
logp = B * LL_observed + (1 - B) * LL_censored
logpvar = pymc3.Potential('logpvar', logp.sum())
self.trace = pymc3.sample(n_simulations=500,
tune=500,
discard_tuned_samples=True,
njobs=1)
print('done')
print('done 2')
def cash_transfers(
average_household_size,
percent_of_transfers_invested,
return_on_investment,
baseline_consumption_per_capita,
discount_rate,
duration_of_investment_benefits,
percent_of_investment_returned_when_benefits_end,
discount_from_negative_spillover,
value_of_increasing_ln_consumption_per_capita_per_annum,
transfer_as_percent_of_total_cost,
):
total_size_of_transfer = 1000
size_of_transfer_per_person = total_size_of_transfer / average_household_size
amount_invested = size_of_transfer_per_person * percent_of_transfers_invested
total_increase_in_consumption_due_to_funds_transferred = (
1 - percent_of_transfers_invested
) * size_of_transfer_per_person
annual_increase_in_consumption_due_to_investment_returns = (
amount_invested * return_on_investment
)
total_increase_in_ln_consumption_due_to_funds_transferred = log(
baseline_consumption_per_capita
+ total_increase_in_consumption_due_to_funds_transferred
) - log(baseline_consumption_per_capita)
future_annual_increase_in_ln_consumption_from_return_on_investments = log(
baseline_consumption_per_capita
+ annual_increase_in_consumption_due_to_investment_returns
) - log(baseline_consumption_per_capita)
present_value_of_future_increases_in_ln_consumption_excluding_final_year = present_value_of_annuity(
discount_rate,
duration_of_investment_benefits - 1,
future_annual_increase_in_ln_consumption_from_return_on_investments,
)
_additional_consumption_in_final_year = (
amount_invested * return_on_investment
+ amount_invested * percent_of_investment_returned_when_benefits_end
)
present_value_of_ln_consumption_increase_in_final_year = (
log(baseline_consumption_per_capita + _additional_consumption_in_final_year)
- log(baseline_consumption_per_capita)
) / (1 + discount_rate) ** duration_of_investment_benefits
present_value_of_all_future_increases_in_ln_consumption = (
present_value_of_ln_consumption_increase_in_final_year
+ present_value_of_future_increases_in_ln_consumption_excluding_final_year
)
total_present_value_of_cash_transfer = (
present_value_of_all_future_increases_in_ln_consumption
+ total_increase_in_ln_consumption_due_to_funds_transferred
)
total_present_value_of_cash_transfer_accounting_for_spillovers = (
1 - discount_from_negative_spillover
) * total_present_value_of_cash_transfer
increase_in_ln_consumption_for_each_dollar_donated = (
total_present_value_of_cash_transfer_accounting_for_spillovers
* transfer_as_percent_of_total_cost
) / size_of_transfer_per_person
value_per_dollar = (
increase_in_ln_consumption_for_each_dollar_donated
* value_of_increasing_ln_consumption_per_capita_per_annum
)
return {"Cash: value per dollar": value_per_dollar}
def income_increases_age_14_and_under(
malaria_prevalance_young,
malaria_prevalence_old,
direct_mortality_in_high_transmission_season,
reduction_in_malaria_after_adjustments,
internal_validity_adjustment,
external_validity_adjustment,
reduction_in_untreated_pop_per_reduction_in_treated_pop,
adjustment_for_higher_percent_covered_in_trial_than_ACCESS,
increase_in_income_from_eliminating_prob_of_malaria_infection_in_youth,
replicability_adjustment_for_malaria_vs_income,
num_yrs_between_anti_malaria_program_and_long_term_benefits,
discount_rate,
duration_of_long_term_benefits,
multiplier_for_sharing_win_households,
value_of_increasing_ln_consumption_per_capita_per_annum,
cost_per_child_targeted,
):
percentage_reduction_in_malaria_prevalance_in_treated_population_after_adherence_and_coverage_adjustments_young = (
malaria_prevalance_young *
direct_mortality_in_high_transmission_season *
reduction_in_malaria_after_adjustments * internal_validity_adjustment *
external_validity_adjustment)
percentage_reduction_in_malaria_prevalance_in_untreated_population_after_adherence_and_coverage_adjustments_old = (
malaria_prevalence_old * direct_mortality_in_high_transmission_season *
reduction_in_malaria_after_adjustments * internal_validity_adjustment *
external_validity_adjustment *
reduction_in_untreated_pop_per_reduction_in_treated_pop *
adjustment_for_higher_percent_covered_in_trial_than_ACCESS)
reduction_in_number_of_people_infected_with_malaria_at_point_in_time_per_1000_under_5s_targeted_young = (
percentage_reduction_in_malaria_prevalance_in_treated_population_after_adherence_and_coverage_adjustments_young
* 1000)
reduction_in_number_of_people_infected_with_malaria_at_point_in_time_per_1000_under_5s_targeted_old = (
percentage_reduction_in_malaria_prevalance_in_untreated_population_after_adherence_and_coverage_adjustments_old
* 1000)
increase_in_ln_income_from_reducing_point_in_time_probability_of_malaria_infection_from_100_to_0_for_individual_for_one_year_between_ages_of_0_and_14 = (
(log(
1 +
increase_in_income_from_eliminating_prob_of_malaria_infection_in_youth
) - log(1)) * replicability_adjustment_for_malaria_vs_income)
benefit_on_one_years_income = (
increase_in_ln_income_from_reducing_point_in_time_probability_of_malaria_infection_from_100_to_0_for_individual_for_one_year_between_ages_of_0_and_14
/ (1 + discount_rate)**
num_yrs_between_anti_malaria_program_and_long_term_benefits)
present_value_of_lifetime_benefits_from_reducing_prevalence_from_1_to_0_for_an_individual_for_one_year_between_ages_of_0_and_14 = present_value_of_annuity(
discount_rate, duration_of_long_term_benefits,
benefit_on_one_years_income) # TODO: end of period
present_value_of_benefits_from_reducing_point_in_time_probability_of_malaria_infection_from_100_to_0_for_individual_for_one_year_between_ages_of_0_and_14 = (
present_value_of_lifetime_benefits_from_reducing_prevalence_from_1_to_0_for_an_individual_for_one_year_between_ages_of_0_and_14
* multiplier_for_sharing_win_households)
total_increase_in_annual_ln_income_for_young_per_1000_under_5s_targeted = (
present_value_of_benefits_from_reducing_point_in_time_probability_of_malaria_infection_from_100_to_0_for_individual_for_one_year_between_ages_of_0_and_14
*
reduction_in_number_of_people_infected_with_malaria_at_point_in_time_per_1000_under_5s_targeted_young
)
total_increase_in_annual_ln_income_for_old_per_1000_under_5s_targeted = (
present_value_of_benefits_from_reducing_point_in_time_probability_of_malaria_infection_from_100_to_0_for_individual_for_one_year_between_ages_of_0_and_14
*
reduction_in_number_of_people_infected_with_malaria_at_point_in_time_per_1000_under_5s_targeted_old
)
value_from_development_benefits_per_1000_under_5s_targeted = (
value_of_increasing_ln_consumption_per_capita_per_annum *
(total_increase_in_annual_ln_income_for_old_per_1000_under_5s_targeted
+
total_increase_in_annual_ln_income_for_young_per_1000_under_5s_targeted
))
value_from_development_per_dollar_wout_levfun = (
value_from_development_benefits_per_1000_under_5s_targeted /
(cost_per_child_targeted * 1000))
return {
"SMC: value from development per dollar w/out lev/fun":
value_from_development_per_dollar_wout_levfun
}