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OLS

+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Tue Dec 10 11:14:16 2019
+
+@author: Martin Renoult
+correspondence: martin.renoult@misu.su.se
+"""
+
+## Library
+
+import numpy as np
+import statsmodels.api as sm
+
+from pymc3 import *
+
+#------------------------------------------------------------------------------
+## Model data
+# x = ECS
+# y = Tropical temperature
+
+# In the following order:
+# PMIP2[MIROC, IPSL, CCSM, ECHAM, FGOALS, HadCM3, ECBILT]
+# PMIP3[NCAR-CCSM4, IPSL-CM5A-LR, MIROC-ESM, MPI-ESM-P, CNRM-CM5, MRI-CGCM3, FGOALS-g2]
+
+x = [4,4.4,2.7,3.4,2.3,3.3,1.8,
+     3.2,4.13,4.67,3.45,3.25,2.6,3.37]
+
+y = [-2.74899797,-2.82983243,-2.11649457,-3.15521371,-2.35793821,-2.77644642,-1.33816631,
+     -2.5957031, -3.3755188, -2.5169983, -2.5567322, -1.6669922, -2.81839, -3.1465664]
+
+# PMIP2 only
+x_pmip2 = [4,4.4,2.7,3.4,2.3,3.3,1.8]
+y_pmip2 = [-2.74899797,-2.82983243,-2.11649457,-3.15521371,-2.35793821,-2.77644642,-1.33816631]
+
+# PMIP2+3
+x_pmip23 = [4,4.4,2.7,3.4,2.3,3.3,1.8,
+     3.2,4.13,4.67,3.45,3.25,2.6,3.37]
+
+y_pmip23 = [-2.74899797,-2.82983243,-2.11649457,-3.15521371,-2.35793821,-2.77644642,-1.33816631,
+     -2.5957031, -3.3755188, -2.5169983, -2.5567322, -1.6669922, -2.81839, -3.1465664]
+
+# PMIP3 only
+#x_3 = [3.2,4.13,4.67,3.45,3.25,2.6,3.37]
+#
+#y_3 = [-2.5957031, -3.3755188, -2.5169983, -2.5567322, -1.6669922, -2.81839, -3.1465664]
+
+list_predict_t_stats = list()
+low_bound = list()
+up_bound = list()
+
+# OLS on the dataset of Schmidt et al., 2014
+y_pmip23 = sm.add_constant(y_pmip23)
+model_schmidt = sm.OLS(x_pmip23, y_pmip23)
+results_schmidt = model_schmidt.fit()
+
+coeff_schmidt = results_schmidt.params
+resid_schmidt = results_schmidt.resid
+mse_resid_schmidt = results_schmidt.mse_resid
+
+y_pmip23 = y_pmip23[:,1:]
+
+# OLS on the dataset of Hargreaves et al., 2012
+y_pmip2 = sm.add_constant(y_pmip2)
+model_hargreaves = sm.OLS(x_pmip2, y_pmip2)
+results_hargreaves = model_hargreaves.fit()
+
+coeff_hargreaves = results_hargreaves.params
+resid_hargreaves = results_hargreaves.resid
+mse_resid_hargreaves = results_hargreaves.mse_resid
+
+y_pmip2 = y_pmip2[:,1:]
+
+ran_renoult = np.linspace(0, 20, 1000)
+ran_schmidt = np.linspace(-6, 10, 500)
+
+prediction_schmidt = (ran_schmidt-coeff_schmidt[0])/coeff_schmidt[1]
+prediction_hargreaves = (ran_schmidt-coeff_hargreaves[0])/coeff_hargreaves[1]
+
+# "Real" observed data of tropical LGM
+T = -2.2
+stdT = 0.4
+distrib_T = np.random.normal(loc=T, scale=stdT, size=100000)
+
+# Inference
+inference_schmidt = distrib_T*coeff_schmidt[1]+coeff_schmidt[0]+np.random.normal(loc=0, scale=mse_resid_schmidt**0.5, size=100000)
+inference_hargreaves = distrib_T*coeff_hargreaves[1]+coeff_hargreaves[0]+np.random.normal(loc=0, scale=mse_resid_hargreaves**0.5, size=100000)
+
+# Some statistics
+median_23 = np.median(inference_schmidt)
+median_23 = np.round(median_23, decimals=2)
+
+median_2 = np.median(inference_hargreaves)
+median_2 = np.round(median_2, decimals=2)
+
+post_stats_90_23 = stats.quantiles(inference_schmidt, qlist=(5, 95))
+
+post_stats_90_2 = stats.quantiles(inference_hargreaves, qlist=(5, 95))
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