def test_correct_number_of_parameters(self): lpost = PSDPosterior(self.ps.freq, self.ps.power, self.model, m=self.ps.m) lpost.logprior = set_logprior(lpost, self.priors) with pytest.raises(IncorrectParameterError): lpost([2,3])
def test_making_posterior(self): lpost = PSDPosterior(self.ps.freq, self.ps.power, self.model, m=self.ps.m) lpost.logprior = set_logprior(lpost, self.priors) assert lpost.x.all() == self.ps.freq.all() assert lpost.y.all() == self.ps.power.all()
def test_compute_highest_outlier_works(self): mp_ind = 5 max_power = 1000.0 ps = Powerspectrum() ps.freq = np.arange(10) ps.power = np.ones_like(ps.freq) ps.power[mp_ind] = max_power ps.m = 1 ps.df = ps.freq[1]-ps.freq[0] ps.norm = "leahy" model = models.Const1D() p_amplitude = lambda amplitude: \ scipy.stats.norm(loc=1.0, scale=1.0).pdf( amplitude) priors = {"amplitude": p_amplitude} lpost = PSDPosterior(ps.freq, ps.power, model, 1) lpost.logprior = set_logprior(lpost, priors) pe = PSDParEst(ps) res = pe.fit(lpost, [1.0]) res.mfit = np.ones_like(ps.freq) max_y, max_x, max_ind = pe._compute_highest_outlier(lpost, res) assert np.isclose(max_y[0], 2*max_power) assert np.isclose(max_x[0], ps.freq[mp_ind]) assert max_ind == mp_ind
def test_logprior(self): t0 = [2.0] lpost = PSDPosterior(self.ps.freq, self.ps.power, self.model, m=self.ps.m) lpost.logprior = set_logprior(lpost, self.priors) lp_test = lpost.logprior(t0) lp = np.log(scipy.stats.norm(2.0, 1.0).pdf(t0)) assert lp == lp_test
def test_calibrate_lrt_works_with_sampling(self): m = 1 nfreq = 10000 freq = np.linspace(1, 10, nfreq) rng = np.random.RandomState(100) noise = rng.exponential(size=nfreq) model = models.Const1D() model.amplitude = 2.0 p = model(freq) power = noise * p ps = Powerspectrum() ps.freq = freq ps.power = power ps.m = m ps.df = freq[1] - freq[0] ps.norm = "leahy" lpost = PSDPosterior(ps.freq, ps.power, model, m=1) p_amplitude_1 = lambda amplitude: \ scipy.stats.norm(loc=2.0, scale=1.0).pdf(amplitude) p_alpha_0 = lambda alpha: \ scipy.stats.uniform(0.0, 5.0).pdf(alpha) p_amplitude_0 = lambda amplitude: \ scipy.stats.norm(loc=self.a2_mean, scale=self.a2_var).pdf( amplitude) priors = {"amplitude": p_amplitude_1} priors2 = {"amplitude_1": p_amplitude_1, "amplitude_0": p_amplitude_0, "alpha_0": p_alpha_0} lpost.logprior = set_logprior(lpost, priors) model2 = models.PowerLaw1D() + models.Const1D() model2.x_0_0.fixed = True lpost2 = PSDPosterior(ps.freq, ps.power, model2, 1) lpost2.logprior = set_logprior(lpost2, priors2) pe = PSDParEst(ps) pval = pe.calibrate_lrt(lpost, [2.0], lpost2, [2.0, 1.0, 2.0], sample=None, max_post=True, nsim=10, nwalkers=100, burnin=100, niter=20, seed=100) assert pval > 0.001
def test_negative_loglikelihood(self): t0 = [2.0] m = self.model(self.ps.freq[1:], t0) loglike = np.sum(self.ps.power[1:]/m + np.log(m)) lpost = PSDPosterior(self.ps.freq, self.ps.power, self.model, m=self.ps.m) lpost.logprior = set_logprior(lpost, self.priors) loglike_test = lpost.loglikelihood(t0, neg=True) assert np.isclose(loglike, loglike_test)
def test_counts_are_nan(self): y = np.nan * np.ones_like(self.ps.freq) ps_nan = copy.copy(self.ps) ps_nan.power = np.nan*np.ones_like(self.ps.freq) t0 = [2.0] m = self.model(self.ps.freq[1:], t0) lpost = PSDPosterior(ps_nan.freq, ps_nan.power, self.model) lpost.logprior = set_logprior(lpost, self.priors) assert np.isclose(lpost(t0), logmin, 1e-5)
def test_negative_posterior(self): t0 = [2.0] m = self.model(self.ps.freq[1:], t0) lpost = PSDPosterior(self.ps.freq, self.ps.power, self.model, m=self.ps.m) lpost.logprior = set_logprior(lpost, self.priors) post_test = lpost(t0, neg=True) loglike = -np.sum(self.ps.power[1:]/m + np.log(m)) logprior = np.log(scipy.stats.norm(2.0, 1.0).pdf(t0)) post = -loglike - logprior assert np.isclose(post_test, post, atol=1.e-10)
def test_loglikelihood(self): t0 = [2.0] self.model.amplitude = t0[0] mean_model = self.model(self.ps.freq) loglike = -np.sum(np.log(mean_model)) - np.sum(self.ps.power/mean_model) lpost = PSDPosterior(self.ps.freq, self.ps.power, self.model, m=self.ps.m) lpost.logprior = set_logprior(lpost, self.priors) loglike_test = lpost.loglikelihood(t0, neg=False) assert np.isclose(loglike, loglike_test)
def test_negative_loglikelihood(self): t0 = [2.0] self.model.amplitude = t0[0] mean_model = self.model(self.ps.freq) loglike = 2.0*self.m*(np.sum(np.log(mean_model)) + np.sum(self.ps.power/mean_model) + np.sum((2.0 / (2. * self.m) - 1.0) * np.log(self.ps.power))) lpost = PSDPosterior(self.ps.freq, self.ps.power, self.model, m=self.ps.m) lpost.logprior = set_logprior(lpost, self.priors) loglike_test = lpost.loglikelihood(t0, neg=True) assert np.isclose(loglike, loglike_test)
def test_negative_posterior(self): t0 = [2.0] self.model.amplitude = t0[0] mean_model = self.model(self.ps.freq) lpost = PSDPosterior(self.ps.freq, self.ps.power, self.model, m=self.ps.m) lpost.logprior = set_logprior(lpost, self.priors) post_test = lpost(t0, neg=True) loglike = -2.0*self.m*(np.sum(np.log(mean_model)) + np.sum(self.ps.power/mean_model) + np.sum((2.0 / (2. * self.m) - 1.0) * np.log(self.ps.power))) logprior = np.log(scipy.stats.norm(2.0, 1.0).pdf(t0)) post = -loglike - logprior assert np.isclose(post_test, post, atol=1.e-10)
def test_calibrate_highest_outlier_works_with_sampling(self): m = 1 nfreq = 100000 seed = 100 freq = np.linspace(1, 10, nfreq) rng = np.random.RandomState(seed) noise = rng.exponential(size=nfreq) model = models.Const1D() model.amplitude = 2.0 p = model(freq) power = noise * p ps = Powerspectrum() ps.freq = freq ps.power = power ps.m = m ps.df = freq[1] - freq[0] ps.norm = "leahy" nsim = 10 lpost = PSDPosterior(ps.freq, ps.power, model, m=1) p_amplitude = lambda amplitude: \ scipy.stats.norm(loc=1.0, scale=1.0).pdf( amplitude) priors = {"amplitude": p_amplitude} lpost.logprior = set_logprior(lpost, priors) pe = PSDParEst(ps) pval = pe.calibrate_highest_outlier(lpost, [2.0], sample=None, max_post=True, seed=seed, nsim=nsim, niter=20, nwalkers=100, burnin=100) assert pval > 0.001
def setup_class(cls): m = 1 nfreq = 100000 freq = np.arange(nfreq) noise = np.random.exponential(size=nfreq) power = noise * 2.0 ps = Powerspectrum() ps.freq = freq ps.power = power ps.m = m ps.df = freq[1] - freq[0] ps.norm = "leahy" cls.ps = ps cls.a_mean, cls.a_var = 2.0, 1.0 cls.model = models.Const1D() p_amplitude = lambda amplitude: \ scipy.stats.norm(loc=cls.a_mean, scale=cls.a_var).pdf(amplitude) cls.priors = {"amplitude": p_amplitude} cls.lpost = PSDPosterior(cls.ps.freq, cls.ps.power, cls.model, m=cls.ps.m) cls.lpost.logprior = set_logprior(cls.lpost, cls.priors) cls.fitmethod = "BFGS" cls.max_post = True cls.t0 = [2.0] cls.neg = True cls.opt = scipy.optimize.minimize(cls.lpost, cls.t0, method=cls.fitmethod, args=cls.neg, tol=1.e-10)
def test_fit_method_works_with_correct_parameter(self): pe = PSDParEst(self.ps) lpost = PSDPosterior(self.ps.freq, self.ps.power, self.model, self.priors, m=self.ps.m) t0 = [2.0, 1, 1, 1] res = pe.fit(lpost, t0) assert isinstance(res, OptimizationResults), "res must be of type " \ "OptimizationResults" pe.plotfits(res, save_plot=True) assert os.path.exists("test_ps_fit.png") os.unlink("test_ps_fit.png") pe.plotfits(res, save_plot=True, log=True) assert os.path.exists("test_ps_fit.png") os.unlink("test_ps_fit.png") pe.plotfits(res, res2=res, save_plot=True) assert os.path.exists("test_ps_fit.png") os.unlink("test_ps_fit.png")
def fit_powerspectrum(ps, model, starting_pars, max_post=False, priors=None, fitmethod="L-BFGS-B"): """ Fit a number of Lorentzians to a power spectrum, possibly including white noise. Each Lorentzian has three parameters (amplitude, centroid position, full-width at half maximum), plus one extra parameter if the white noise level should be fit as well. Priors for each parameter can be included in case `max_post = True`, in which case the function will attempt a Maximum-A-Posteriori fit. Priors must be specified as a dictionary with one entry for each parameter. The parameter names are `(amplitude_i, x_0_i, fwhm_i)` for each `i` out of a total of `N` Lorentzians. The white noise level has a parameter `amplitude_(N+1)`. For example, a model with two Lorentzians and a white noise level would have parameters: [amplitude_0, x_0_0, fwhm_0, amplitude_1, x_0_1, fwhm_1, amplitude_2]. Parameters ---------- ps : Powerspectrum A Powerspectrum object with the data to be fit model: astropy.modeling.models class instance The parametric model supposed to represent the data. For details see the astropy.modeling documentation starting_pars : iterable The list of starting guesses for the optimizer. See explanation above for ordering of parameters in this list. fit_whitenoise : bool, optional, default True If True, the code will attempt to fit a white noise level along with the Lorentzians. Be sure to include a starting parameter for the optimizer in `starting_pars`! max_post : bool, optional, default False If True, perform a Maximum-A-Posteriori fit of the data rather than a Maximum Likelihood fit. Note that this requires priors to be specified, otherwise this will cause an exception! priors : {dict | None}, optional, default None Dictionary with priors for the MAP fit. This should be of the form {"parameter name": probability distribution, ...} fitmethod : string, optional, default "L-BFGS-B" Specifies an optimization algorithm to use. Supply any valid option for `scipy.optimize.minimize`. Returns ------- parest : PSDParEst object A PSDParEst object for further analysis res : OptimizationResults object The OptimizationResults object storing useful results and quantities relating to the fit Example ------- We start by making an example power spectrum with three Lorentzians >>> m = 1 >>> nfreq = 100000 >>> freq = np.linspace(1, 1000, nfreq) >>> np.random.seed(100) # set the seed for the random number generator >>> noise = np.random.exponential(size=nfreq) >>> model = models.PowerLaw1D() + models.Const1D() >>> model.x_0_0.fixed = True >>> alpha_0 = 2.0 >>> amplitude_0 = 100.0 >>> amplitude_1 = 2.0 >>> model.alpha_0 = alpha_0 >>> model.amplitude_0 = amplitude_0 >>> model.amplitude_1 = amplitude_1 >>> p = model(freq) >>> power = noise * p >>> ps = Powerspectrum() >>> ps.freq = freq >>> ps.power = power >>> ps.m = m >>> ps.df = freq[1] - freq[0] >>> ps.norm = "leahy" Now we have to guess starting parameters. For each Lorentzian, we have amplitude, centroid position and fwhm, and this pattern repeats for each Lorentzian in the fit. The white noise level is the last parameter. >>> t0 = [80, 1.5, 2.5] Let's also make a model to test: >>> model_to_test = models.PowerLaw1D() + models.Const1D() >>> model_to_test.x_0_0.fixed = True We're ready for doing the fit: >>> parest, res = fit_powerspectrum(ps, model_to_test, t0) `res` contains a whole array of useful information about the fit, for example the parameters at the optimum: >>> p_opt = res.p_opt """ if priors: lpost = PSDPosterior(ps, model, priors=priors) else: lpost = PSDLogLikelihood(ps.freq, ps.power, model, m=ps.m) parest = PSDParEst(ps, fitmethod=fitmethod, max_post=max_post) res = parest.fit(lpost, starting_pars, neg=True) return parest, res
def test_logprior_fails_without_prior(self): lpost = PSDPosterior(self.ps.freq, self.ps.power, self.model, m=self.ps.m) with pytest.raises(AttributeError): lpost.logprior([1])
def test_correct_number_of_parameters(self): lpost = PSDPosterior(self.ps, self.model) lpost.logprior = set_logprior(lpost, self.priors) with pytest.raises(IncorrectParameterError): lpost([2,3])
def test_making_posterior(self): lpost = PSDPosterior(self.ps, self.model) lpost.logprior = set_logprior(lpost, self.priors) assert lpost.x.all() == self.ps.freq.all() assert lpost.y.all() == self.ps.power.all()
def test_logprior_fails_without_prior(self): lpost = PSDPosterior(self.ps, self.model) with pytest.raises(AttributeError): lpost.logprior([1])
def setup_class(cls): m = 1 nfreq = 100 freq = np.linspace(0, 10.0, nfreq + 1)[1:] rng = np.random.RandomState(100) # set the seed for the random number generator noise = rng.exponential(size=nfreq) cls.model = models.Lorentz1D() + models.Const1D() cls.x_0_0 = 2.0 cls.fwhm_0 = 0.05 cls.amplitude_0 = 1000.0 cls.amplitude_1 = 2.0 cls.model.x_0_0 = cls.x_0_0 cls.model.fwhm_0 = cls.fwhm_0 cls.model.amplitude_0 = cls.amplitude_0 cls.model.amplitude_1 = cls.amplitude_1 p = cls.model(freq) np.random.seed(400) power = noise*p ps = Powerspectrum() ps.freq = freq ps.power = power ps.m = m ps.df = freq[1]-freq[0] ps.norm = "leahy" cls.ps = ps cls.a_mean, cls.a_var = 2.0, 1.0 cls.a2_mean, cls.a2_var = 100.0, 10.0 p_amplitude_1 = lambda amplitude: \ scipy.stats.norm(loc=cls.a_mean, scale=cls.a_var).pdf(amplitude) p_x_0_0 = lambda alpha: \ scipy.stats.uniform(0.0, 5.0).pdf(alpha) p_fwhm_0 = lambda alpha: \ scipy.stats.uniform(0.0, 0.5).pdf(alpha) p_amplitude_0 = lambda amplitude: \ scipy.stats.norm(loc=cls.a2_mean, scale=cls.a2_var).pdf(amplitude) cls.priors = {"amplitude_1": p_amplitude_1, "amplitude_0": p_amplitude_0, "x_0_0": p_x_0_0, "fwhm_0": p_fwhm_0} cls.lpost = PSDPosterior(cls.ps.freq, cls.ps.power, cls.model, m=cls.ps.m) cls.lpost.logprior = set_logprior(cls.lpost, cls.priors) cls.fitmethod = "powell" cls.max_post = True cls.t0 = [cls.x_0_0, cls.fwhm_0, cls.amplitude_0, cls.amplitude_1] cls.neg = True
# flat prior for the power law index p_alpha = lambda alpha: ((-1. <= alpha) & (alpha <= 5.)) # flat prior for the power law amplitude p_amplitude = lambda amplitude: ((0.01 <= amplitude) & (amplitude <= 10.0)) # normal prior for the white noise parameter p_whitenoise = lambda white_noise: scipy.stats.norm(2.0, 0.1).pdf(white_noise) priors = {} priors["alpha_0"] = p_alpha priors["amplitude_0"] = p_amplitude priors["amplitude_1"] = p_whitenoise starting_pars = [3.0, 1.0, 2.4] lpost = PSDPosterior(ps.freq, ps.power, plc, priors=priors, m=ps.m) parest = PSDParEst(ps, fitmethod='BFGS', max_post=True) res = parest.fit(lpost, starting_pars) sample = parest.sample(lpost, res.p_opt, cov=res.cov, nwalkers=400, niter=100, burnin=200, namestr="psd_modeling_test") max_power, max_freq, max_ind = parest._compute_highest_outlier(lpost, res) print(max_power) pval = parest.calibrate_highest_outlier(lpost, starting_pars,
def test_fit_method_works_with_correct_parameter(self): pe = PSDParEst(self.ps) lpost = PSDPosterior(self.ps, self.model, self.priors) t0 = [2.0, 1, 1, 1] res = pe.fit(lpost, t0)
def setup_class(cls): m = 1 nfreq = 100000 freq = np.linspace(1, 1000, nfreq) np.random.seed(100) # set the seed for the random number generator noise = np.random.exponential(size=nfreq) cls.model = models.PowerLaw1D() + models.Const1D() cls.model.x_0_0.fixed = True cls.alpha_0 = 2.0 cls.amplitude_0 = 100.0 cls.amplitude_1 = 2.0 cls.model.alpha_0 = cls.alpha_0 cls.model.amplitude_0 = cls.amplitude_0 cls.model.amplitude_1 = cls.amplitude_1 p = cls.model(freq) power = noise * p ps = Powerspectrum() ps.freq = freq ps.power = power ps.m = m ps.df = freq[1] - freq[0] ps.norm = "leahy" cls.ps = ps cls.a_mean, cls.a_var = 2.0, 1.0 cls.a2_mean, cls.a2_var = 100.0, 10.0 p_amplitude_1 = lambda amplitude: \ scipy.stats.norm(loc=cls.a_mean, scale=cls.a_var).pdf(amplitude) p_alpha_0 = lambda alpha: \ scipy.stats.uniform(0.0, 5.0).pdf(alpha) p_amplitude_0 = lambda amplitude: \ scipy.stats.norm(loc=cls.a2_mean, scale=cls.a2_var).pdf( amplitude) cls.priors = { "amplitude_1": p_amplitude_1, "amplitude_0": p_amplitude_0, "alpha_0": p_alpha_0 } cls.lpost = PSDPosterior(cls.ps, cls.model) cls.lpost.logprior = set_logprior(cls.lpost, cls.priors) cls.fitmethod = "BFGS" cls.max_post = True cls.t0 = [cls.amplitude_0, cls.alpha_0, cls.amplitude_1] cls.neg = True cls.opt = scipy.optimize.minimize(cls.lpost, cls.t0, method=cls.fitmethod, args=cls.neg, tol=1.e-5) cls.optres = OptimizationResultsSubclassDummy(cls.lpost, cls.opt, neg=True)