How to use the abcpy.backends.BackendDummy function in abcpy

def test(self):
        model = Normal([1, 0.1])
        Manager = AcceptedParametersManager([model])
        backend = Backend()
        Manager.update_kernel_values(backend, [1])
        self.assertEqual(Manager.kernel_parameters_bds.value(),[1])

def setUp(self):
        # find spark and initialize it
        self.backend = BackendDummy()

        # define a uniform prior distribution
        mu = Uniform([[-5.0], [5.0]], name='mu')
        sigma = Uniform([[0.0], [10.0]], name='sigma')
        # define a Gaussian model
        self.model = Normal([mu, sigma])

        # define a distance function
        stat_calc = Identity(degree=2, cross=0)
        self.dist_calc = Euclidean(stat_calc)

        # create fake observed data
        #self.observation = self.model.forward_simulate(1, np.random.RandomState(1))[0].tolist()
        self.observation = [np.array(9.8)]

def test_sample(self):
        # setup backend
        backend = BackendDummy()
        
        # define a uniform prior distribution
        mu = Uniform([[-5.0], [5.0]], name='mu')
        sigma = Uniform([[0.0], [10.0]], name='sigma')
        # define a Gaussian model
        self.model = Normal([mu,sigma])

        # define sufficient statistics for the model
        stat_calc = Identity(degree = 2, cross = 0)

        # create fake observed data
        #y_obs = self.model.forward_simulate(1, np.random.RandomState(1))[0].tolist()
        y_obs = [np.array(9.8)]
      
        # Define the likelihood function
        likfun = SynLiklihood(stat_calc)

def setUp(self):
        # find spark and initialize it
        self.backend = BackendDummy()

        # define a uniform prior distribution
        mu = Uniform([[-5.0], [5.0]], name='mu')
        sigma = Uniform([[0.0], [10.0]], name='sigma')
        # define a Gaussian model
        self.model = Normal([mu, sigma])

        # define a distance function
        stat_calc = Identity(degree=2, cross=0)
        self.dist_calc = Euclidean(stat_calc)

        # create fake observed data
        #self.observation = self.model.forward_simulate(1, np.random.RandomState(1))[0].tolist()
        self.observation = [np.array(9.8)]

# A quantity determining whether a student receives a scholarship, including his social background
    final_scholarship = scholarship_without_additional_effects + 3*background

    # Define a summary statistics for final grade and final scholarship
    from abcpy.statistics import Identity
    statistics_calculator_final_grade = Identity(degree = 2, cross = False)
    statistics_calculator_final_scholarship = Identity(degree = 3, cross = False)

    # Define a distance measure for final grade and final scholarship
    from abcpy.distances import Euclidean
    distance_calculator_final_grade = Euclidean(statistics_calculator_final_grade)
    distance_calculator_final_scholarship = Euclidean(statistics_calculator_final_scholarship)

    # Define a backend
    from abcpy.backends import BackendDummy as Backend
    backend = Backend()

    # Define a perturbation kernel
    from abcpy.perturbationkernel import DefaultKernel
    kernel = DefaultKernel([school_location, class_size, grade_without_additional_effects, \
                            background, scholarship_without_additional_effects])

    # Define sampling parameters
    T, n_sample, n_samples_per_param = 3, 250, 10
    eps_arr = np.array([.75])
    epsilon_percentile = 10

    # Define sampler
    from abcpy.inferences import PMCABC
    sampler = PMCABC([final_grade, final_scholarship], \
                     [distance_calculator_final_grade, distance_calculator_final_scholarship], backend, kernel)

def infer_parameters():
    # define backend
    # Note, the dummy backend does not parallelize the code!
    from abcpy.backends import BackendDummy as Backend
    backend = Backend()

    # define observation for true parameters mean=170, std=15
    height_obs = [160.82499176, 167.24266737, 185.71695756, 153.7045709, 163.40568812, 140.70658699, 169.59102084, 172.81041696, 187.38782738, 179.66358934, 176.63417241, 189.16082803, 181.98288443, 170.18565017, 183.78493886, 166.58387299, 161.9521899, 155.69213073, 156.17867343, 144.51580379, 170.29847515, 197.96767899, 153.36646527, 162.22710198, 158.70012047, 178.53470703, 170.77697743, 164.31392633, 165.88595994, 177.38083686, 146.67058471763457, 179.41946565658628, 238.02751620619537, 206.22458790620766, 220.89530574344568, 221.04082532837026, 142.25301427453394, 261.37656571434275, 171.63761180867033, 210.28121820385866, 237.29130237612236, 175.75558340169619, 224.54340549862235, 197.42448680731226, 165.88273684581381, 166.55094082844519, 229.54308602661584, 222.99844054358519, 185.30223966014586, 152.69149367593846, 206.94372818527413, 256.35498655339154, 165.43140916577741, 250.19273595481803, 148.87781549665536, 223.05547559193792, 230.03418198709608, 146.13611923127021, 138.24716809523139, 179.26755740864527, 141.21704876815426, 170.89587081800852, 222.96391329259626, 188.27229523693822, 202.67075179617672, 211.75963110985992, 217.45423324370509]

    # define prior
    from abcpy.continuousmodels import Uniform
    mu = Uniform([[150], [200]], )
    sigma = Uniform([[5], [25]], )

    # define the model
    from abcpy.continuousmodels import Normal
    height = Normal([mu, sigma], )

    # define statistics
    from abcpy.statistics import Identity
    statistics_calculator = Identity(degree=3, cross=True)

# define statistics
    from abcpy.statistics import Identity
    statistics_calculator = Identity(degree = 2, cross = False)
    
    # define distance
    from abcpy.distances import LogReg
    distance_calculator = LogReg(statistics_calculator)
    
    # define kernel
    from abcpy.perturbationkernel import DefaultKernel
    kernel = DefaultKernel([mu, sigma])

    # define backend
    # Note, the dummy backend does not parallelize the code!
    from abcpy.backends import BackendDummy as Backend
    backend = Backend()
    
    # define sampling scheme
    from abcpy.inferences import PMCABC
    sampler = PMCABC([height], [distance_calculator], backend, kernel, seed=1)
    
    # sample from scheme
    T, n_sample, n_samples_per_param = 3, 250, 10
    eps_arr = np.array([.75])
    epsilon_percentile = 10
    journal = sampler.sample([height_obs],  T, eps_arr, n_sample, n_samples_per_param, epsilon_percentile)

    return journal

prior = Uniform([[150, 5],[200, 25]])
    
    # define the model
    model = Gaussian([prior])

    # define statistics
    from abcpy.statistics import Identity
    statistics_calculator = Identity(degree = 2, cross = False)
    
    # define distance
    from abcpy.distances import LogReg
    distance_calculator = LogReg(statistics_calculator)
    
    # define backend
    from abcpy.backends import BackendDummy as Backend
    backend = Backend()
    
    # define sampling scheme
    from abcpy.inferences import PMCABC
    sampler = PMCABC([model], distance_calculator, backend)
    
    # sample from scheme
    T, n_sample, n_samples_per_param = 3, 250, 10
    eps_arr = np.array([.75])
    epsilon_percentile = 10
    journal = sampler.sample([y_obs],  T, eps_arr, n_sample, n_samples_per_param, epsilon_percentile)

    return journal