from uqpylab import sessions
import numpy as np
import math
import scipy.io

# Start the session
mySession = sessions.cloud()
# (Optional) Get a convenient handle to the command line interface
uq = mySession.cli
# Reset the session
mySession.reset()

Processing .

.

 done!

 uqpylab.sessions :: INFO     :: This is UQ[py]Lab, version 1.00, running on https://uqcloud.ethz.ch. 
                                 UQ[py]Lab is free software, published under the open source BSD 3-clause license.
                                 To request special permissions, please contact:
                                  - Stefano Marelli (marelli@ibk.baug.ethz.ch).
                                 A new session (2cb16c358510429babf72cfc697c58ed) started.

 uqpylab.sessions :: INFO     :: Reset successful.

uq.rng(100, 'twister');

file_location = './Bayesian_Data'
mat = scipy.io.loadmat('{}/{}'.format(file_location,'uq_Example_BayesianPreyPred.mat'))
Data = mat['Data'][0][0]

normYear = Data[0] - Data[0][0]

ModelOpts = {'Type': 'Model', 
             'ModelFun':'predatorPreyModel.model',
             'Parameters': {'time': normYear.tolist()},
             'isVectorized': True
            }
myForwardModel = uq.createModel(ModelOpts)

PriorOpts = {
    'Name': 'Prior distribution on PredPrey parameters',
    'Marginals': [
        {
            'Name': 'alpha', 
            'Type': 'LogNormal',
            'Moments': [1, 0.1] 
        },
        {
            'Name': 'beta', 
            'Type': 'LogNormal',
            'Moments': [0.05, 0.005] 
        },
        {
            'Name': 'gamma', 
            'Type': 'LogNormal',
            'Moments': [1, 0.1] 
        },
        {
            'Name': 'delta', 
            'Type': 'LogNormal',
            'Moments': [0.05, 0.005] 
        },
        {
            'Name': 'initH', 
            'Type': 'LogNormal',
            'Parameters': [math.log(10), 1] 
        },
        {
            'Name': 'initL',
            'Type': 'LogNormal',
            'Parameters': [math.log(10), 1]
        }
    ]
}
    
myPriorDist = uq.createInput(PriorOpts)

DataHare = Data[2]/1000
DataLynx = Data[1]/1000

myData = [
    {
        'y': [DataHare.tolist()], # in 1000
        'Name': 'Hare data',
        'MOMap': [list(range(1,22))] # Output ID
    },
    {
        'y': [DataLynx.tolist()], # in 1000
        'Name': 'Lynx data',
        'MOMap': [list(range(22,43))] # Output ID
    }
]

SigmaOpts = {
    'Marginals': {
        'Name': 'Sigma2L',
        'Type': 'LogNormal',
        'Parameters': [-1, 1]
    }
}

mySigmaDist1 = uq.createInput(SigmaOpts)

SigmaOpts = {
    'Marginals': {
        'Name': 'Sigma2H',
        'Type': 'LogNormal',
        'Parameters': [-1, 1]
    }
}

mySigmaDist2 = uq.createInput(SigmaOpts)

DiscrepancyOpts = [
    {
        'Type': 'Gaussian',
        'Prior': mySigmaDist1['Name']
    },
    {
        'Type': 'Gaussian',
        'Prior': mySigmaDist2['Name']
    }
]

Solver = {
    'Type': 'MCMC',
    'MCMC': {
        'Sampler': 'AM', 
        'Steps': 100, 
        'NChains': 100, 
    }
}

BayesOpts = {
    'Type': 'Inversion',
    'Name': 'Bayesian model',
    'Prior': myPriorDist['Name'],
    'Data': myData,
    'Discrepancy': DiscrepancyOpts,
    'Solver': Solver
}

myBayesianAnalysis = uq.createAnalysis(BayesOpts)

 uqpylab.sessions :: INFO     :: Received intermediate compute request, function: predatorPreyModel.model.

 uqpylab.sessions :: INFO     :: Carrying out local computation...

 uqpylab.sessions :: INFO     :: Local computation complete.

 uqpylab.sessions :: INFO     :: Starting transmission of intermediate compute results ((100, 42))...

 uqpylab.sessions :: INFO     :: Intermediate compute results sent.

 uqpylab.sessions :: INFO     :: Received intermediate compute request, function: predatorPreyModel.model.

 uqpylab.sessions :: INFO     :: Carrying out local computation...

 uqpylab.sessions :: INFO     :: Local computation complete.

 uqpylab.sessions :: INFO     :: Starting transmission of intermediate compute results ((56, 42))...

 uqpylab.sessions :: INFO     :: Intermediate compute results sent.

uq.print(myBayesianAnalysis)

%----------------------- Inversion output -----------------------%
   Number of calibrated model parameters:         6
   Number of non-calibrated model parameters:     0

   Number of calibrated discrepancy parameters:   2

%------------------- Data and Discrepancy
%  Data-/Discrepancy group 1:
   Number of independent observations:            1

   Discrepancy:
      Type:                                       Gaussian
      Discrepancy family:                         Scalar
      Discrepancy parameters known:               No

   Associated outputs:
      Model 1: 
         Output dimensions:                       1
                                                  to
                                                  21


%  Data-/Discrepancy group 2:
   Number of independent observations:            1

   Discrepancy:
      Type:                                       Gaussian
      Discrepancy family:                         Scalar
      Discrepancy parameters known:               No

   Associated outputs:
      Model 1: 
         Output dimensions:                       22
                                                  to
                                                  42


%------------------- Solver
   Solution method:                               MCMC

   Algorithm:                                     AM
   Duration (HH:MM:SS):                           00:19:52
   Number of sample points:                       1.00e+04

%------------------- Posterior Marginals
------------------------------------------------------------------
| Parameter | Mean  | Std    | (0.025-0.97) Quant. | Type        |
------------------------------------------------------------------
| alpha     | 0.99  | 0.16   | (0.64 - 1.3)        | Model       |
| beta      | 0.05  | 0.0065 | (0.038 - 0.063)     | Model       |
| gamma     | 1     | 0.15   | (0.76 - 1.3)        | Model       |
| delta     | 0.047 | 0.0082 | (0.033 - 0.065)     | Model       |
| initH     | 19    | 7.8    | (6.5 - 35)          | Model       |
| initL     | 15    | 8.9    | (0.66 - 32)         | Model       |
| Sigma2L   | 3     | 0.93   | (1.1 - 5.2)         | Discrepancy |
| Sigma2H   | 2.4   | 0.87   | (0.86 - 4.4)        | Discrepancy |
------------------------------------------------------------------

%------------------- Point estimate
--------------------------------------
| Parameter | Mean  | Parameter Type |
--------------------------------------
| alpha     | 0.99  | Model          |
| beta      | 0.05  | Model          |
| gamma     | 1     | Model          |
| delta     | 0.047 | Model          |
| initH     | 19    | Model          |
| initL     | 15    | Model          |
| Sigma2L   | 3     | Discrepancy    |
| Sigma2H   | 2.4   | Discrepancy    |
--------------------------------------

%------------------- Correlation matrix (model parameters)
-------------------------------------------------------------------
|       |  alpha     beta      gamma    delta     initH    initL  |
-------------------------------------------------------------------
| alpha |  1         -0.047    0.1      -0.061    -0.12    0.4    |
| beta  |  -0.047    1         0.024    0.043     0.093    -0.16  |
| gamma |  0.1       0.024     1        0.16      0.23     0.2    |
| delta |  -0.061    0.043     0.16     1         -0.25    0.039  |
| initH |  -0.12     0.093     0.23     -0.25     1        0.42   |
| initL |  0.4       -0.16     0.2      0.039     0.42     1      |
-------------------------------------------------------------------

%------------------- Correlation matrix (discrepancy parameters)
----------------------------------
|         |  Sigma2L    Sigma2H  |
----------------------------------
| Sigma2L |  1          0.62     |
| Sigma2H |  0.62       1        |
----------------------------------

uq.display(myBayesianAnalysis, trace=1);

badChainsIndex = np.array(myBayesianAnalysis['Results']['Sample'])[-1,0,:] > 0.8

myBayesianAnalysis = uq.postProcessInversion(myBayesianAnalysis,
                            'badChains', badChainsIndex.tolist(),
                            'prior', 1000,
                            'priorPredictive', 1000,
                            'posteriorPredictive', 1000,
                    )

 uqpylab.sessions :: INFO     :: Received intermediate compute request, function: predatorPreyModel.model.

 uqpylab.sessions :: INFO     :: Carrying out local computation...

 uqpylab.sessions :: INFO     :: Local computation complete.

 uqpylab.sessions :: INFO     :: Starting transmission of intermediate compute results ((1, 42))...

 uqpylab.sessions :: INFO     :: Intermediate compute results sent.

 uqpylab.sessions :: INFO     :: Received intermediate compute request, function: predatorPreyModel.model.

 uqpylab.sessions :: INFO     :: Carrying out local computation...

 uqpylab.sessions :: INFO     :: Local computation complete.

 uqpylab.sessions :: INFO     :: Starting transmission of intermediate compute results ((1000, 42))...

 uqpylab.sessions :: INFO     :: Intermediate compute results sent.

uq.display(myBayesianAnalysis);

mySession.quit()

 uqpylab.sessions :: INFO     :: Session 2cb16c358510429babf72cfc697c58ed terminated.

True

INVERSION: PREDATOR-PREY MODEL CALIBRATION¶

Package imports¶

Start a remote UQCloud session¶

Set the random seed for reproducibility¶

Forward model¶

Prior distribution of the model parameters¶

Measurement data¶

Discrepancy model¶

Bayesian analysis¶

MCMC solver options¶

Posterior sample generation¶

Posterior sample post-processing¶

Terminate the remote UQCloud session¶