OptBayesExptNoiseParam class

class optbayesexpt.obe_noiseparam.OptBayesExptNoiseParameter(measurement_model, setting_values, parameter_samples, constants, noise_parameter_index=None, **kwargs)

Bases: OptBayesExpt

OptBayesExpt adding measurement uncertainty as an unknown parameter.

OptBayesExptNoiseParameter is designed for cases where the experimental uncertainty / standard deviation of the measurement noise is an unknown. The standard deviation of the measurement noise is included as one of the parameters. The methods rely on several assumptions:

• The noise in measurement data is well-described by additive, normally-distributed (Gaussian) noise.

• The noise is independent of settings and other parameters.

Arguments:

• measurement_model (function) – A function accepting (settings, parameters, constants) arguments and returning model values of experiment outputs. See the model_function arg of OptBayesExpt.

• setting_values (tuple of arrays) – Arrays of allowed values for each setting. See the setting_values arg of OptBayesExpt.

• parameter_samples (tuple of arrays) – random draws of each model parameter representing the prior probability distribution. See the parameter_samples arg of OptBayesExpt. One of the parameter_sample arrays must be the standard deviation of the measurement noise, idendified by the noise_parameter_index arg.

• constants (tuple) – settings or parameters that are assumed constant. See the constants arg of OptBayesExpt.

• noise_parameter_index (int or tuple) – identifies which of the arrays in the paramter_samples input are uncertainty parameters. For multi-channel measurements, the tuple identifies uncertainty parameters corresponding to measurement channels. In cases where channels have the same noise characteristics, indices may be repeated in the tuple.

• **kwargs – Keyword arguments passed to the parent classes.

Attributes:

enforce_parameter_constraints()

Detects and nullifies disallowed parameter values

Constrains the noise parameter to be positive. Negative uncertainties lead to negative likelihoods, negative particle weights and other abominations. Overwrites the OptBayesExpt stub method.

likelihood(y_model, measurement_record)

Calculates the likelihood of a measurement result.

For each parameter combination, estimate the probability of obtaining the results provided in measurement_result.

Under these assumptions, and model values \(y_{model}\) as a function of parameters, the likelihood is a Gaussian function proportional to \(\sigma^{-1} \exp [-(y_{model} - y_{meas})^2 / (2 \sigma^2)]\).

Parameters:

• y_model (ndarray) – model_function() results evaluated for all parameters.

• measurement_record (tuple) –

  The measurement conditions and results, supplied by the user to update_pdf(). The first two elements of measurement_record are:

  • settings (tuple)

  • measurement value (float or tuple)

  further entries in the measurement_record are ignored.

Returns:

an array of probabilities corresponding to the parameters in self.allparameters.

noise_parameter_index

Stores the noise_parameter_index argument

Type:

int

yvar_noise_model()

Calculates the mean variance from the noise parameter.

Overwrites OptBayesExpt method, replacing default_noise_std ** 2 with the mean variance calculated from the noise parameter. Used in calculating utility.

Returns: (float) average variance.