Sampling Technique to add uncertainity

I have a csv file in which I have data of temperature at 132 points. Now I want to add uncertainity in my data. How can I add uncertainity using monte carlo markov chain?

Answer 1

[Balavignesh]

Hi Aman,

I understand that you are seeking to introduce uncertainty into your dataset using the Monte Carlo Markov Chain (MCMC) method. I recommend utilizing 'readmatrix' MATLAB function to import the 'TEMP_373.csv' file and subsequently defining a model. For simplicity, I am assuming a normal distribution to characterize the uncertainty. Following this, the MCMC algorithm can be employed to sample from the posterior distribution of the model parameters, enabling the generation of uncertain temperature data.

The provided example code serves to illustrate this process.

% Step 1: Read the CSV file
temperature_data = readmatrix('TEMP_373.csv'); % Assuming the file contains a single column of temperature data

% Step 2: Define the Model
mu_prior = mean(temperature_data); % Prior mean
sigma_prior = std(temperature_data); % Prior standard deviation

% Step 3: Implement Metropolis-Hastings MCMC
numIterations = 10000; % Number of MCMC iterations
chain = zeros(numIterations, 2); % Initialize the parameter chain

% Initialize the first state of the chain
current_mu = mu_prior;
current_sigma = sigma_prior;

% Define the proposal distribution standard deviations
proposal_mu = 0.5;
proposal_sigma = 0.5;

% Run the MCMC algorithm
for i = 1:numIterations
    % Propose new parameters
    proposed_mu = normrnd(current_mu, proposal_mu);
    proposed_sigma = normrnd(current_sigma, proposal_sigma);
    
    % Calculate the likelihood of the proposed parameters
    likelihood_current = prod(normpdf(temperature_data, current_mu, current_sigma));
    likelihood_proposed = prod(normpdf(temperature_data, proposed_mu, proposed_sigma));
    
    % Calculate the prior probability of the proposed parameters
    prior_current = normpdf(current_mu, mu_prior, sigma_prior) * normpdf(current_sigma, sigma_prior, sigma_prior);
    prior_proposed = normpdf(proposed_mu, mu_prior, sigma_prior) * normpdf(proposed_sigma, sigma_prior, sigma_prior);
    
    % Calculate the acceptance ratio
    acceptance_ratio = min(1, (likelihood_proposed * prior_proposed) / (likelihood_current * prior_current));
    
    % Accept or reject the proposed parameters
    if rand() < acceptance_ratio
        current_mu = proposed_mu;
        current_sigma = proposed_sigma;
    end
    
    % Save the parameters to the chain
    chain(i, :) = [current_mu, current_sigma];
end

% Step 4: Generate Uncertain Data
numSamples = 1000; % Number of samples to generate
uncertain_temperatures = normrnd(chain(end, 1), chain(end, 2), numSamples, 1); % Generate uncertain temperature data based on the final sampled parameters

Kindly have a look at the following documentation links to have more information on:

• 'Monte Carlo Markov Chain': https://www.mathworks.com/help/econ/sampleroptions.html
• 'Normal Distribution': https://www.mathworks.com/help/stats/normal-distribution.html
• 'readmatrix' function: https://www.mathworks.com/help/matlab/ref/readmatrix.html

Thanks and regards,

Balavignesh