mcmc method  (Varian Medical)

Journal: Earth and Space Science (Hoboken, N.j.)

Article Title: Reconstruction of GRACE Mass Change Time Series Using a Bayesian Framework

doi: 10.1029/2021EA002162

Figure Lengend Snippet: Flow chart of the method used to impute the missing solutions within and between Gravity Recovery and Climate Experiment and its Follow On (GRACE (‐FO)) missions. First, the informative priors were derived from the GRACE (‐FO) for a single grid point/basin time series as the ranges of the intercepts, slopes, variability, amplitudes, and frequencies of the annual and semiannual cycles in the GRACE (‐FO) time series, assuming an additive generative model describing the geophysical signal in GRACE data as long‐term variability (secular trend + interannual to decadal variability), annual, and semi‐annual. Second, we combined the likelihood data and the priors in the Markov Chain Monte Carlo sampling to generate posterior distributions for each of the component storages. Third, we merged the median of the posteriors for the component storages to reconstruct the full GRACE (‐FO) total water storage and its uncertainty at 95% credible interval. We added the residuals back to the observed time series to preserve the same variability as the original GRACE time series. We applied 5‐fold cross validations to validate the model internally and generate a predictive posterior distribution that can be used to infer the present and near future of the total signal.

Article Snippet: We then used the MCMC method to generate 2,000 samples from the posterior distribution ( P ( θ | D ) for each component (Durbin & Koopman, ; Harvey, ; Scott & Varian, ) (Figure ).

Techniques: Derivative Assay, Sampling

Journal: Earth and Space Science (Hoboken, N.j.)

Article Title: Reconstruction of GRACE Mass Change Time Series Using a Bayesian Framework

doi: 10.1029/2021EA002162

Figure Lengend Snippet: Modeled total water storage during the Gravity Recovery and Climate Experiment (GRACE) and GRACE‐Follow On gap as the sum of the median posterior distribution of long‐term variability (variability ≥12‐month, including secular trend and interannual‐decadal variations), annual and semi‐annual signals between April 2002 and April 2021, sampled from 2,000 steps using Markov Chain Monte Carlo with the No‐U‐Turn Sampling method. Uncertainties associated with these signals are provided in supplementary materials at 5% and 95% levels (Figures S2, S3 in Supporting Information ).

Article Snippet: We then used the MCMC method to generate 2,000 samples from the posterior distribution ( P ( θ | D ) for each component (Durbin & Koopman, ; Harvey, ; Scott & Varian, ) (Figure ).

Techniques: Sampling

Journal: Earth and Space Science (Hoboken, N.j.)

Article Title: Reconstruction of GRACE Mass Change Time Series Using a Bayesian Framework

doi: 10.1029/2021EA002162

Figure Lengend Snippet: [a] Markov Chain Monte Carlo regression model diagnostic test with coefficient of determination (r 2 ). [b] Empirical cumulative density function (ecdf) for r 2 showing ≥80% of the grid cells have r 2 ≥ 58%. Variabilities in the predictable signal and the residuals are provided in SI (Figure S5 in Supporting Information ).

Article Snippet: We then used the MCMC method to generate 2,000 samples from the posterior distribution ( P ( θ | D ) for each component (Durbin & Koopman, ; Harvey, ; Scott & Varian, ) (Figure ).

Techniques: Diagnostic Assay