Słownik AI
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Bayesian Smoothing
Technique for posterior estimation of hidden states in a time series using all past and future observations. Unlike filtering which only uses past observations, smoothing provides more accurate estimates by exploiting the complete information of the series.
Bayesian State Space Model
Probabilistic framework modeling time series as an unobservable latent process evolving in a state space, with observations depending on these states. The Bayesian approach allows simultaneous inference of model parameters and hidden states while quantifying uncertainty.
Temporal Markov Chain Monte Carlo (MCMC) Methods
Sampling techniques adapted for inference in Bayesian time series models, where Markov chains explore the parameter and hidden state space. They allow approximation of complex posterior distributions when analytical solutions are impossible.
Bayesian Particle Filter
Sequential filtering algorithm for nonlinear and non-Gaussian models, using a set of weighted particles to represent the state probability distribution. It is particularly suitable for Bayesian models where the Gaussian approximation of the Kalman filter is invalid.
Predictive Distribution Forecasting
Bayesian approach where forecasting is not a single point but a complete probability distribution integrating parameter and noise uncertainty. It allows generation of credibility intervals and probabilistic scenarios for future values.
Temporal Gaussian Process
Nonparametric Bayesian approach where the underlying function of the time series is modeled as a Gaussian process with a temporal covariance function. It offers remarkable flexibility for capturing complex patterns while providing analytical uncertainties on forecasts.
Variational Inference for Time Series
Deterministic approximation method for posterior distributions in Bayesian time series models, optimizing a family of simple distributions to minimize divergence from the true distribution. It constitutes a faster alternative to MCMC for large datasets.
Bayesian Regime Switching Model
Class of models where the parameters of the generating process can change according to a hidden Markov chain, with Bayesian inference to estimate regimes and their probabilities. They are particularly suitable for time series exhibiting heterogeneous behaviors or structural breaks.
Bayesian Rauch-Tung-Striebel (RTS) Filter
Optimal smoothing algorithm for linear Gaussian models, performing a backward pass on Kalman filter estimates to incorporate future information. In the Bayesian framework, it provides exact posterior distributions of hidden states conditional on all observations.
Bayesian Stochastic Volatility Model
Bayesian specification where the variance of a time series noise evolves according to a latent stochastic process, often modeled by an AR(1). The Bayesian approach allows rigorous inference on past and future volatility, essential in finance and econometrics.
Bayesian Model Averaging (BMA)
Method combining multiple forecasting models using Bayesian posterior probabilities as weights, integrating both model uncertainty and parameter uncertainty. It often outperforms individual models by exploiting their complementary strengths.
Bayesian Duration Model
Bayesian approach for modeling the elapsed time between events in a time series, using distributions such as Weibull or log-logistic with random parameters. It allows incorporating covariates and quantifying uncertainty about future occurrence times.
Online Bayesian Inference
Sequential inference paradigm where posterior distributions are updated as new observations arrive, without needing to re-analyze all past data. It is crucial for real-time applications such as anomaly detection or state tracking.