Enhanced Random Processes

Enhanced Random Processes in Mathematica 10

Mathematica Version 10 expands on the already extensive random process framework with new processes, including hidden Markov models. Hidden Markov models are typically used to infer the hidden internal state from emissions, as in communication decoding, speech recognition, and biological sequence analysis. The random process framework also adds advanced time series processes and transformations of existing processes, as well as significantly improves computation with slice distributions - the bridge from random processes to random variables - often giving definite conclusions about expected process behavior from models.

  • Support for scalar- and vector-valued hidden Markov processes. »
  • Support for hidden Markov processes with discrete or continuous emissions.
  • Support for hidden Markov processes with silent states.
  • Find the sequence of hidden states from emissions using Viterbi and other decoding methods. »
  • Automatically estimate hidden Markov process parameters from data.
  • Build new processes as transformations of other processes. »
  • Support for white non-Gaussian noise process. »
  • Support for colored Gaussian noise process.
  • Support for serial autocorrelation test of time series. »
  • Substantially improved support for computation with time slices of processes across all random processes.
  • Substantially improved simulation performance for most random processes.
  • Substantial robustness and performance improvements of parameter estimation for many processes.

Hidden Markov Processes with Discrete or Continuous, Univariate or Multivariate Emissions »

Hidden Markov Processes with Silent States »

Find Hidden States Underlying Given Emissions of HMM Process »

Estimate Hidden Markov Processes from Data »

Perform Typo Correction without a Dictionary »

Track Player Movement in a First-Person Shooter Game »

Find a Splice Site in a DNA Sequence »

Track Lizard Movement with a Capture-Recapture Model

Use TransformedProcess to Create a Custom Process »

Study the Stochastic Exponential Function »

Simulate the Surplus Process for Insurance »

Model Option Prices Using Merton Jump-Diffusion »

Generate White Noise Based on Any Distribution »

Apply ARMA Filter to a Heavy-Tailed White Noise Process »

Test for Serial Correlation »

Fractional Gaussian Noise versus FARIMA Noise »

Improved Support of Random Processes in Expectation »

Improved Support of Random Processes in Probability »

Identify Regularly Sampled Ornstein–Uhlenbeck Process as an Autoregressive Process »

Improved Documentation for Probability and Statistics »