Markov Models Tool
Visualize and understand Markov chains, hidden Markov models (HMMs), and their applications in sequence prediction, speech recognition, and bioinformatics.
What are Markov Models?
Markov models are stochastic models used to model randomly changing systems where the future state depends only on the current state (Markov property). Markov chains model observable states, while Hidden Markov Models (HMMs) model systems where states are hidden but produce observable outputs.
Sequence Input
Markov Model Visualization
Building Markov Model...
How Markov Models Work
Markov models assume the Markov property: the future state depends only on the current state, not on the sequence of events that preceded it. The model is defined by a set of states and transition probabilities between them.
Model Types & Applications
Weather Prediction
Bioinformatics (DNA)
Speech Recognition
Model Results & Analysis
The transition matrix shows the probability of moving from one state to another. Each row sums to 1 (100% probability).
| From\To | Sunny | Cloudy | Rainy |
|---|
The stationary distribution represents the long-term probability of being in each state, regardless of the starting state.
Understanding Stationary Distribution
The stationary distribution π satisfies πP = π, where P is the transition matrix. It represents the equilibrium state of the Markov chain. For ergodic Markov chains, the stationary distribution exists and is unique.
Use the trained Markov model to predict the next state or generate new sequences.
Prediction Accuracy
How to Add This Markov Models Tool to Your Blogger Site
Step 1: Copy All Code
Select all the code on this page (click and drag or press Ctrl+A then Ctrl+C). The entire page is a single HTML file.
Step 2: Create New Blog Post
In your Blogger dashboard, create a new post or edit an existing one where you want to add the tool.
Step 3: Switch to HTML Mode
Click the "HTML" button in the post editor to switch from Compose to HTML mode.
Step 4: Paste & Publish
Paste the copied code (Ctrl+V) into the HTML editor, then publish or update your post.
Where Are Markov Models Used?
Markov models are fundamental to: Natural Language Processing (text generation, POS tagging), Speech Recognition (Siri, Alexa, Google Assistant), Bioinformatics (DNA/protein sequence analysis), Finance (stock price prediction, credit ratings), Queueing Theory (network traffic, call centers), Games (Monopoly, board games), and PageRank Algorithm (Google search ranking).
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