Markov Chains

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Error: {{appState.message.error}}


State Diagram

Initial state:
Distribution edit

Start state distribution

{{s.label}}: {{appState.startProbabilityLabels[$index]}}

Total steps: {{features.equilibrium.numSteps}}
End edit
{{s.label}} Done
Simulations: {{features.hittingTimes.numSims}}
Current: Previous:

Transition Matrix

More options:

Error: Number of nodes must be between {{settings.minNodes}} and {{settings.maxNodes}}.

Error: Highlighted row(s) do not sum to 1. Fix and then click the Apply button again.

Tip: Use the Tab key to move to the next cell.

Simulation Results

State Count Proportion Equilibrium
{{state.label}} {{counts[state.label] || 0}} {{proportions[state.label] || "-"}} {{features.equilibrium.equilibrium ? features.equilibrium.equilibrium[$index].toFixed(4) : "-"}}
Total {{features.equilibrium.DATA.length}}

Simulating Hitting Times {{getCompletion()}}

{{features.hittingTimes.fromStateLabel}}   {{features.hittingTimes.toStateLabel}}

Finite hitting times: {{features.hittingTimes.finiteTimes.length || 0}} / {{features.hittingTimes.times.length || 0}}

Distribution of hitting times
(finite times only)

Summary of hitting times
(finite times only)

Theoretical mean {{expected}}
Sample mean {{features.hittingTimes.finiteTimes | statisticFilter:"mean":3:true}}
Maximum {{features.hittingTimes.finiteTimes | statisticFilter:"max"}}
Minimum {{features.hittingTimes.finiteTimes | statisticFilter:"min"}}

Entrapment States

The checkbox for [AB] (row A, column B) would be interpreted as: Given we are currently in state A, is it impossible to ever reach state B? Tick the checkbox if you think it isn't possible. The diagonal checkboxes, for example [AA], are interpreted as: Starting from this state, is it possible to ever return here? If you think all states can be reached from a given state, select the None checkbox for that row. Then when you are done, click the Check button to see if you identified the entrapment states correctly.

{{state.label}} None


Markov diagram based on Setosa blog Sound effects from freeSFX