Hidden Markov Forward Calculator
Calculate binary observation likelihood and filtered state probabilities for a two-state hidden Markov model.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Emit the first observation from the entered prior, then transition before each later observation and normalize at every step.
Forward weight=emission likelihood×sum(previous filtered probability×transition)
Worked example
Identical emission rows0.5,0.5 give a length-four observation likelihood1/16.
Assumptions and input details
Fixed two-state parameters, no training, backward smoothing or Viterbi decoding. Each probability row must sum to one. Impossible observation sequences are rejected rather than assigned a finite log likelihood.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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