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Likelihood Calculation

This document explains how the system learns and uses likelihood probabilities for each sensor entity.

Overview

Likelihoods represent how reliable each sensor is as evidence of occupancy. The system uses different analysis methods depending on sensor type:

  • Numeric Sensors (temperature, humidity, CO2, etc.): Learn statistical distributions using correlation analysis with Gaussian PDFs.
  • Binary Sensors (media players, appliances, doors, windows): Calculate static probabilities from duration-based interval overlap analysis.
  • Motion Sensors: Use user-configurable static probabilities (not learned).

Important: Motion sensors do not have learned likelihoods. Instead, they use user-configurable likelihoods that can be set per area during configuration (defaults: prob_given_true=0.95, prob_given_false=0.02). This is because motion sensors are used as ground truth to determine occupied intervals. Learning motion sensor likelihoods would create a circular dependency.

Likelihood Analysis Process

The analysis process runs periodically (typically hourly) as part of the analysis cycle.

See Sensor Correlation Analysis Chain for the detailed flow.

Analysis Methods by Sensor Type:

  1. Numeric Sensors: Use correlation analysis to learn Gaussian distributions (Mean and Standard Deviation) for occupied and unoccupied states. Likelihoods are calculated dynamically at runtime using Gaussian PDFs.

  2. Binary Sensors: Use duration-based analysis to calculate static probabilities directly from interval overlap durations. These are stored as prob_given_true and prob_given_false values.

  3. Motion Sensors: Use configured static probabilities (not analyzed).

How Likelihoods Are Used in Real-Time Calculation

During real-time probability calculation, likelihoods are retrieved differently based on sensor type.

Numeric Sensors: Dynamic PDF Calculation

For numeric sensors with learned Gaussian parameters, the system calculates two probability densities dynamically:

\[ f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}(\frac{x-\mu}{\sigma})^2} \]
  1. \(P(x | Occupied)\): Likelihood of current value \(x\) given the "Occupied" distribution.
  2. \(P(x | Unoccupied)\): Likelihood of current value \(x\) given the "Unoccupied" distribution.

If the sensor state is unavailable (e.g., "unknown"), the system uses a representative value (average of occupied and unoccupied means) to calculate probabilities.

Binary Sensors: Static Probabilities

For binary sensors (media, appliances, doors, windows), the system uses static probabilities calculated from duration-based analysis:

  • \(P(Active | Occupied)\): Probability that the sensor is active when the area is occupied.
  • \(P(Active | Unoccupied)\): Probability that the sensor is active when the area is unoccupied.

These values are stored directly and used regardless of the current sensor state.

Motion Sensors: Configured Probabilities

Motion sensors use the user-configured static probabilities set during area configuration.

Decay-Adjusted Likelihoods

When an entity is decaying (e.g., motion sensor that just turned off), its likelihoods are interpolated toward neutral (0.5). This gradually reduces the influence of stale evidence as decay progresses.

Weight Application

The likelihoods are weighted by the entity's configured weight:

contribution_true = log(p_t) * entity.weight
contribution_false = log(p_f) * entity.weight

Higher weights mean the entity's evidence has more influence on the final probability.

Database Schema

Correlations Table

Stores analysis results for both numeric sensors and binary sensors:

For Numeric Sensors (Gaussian parameters):

  • area_name, entity_id
  • correlation_type: "strong_positive", "strong_negative", or "none"
  • mean_value_when_occupied, std_dev_when_occupied
  • mean_value_when_unoccupied, std_dev_when_unoccupied
  • correlation_coefficient, confidence

For Binary Sensors (static probabilities):

  • area_name, entity_id
  • correlation_type: "binary_likelihood"
  • mean_value_when_occupied: Stores prob_given_true
  • mean_value_when_unoccupied: Stores prob_given_false
  • correlation_coefficient: None (not applicable for binary sensors)

For Both Types:

  • analysis_error: Reason why analysis failed or was not performed (e.g., "no_correlation", "too_few_samples", "no_occupied_intervals"). This value is persisted and restored when entities are reloaded.

Entities Table

Stores current entity state and configuration:

  • prob_given_true: Probability sensor is active when occupied (for binary sensors, loaded from Correlations table)
  • prob_given_false: Probability sensor is active when unoccupied (for binary sensors, loaded from Correlations table)
  • learned_gaussian_params: JSON field storing Gaussian parameters (for numeric sensors, loaded from Correlations table)
  • analysis_error: Reason why analysis failed or was not performed (loaded from Correlations table)

NumericSamples Table

Stores raw numeric sensor values with timestamps.

Intervals Table

Stores binary sensor state intervals (on/off periods) used for duration-based analysis.

Default Likelihoods

If history-based learning is disabled, insufficient data is available, or correlation fails, the system uses default static likelihoods from the entity type definition.

Default values vary by entity type:

  • Motion sensors: High P(Active | Occupied), low P(Active | Not Occupied) (configured per area)
  • Media players: Medium P(Active | Occupied), very low P(Active | Not Occupied)
  • Environmental sensors: Low P(Active | Occupied), low P(Active | Not Occupied)

Note: These defaults are used directly from EntityType when Gaussian parameters are unavailable. The system does not store fallback values in the database for non-motion sensors.

For non-motion sensors, these defaults are replaced by learned values once sufficient historical data is available.

See Also