Bayesian


The bayesian binary sensor platform observes the state from multiple sensors and uses Bayes’ rule to estimate the probability that an event has occurred given the state of the observed sensors. If the estimated posterior probability is above the probability_threshold, the sensor is on otherwise it is off.

This allows for the detection of complex events that may not be readily observable, e.g., cooking, showering, in bed, the start of a morning routine, etc. It can also be used to gain greater confidence about events that are directly observable, but for which the sensors can be unreliable, e.g., presence.

Theory

A key concept in Bayes’ Rule is the difference between the probability of the ‘event given the observation’ and the probability of the ‘observation given the event’. In some cases these probabilities will be similar. The probability that someone is in the room given that motion is detected is similar to the probability motion is detected given that someone is in the room. In other cases, the distinction is much more important. The probability I have just arrived home (the event) each time the front door contact sensor reports open (the observation) (p=0.2) is not the same as the probability the front door contact sensor reports open (the observation) when I come home (the event) (p=0.999).

In the configuration use the probability of the observation (the sensor state in question) given the event (the assumed state of the Bayesian binary_sensor).

Estimating probabilities

  1. Avoid 0 and 1, these will mess with the odds and are rarely true - sensors fail.
  2. When using 0.99 and 0.001. The number of 9s and 0s matters.
  3. Most probabilities will be time-based - the fraction of time something is true is also the probability it will be true.
  4. Use your Home Assistant history to help estimate the probabilities.
    • prob_given_true: - Select the sensor in question over a time range when you think the bayesian sensor should have been true. prob_given_true: is the fraction of the time the sensor was in to_state:.
    • prob_given_false: - Select the sensor in question over a time range when you think the bayesian sensor should have been false. prob_given_false: is the fraction of the time the sensor was in to_state:.
  5. Don’t work backwards by tweaking prob_given_true: and prob_given_false: to give the results and behaviors you want, use #4 to try and get probabilities as close to the ‘truth’ as you can, if your behavior is not as expected consider adding more sensors or see #6.
  6. If your Bayesian sensor ends up triggering on too easily, re-check that the probabilities set and estimated make sense, then consider increasing probability_threshold: and vice-versa.

Configuration

To enable the Bayesian sensor, add the following lines to your configuration.yaml:

# Example configuration.yaml entry
binary_sensor:
  - platform: bayesian
    prior: 0.1
    observations:
      - entity_id: "switch.kitchen_lights"
        prob_given_true: 0.6
        prob_given_false: 0.2
        platform: "state"
        to_state: "on"

Configuration Variables

prior float Required

The prior probability of the event (0 to 1). At any point in time (ignoring all external influences) how likely is this event to be occurring?

probability_threshold float (Optional, default: 0.5)

The posterior probability at which the sensor should trigger to on. use higher values to reduce false positives (and increase false negatives) Note: If the threshold is higher than the prior then the default state will be off

name string (Optional, default: Bayesian Binary Sensor)

Name of the sensor to use in the frontend.

unique_id string (Optional)

An ID that uniquely identifies this bayesian entity. If two entities have the same unique ID, Home Assistant will raise an exception.

device_class string (Optional)

Sets the class of the device, changing the device state and icon that is displayed on the frontend.

observations list Required

The observations which should influence the probability that the given event is occurring.

platform string Required

The supported platforms are state, numeric_state, and template. They are modeled after their corresponding triggers for automations, requiring to_state (for state), below and/or above (for numeric_state) and value_template (for template).

entity_id string (Optional)

Name of the entity to monitor. Required for state and numeric_state.

to_state string (Optional)

The entity state that defines the observation. Required (for state).

value_template template (Optional)

Defines the template to be used, should evaluate to true or false. Required for template.

prob_given_true float Required

Assuming the bayesian binary_sensor is true, the probability the entity state is occurring.

prob_given_false float Required

Assuming the bayesian binary_sensor is false the probability the entity state is occurring.

Full examples

The following is an example for the state observation platform.

# Example configuration.yaml entry
binary_sensor:
  platform: "bayesian"
  name: "in_bed"
  unique_id: "172b6ef1-e37e-4f04-8d64-891e84c02b43" # generated on https://www.uuidgenerator.net/
  prior: 0.25 # I spend 6 hours a day in bed 6hr/24hr is 0.25 
  probability_threshold: 0.8 # I am going to be using this sensor to turn out the lights so I only want to to activate when I am sure
  observations:
    - platform: "state"
      entity_id: "sensor.living_room_motion"
      prob_given_true: 0.05 # If I am in bed then I shouldn't be in the living room, very occasionally I have guests, however
      prob_given_false: 0.2 # My sensor history shows If I am not in bed I spend about a fifth of my time in the living room
      to_state: "on"
    - platform: "state"
      entity_id: "sensor.basement_motion"
      prob_given_true: 0.5 # My sensor history shows, when I am in bed, my basement motion sensor is active about half the time because of my cat
      prob_given_false: 0.3 # As above but my cat tends to spend more time upstairs or outside when I am awake and I rarely use the basement
      to_state: "on"
    - platform: "state"
      entity_id: "sensor.bedroom_motion"
      prob_given_true: 0.5 # My sensor history shows when I am in bed the sensor picks me up about half the time
      prob_given_false: 0.1 # My sensor history shows I spend about 10% of my waking hours in my bedroom
      to_state: "on"
    - platform: "state"
      entity_id: "sun.sun"
      prob_given_true: 0.7 # If I am in bed then there is a good chance the sun will be down, but in the summer mornings I may still be in bed
      prob_given_false: 0.45 # If I am am awake then there is a reasonable chance the sun will be below the horizon - especially in winter
      to_state: "below_horizon"
    - platform: "state"
      entity_id: "sensor.android_charger_type"
      prob_given_true: 0.95 # When I am in bed, I nearly always plug my phone in to charge
      prob_given_false: 0.1 # When I am awake, I occasionally AC charge my phone
      to_state: "ac"

Next up an example which targets the numeric_state observation platform, as seen in the configuration it requires below and/or above instead of to_state.

# Example configuration.yaml entry
binary_sensor:
  name: "Heat On"
  platform: "bayesian"
  prior: 0.2
  probability_threshold: 0.9
  observations:
    - platform: "numeric_state"
      entity_id: "sensor.outside_air_temperature_fahrenheit"
      prob_given_true: 0.95
      prob_given_false: 0.05
      below: 50

Finally, here’s an example for template observation platform, as seen in the configuration it requires value_template. This template will evaluate to true if the device tracker device_tracker.paulus shows not_home and it last changed its status more than 5 minutes ago.

# Example configuration.yaml entry
binary_sensor:
  name: "Paulus Home"
  platform: "bayesian"
  device_class: "presence"
  prior: 0.5
  probability_threshold: 0.9
  observations:
    - platform: template
      value_template: >
        {{is_state('device_tracker.paulus','not_home') and ((as_timestamp(now()) - as_timestamp(states.device_tracker.paulus.last_changed)) > 300)}}
      prob_given_true: 0.05
      prob_given_false: 0.99