Bayesian

A Bayesian helper is a virtual binary sensor that determines its state based on the combination of multiple other sensors using probabilistic methods.

This approach enables the detection of complex events that are not directly or easily measurable, such as cooking, showering, being in bed, or starting a morning routine. Additionally, it can improve confidence and reliability in measurable events where sensors may be unreliable, such as some presence detectors.

Bayesian works by applying Bayes’ rule. It estimates the likelihood that a specific event is occurring based on the combination of the states of ‘observed’ sensors and a baseline, (prior) probability. When the calculated probability - known as a ‘posterior’ - exceeds the defined probability_threshold, the bayesian sensor will turn on; otherwise, it will be off.

Both UI and YAML setups are supported, importantly YAML uses probabilities of 0 to 1 whereas the UI uses percentages, 0 to 100.

Theory

A fundamental concept in Bayes’ Rule is the distinction between the probability of an event given an observation and the probability of an observation given an event. These two probabilities are not interchangeable and must be considered separately. While they may be similar in some cases — for example, when motion sensors are accurate, the probability that someone is in the room given that motion is detected is often close to the probability that motion is detected given someone is in the room.

Now consider the above, but in a home that has cats. The probability that the room is human-occupied given that motion detected may be quite low (e.g. 20%, p=0.2) if the room is popular with the cats. However, the probability that motion is detected given that it is occupied by a human is high (e.g 95%, p = 0.95) if our motion sensor is accurate. Said succinctly, not all motion is human, but all humans move.

When configuring these conditional probabilities, define the probability of the sensor observation (e.g motion detected) given the thing you are trying to estimate (e.g human-occupancy of the room).

Configuration

To add the Bayesian service to your Home Assistant instance, use this My button:

Once you have created a Bayesian helper, you can add and edit ‘observations’ here:

To configure a YAML Bayesian sensor, add an entry using the following structure to your configuration.yamlThe configuration.yaml file is the main configuration file for Home Assistant. It lists the integrations to be loaded and their specific configurations. In some cases, the configuration needs to be edited manually directly in the configuration.yaml file. Most integrations can be configured in the UI. [Learn more] file. After changing the configuration.yamlThe configuration.yaml file is the main configuration file for Home Assistant. It lists the integrations to be loaded and their specific configurations. In some cases, the configuration needs to be edited manually directly in the configuration.yaml file. Most integrations can be configured in the UI. [Learn more] file, restart Home Assistant to apply the changes.

# Example configuration.yaml entry
binary_sensor:
  - platform: bayesian
    name: "Kitchen Occupied by Humans"
    prior: 0.3 # The kitchen is occupied by humans about 30% of the time
    probability_threshold: 0.5 # I care about false positives and false negatives equally
    observations:
      - entity_id: "binary_sensor.kitchen_motion"
        prob_given_true: 0.95 # When humans are in the kitchen, the motion sensor detects them 95% of the time
        prob_given_false: 0.33 # When no humans are in the kitchen, the cats trigger the motion sensor 33% of the time
        platform: "state"
        to_state: "on"

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.
   • Probability when Bayesian sensor on (prob_given_true:) - Select the sensor in question over a time range when you think the bayesian sensor should have been on. prob_given_true: is the fraction of the time the sensor was in to_state:.
   • Probability when Bayesian sensor off (prob_given_false:) - Select the sensor in question over a time range when you think the bayesian sensor should have been off. 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 force desired outcomes; use guideline #4 to estimate probabilities as accurately as possible. If the behavior still isn’t 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 make sense, then consider increasing probability_threshold: and vice versa.

Full examples

These are a number of worked examples which you may find helpful for each of the state types.

State

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"

Numeric State

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

Template

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

Multiple state and numeric entries per entity

Lastly, an example illustrates how to configure Bayesian when there are more than two states of interest and several possible numeric ranges. When an entity can hold more than 2 values of interest (numeric ranges or states), then you may wish to specify probabilities for each possible value. Once you have specified more than one, Bayesian cannot infer anything about states or numeric values that are unspecified, like it usually does, so it is recommended that all possible values are included. As above, the prob_given_trues of all the possible states should sum to 1, as should the prob_given_falses. If a value that has not been specified is observed, then the observation will be ignored as it would be if the entity were UNKNOWN or UNAVAILABLE.

When multiple ranges are defined for the same entity, below is inclusive (≤) for any range that specifies it. For a single range, above and below remain exclusive.

This is an example sensor that can detect if the bins have been left on the side of the road and need to be brought closer to the house. It combines a theoretical presence sensor that gives a numeric signal strength and an API sensor from local government that can have 3 possible states: due when collection is due in the next 24 hours, collected when collection has happened in the last 24 hours, and not_due at other times.

# Example configuration.yaml entry
binary_sensor:
  name: "Bins need bringing in"
  platform: "bayesian"
  prior: 0.14 # bins are left out for usually about one day a week
  probability_threshold: 0.5
  observations:
    - platform: "numeric_state"
      entity_id: "sensor.signal_strength"
      prob_given_true: 0.01 # if the bins are out and need bringing in there is only a 1% chance we will get a strong signal of above 10
      prob_given_false: 0.3 # if the bins are not out, we still tend not to get a signal this strong
      above: 10
    - platform: "numeric_state"
      entity_id: "sensor.signal_strength"
      prob_given_true: 0.02
      prob_given_false: 0.5 #if the bins are not out, we often get a signal this strong
      above: 5
      below: 10
    - platform: "numeric_state"
      entity_id: "sensor.signal_strength"
      prob_given_true: 0.07
      prob_given_false: 0.1
      above: 0
      below: 5
    - platform: "numeric_state"
      entity_id: "sensor.signal_strength"
      prob_given_true: 0.3
      prob_given_false: 0.07
      above: -10
      below: 0
    - platform: "numeric_state"
      entity_id: "sensor.signal_strength"
      prob_given_true: 0.6 #if the bins are out, we often get a signal this weak or even weaker
      prob_given_false: 0.03
      below: -10
    # then lets say we want to combine this with an imaginary sensor.bin_collection which reads a local government API that can have one of three values (collected, due, not due)
    - platform: "state"
      entity_id: "sensor.bin_collection"
      prob_given_true: 0.8 # If the bins need bringing in, usually it's because they've just been collected
      prob_given_false: 0.05 # 
      to_state: "collected"
    - platform: "state"
      entity_id: "sensor.bin_collection"
      prob_given_true: 0.05 # If the bins need bringing in, then the sensor.bin_collection shouldn't be 'due'
      prob_given_false: 0.11 # The sensor will be 'due' for about 1 day a week (the 24 hours before collection)
      to_state: "due"
    - platform: "state"
      entity_id: "sensor.bin_collection"
      prob_given_true: 0.15 #All the prob_given_true should add to 1
      prob_given_false: 0.84 # All the prob_given_false should add to 1
      to_state: "not due"