# Bayesian

The `bayesian` binary sensor platform observes the state from multiple sensors. It uses Bayes’ rule to estimate the probability that an event is occurring 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 when motion sensors are accurate. In other cases, the distinction is much more important. The probability one has 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 one comes home (the event) (p=0.999). This difference is because one opens the door several times a day for other purposes.

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 `9`s and `0`s 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
``````