Bayesian Decision Theory

• Bayesian probability
• Decision theory
• Free Energy Principle

Bayesian decision theory is another name for Evidential Decision Theory (EDT).

Suppose we intend to meet a friend tomorrow, and expect an 0.5 chance of raining. If we are choosing between various options for the meeting, with the pleasantness of some of the options (such as going to the park) being affected by the possibility of rain, we can assign values to the different options with or withwithout rain. We can then pick the option whose expected value is the highest, given the probability of rain.

From the perspective of Bayesian decision theory, any kind of probability distribution - such as the distribution for tomorrow's weather - represents a prior distribution. That is, it represents how we believeexpect today the weather is going to be tomorrow. This contrasts with frequentist inference, the classical probability interpretation, where conclusions about an experiment are drawn from a set of repetitions of such experience, each producing statistically independent results. For a frequentist, a probability function would be a simple distribution function with no special meaning.

Suppose we know that we're goingintend to meet a friend tomorrow, and that there's a .5expect an 0.5 chance for itof raining. If we are choosing between various options of how to spendfor the next day,meeting, with the pleasantness of some of the options (such as going to the park) being affected by the possibility of rain, we can assign values to the different options with or with rain. We can then pick the option whose expected value is the highest, given the probability of rain.

One definition of Rationality rationality, used both on Less Wrong and in economics and psychology, is behavior which obeys the rules of Bayesian decision theory. Due to computational constraints, this is impossible to do perfectly, but naturally evolved brains do seem to mirror these probabilistic methods when they adapt to an uncertain environment. Although they can't follow it perfectly and often err, brains do seem to often approximate the correct theory by constructing Bayesian models of their environment and then using these models to make decisions. Such models and distributions are constantly being updated andmay be reconfigured according to feedback from the environment.

ConsiderFrom the perspective of Bayesian decision theory, any kind of probability distribution - such as the distribution for tomorrow's weather for tomorrow (encompassing several variables such as humidity, rain or temperature). From a Bayesian perspective, that- represents a prior distribution. That is, it represents how we believe today the weather is going to be tomorrow. This contrasts with frequentist inference, the classical probability interpretation, where conclusions about an experiment are drawn from a set of repetitions of such experience, each producing statistically independent results. For a frequentist, a probability function would be a simple distribution function with no special meaning. A

Suppose we know that we're going to meet a friend tomorrow, and that there's a .5 chance for it raining. If we are choosing between various options of how to spend the next day, with the pleasantness of some of the options (such as going to the park) being affected by the possibility of rain, we can assign values to the different options with or with rain. We can then pick the option whose expected value is the highest, given the probability of rain.

One definition of Rationality rationality, used both on Less Wrong and in economics and psychology, is behavior which obeys the rules of Bayesian decision ruletheory. Due to computational constraints, this is one that consistently triesimpossible to make decisions which minimize the risk of the probability distribution. Such risk can be seen as the difference between the prior beliefs and the real outcomes - the prediction and the actual weather tomorrow.

Computer algorithms such as those studied in the subject of Machine learning can also use Bayesian methods. Besides these explicit implementations, it also has been observed thatdo perfectly, but naturally evolved brains nervous systemsdo seem to mirror mirror these probabilistic methods when they adapt to an uncertain environment. Such systems, like the human brain,Although they can't follow it perfectly and often err, brains do seem to constructoften approximate the correct theory by constructing Bayesian models of their environment and then useusing these models to make decisions. Such models and distributions are constantly being updated and reconfigured according to feedback from the environment.

Bayesian reasoning in everyday life

What Less Wrong refers to as Rationality is an effort to make conscious thoughts and decisions a better approximation of Bayesian decision theory, in order to better understand the world and achieve one's goals. This process can involve applying math to reality in a simplified and extremely useful way:

You receive a phone call from a friend inviting you to do something tomorrow - playing a board game, as you usually do. The question arises: where to play? At your apartment or ouside in the park?

You check the weather forecast and conclude there's a 50% chance of rain. Since playing the game implies being stuck in the place you chose, you add another decision to your model - to just talk instead of playing. That way you can move according to the weather.

If you attribute different preferences to both the activity and the location while considering the influence of the probability of raining, you can build a model to help you decide and clarify the problem. That way you can define both variables in a more informed and balanced mode, thus being able to make better decisions.

If you attribute different preferences to both the activity and the location while considering the influence of the probability of raining, you can build a model to help you decide and clarify the problem. That way you can define both variables in a more informed and balanced mode, makingthus being able to make better decisions.

What Less Wrong refers to as Rationality is an effort to make conscious thoughts and decisions a better approximation of Bayesian decision theory, in order to better understand the world and achieve one's goals. This process can be seen asinvolve applying math to reality in a simplified and extremely useful way:

You check the weather forecast and conclude there's a 50% chance of rain. Since playing the game implies being stuck in the place you chose, you add another decision to your model - to just talk instead of playing. That way you can move according to the weather.

If you attribute different preferences to both the activity and the location while considering the influence of the probability of raining, you can build a model to help you decide and clarify the problem. That way you can define both variables in a more informed and balanced mode.mode, making better decisions.

Bayesian reasoning in everyday life

What Less Wrong refers to as Rationality is an effort to make conscious thoughts and decisions a better approximation of Bayesian decision theory, in order to better understand the world and achieve one's goals. This process can be seen as applying math to reality in a simplified and extremely useful way:

You receive a phone call from a friend inviting you to do something tomorrow - playing a board game, as you usually do. The question arises: where to play? At your apartment or ouside in the park?

You check the weather forecast and conclude there's a 50% chance of rain. Since playing the game implies being stuck in the place you chose, you add another decision to your model - just talk instead of playing. That way you can move according to the weather.

If you attribute different preferences to both the activity and the location while considering the influence of the probability of raining, you can build a model to help you decide and clarify the problem. That way you can define both variables in a more informed and balanced mode.