More about Inference

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More about Inference

• Chapter 3

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Overview

• Introduction
• Assumptions in Inference
• Inferring unknown parameters
• Model comparison as inference
• An example using Bayes theorem

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Intro (1) Bayes Theorem
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Intro (2) Bayes Rule ExampleThe noisy channel
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Intro (3) The noisy channel
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Assumptions in inference (1)

• Once assumptions are made,
• the inferences are objective and unique,
• reproducible with complete agreement by anyone
  who has the same information and makes the
  assumptions.

Posterior represents a Degree of belief
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Assumptions in inference (2)

• When assumptions are explicit, they are easier to
  criticize, and easier to modify.

We can quantify the sensitivity of our inferences
to the details of the assumptions.
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Assumptions in inference (3)

• When we are not sure which various alternative
  assumptions is the most appropriate for a
  problem, we can threat this question as another
  inference task.

Given the data D we can compare alternative
assumptions H where I denotes the highest
assumptions.
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Assumptions in inference (4)

• We can take into account our uncertainty
  regarding assumptions when we make subsequent
  predictions.

Predictions about some quantity x that take into
account the uncertainty about 0 (using the sum
rule Eq.2.7)
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Inferring unknown parameters
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Model comparison as inference
(1) Parameter estimation
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A known example using BT (1)
1 or 2 ?
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A known example using BT (2)
Hypothesis Hi the price is behind door i Data D
door number that is opened by host
Priors
Likelihoods
Posteriors
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A known example using BT (3)
P(D3) is the normalizing constant and equals 1/2
The participant should switch to box 2! If
he/she wants a better change on a price
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Any Questions?