Chain Rule

Autoregressive Conditional Probability

General Notation for Conditional Probability Models

Prediction via Optimization

A language model is analyzing a text corpus of 10,000 two-word phrases. The analysis reveals the following counts:

• The word 'deep' is the first word in 400 phrases.
• The word 'learning' is the second word in 250 phrases.
• The specific phrase 'deep learning' occurs 80 times.

Based on this data, what is the probability that the second word of a phrase is 'learning', given that the first word is 'deep'?

Predictive Text Model Comparison

Interpreting Conditional Probabilities in Text

Time Series Analysis and Its Applications: With R Examples (Third edition)

Time Series learning

Interrupted Time-Series Design

Which of the following best describes the defining characteristic of a time series in psychological research?

Match each component of a time series design with its correct description in a psychological study context.

A clinical psychologist monitors a patient's self-reported anxiety levels every morning for three months to evaluate the stability of their symptoms during a new treatment. Because these quantitative measurements are taken at sequential intervals over a continuous period, the psychologist is using a(n) ________.

True or False: A psychologist who monitors a patient's self-reported anxiety ($a$) every morning for a year, but then collapses all those data points into a single annual mean ($\bar{x}$) for their final report, is effectively performing a time series analysis.

Stationary Dynamics

FTSE 100 Sequence Data Example

Autoregressive Conditional Probability

Synthetic Sequence Data

In the context of research methods, which of the following best defines a 'time series'?

Match each core component of a time-series design to its corresponding application in a study monitoring how student sleep quality changes throughout an academic year.

A researcher tracks the number of daily calls to a suicide prevention hotline for $90$ consecutive days to see if the frequency of calls increases during the winter holidays. True or False: This research approach is an example of a time series.

A researcher wants to use a time series approach to investigate weekly levels of test anxiety among first-year university students across one full academic semester. Arrange the following steps in the logical order required to correctly design and execute this time series study.

What is the primary purpose of utilizing a time series approach in psychological research?

A researcher monitors a group's average weekly mood ratings for an entire year to evaluate the impact of a new wellness program. Why is this time-series approach more informative than simply comparing one week of ratings before the program to one week after?

A researcher claims that a new school-wide mindfulness program significantly reduced student stress based on a single measurement taken two weeks after the program began. To evaluate whether this claim is justified or if the low stress levels are merely a temporary fluctuation, a critic would argue that the researcher should have used a(n) _____ to examine data at sequential intervals over a continuous period.