Thinking Probabilistically; Chp. 1

Question 1

What is experimental design?

Answer 1

A branch of statistics that deals with data collection

Question 2

Explain Exploratory Data Analysis: EDA

Answer 2

This is about numerical summaries, such as the mean , mode, standard deviation, and interquartile ranges. EDA is also about visually inspecting the data, using tools you may be already familiar with , such as histograms and scatterplots

Question 3

Explain Inferential Statistics

Answer 3

this is about making statements beyond the current data. We may want to understand some particular phenomenon, or maybe we want to make predictions for the future data points, or we want to choose among several competing explanations for the same observations. Inferential statistics is a set of methods and tools that will help us to answer these types of questions.

Question 4

If we are the ones in charge of generating or gathering the data , it is always good to …..?

Answer 4

first think carefully about the questions we want to answer and which methods we will use and only than proceed to get the data. Why?

Question 5

what does the word ontological mean?

Answer 5

adjective: ontological
1. relating to the branch of metaphysics dealing with the nature of being.
“ontological arguments”
2. showing the relations between the concepts and categories in a subject area or domain.
“an ontological database”

Question 6

What does stochastic mean?

Answer 6

adjective : TECHNICAL
adjective: stochastic
randomly determined; having a random probability distribution or pattern that may be analyzed statistically but may not be predicted precisely.

Question 7

Data does not speak but through …?

Answer 7

Models. We need to interpret data in the context of models. Including metal and formal ones.

Question 8

Models are …?

Answer 8

simplified descriptions of a given system or process that, for some reason , we are interested in.

(Those descriptions are deliberately designed to capture only the most relevant aspects of the system and not to explain every minor detail)

Question 9

What is the first step in the Bayesian modeling process?

Answer 9

1. Given some data and some assumptions on how this data could have been generated, we design a model by combining building blocks known as probability distributions. Most of the time these models are crude approximations, but most of the time it is all we need.

Question 10

What is the 2nd step of the bayseian modeling process?

Answer 10

2. We use bayes’ theorem to add data to our models and derive the logical consequences of combining the data and our assumptions. We say we are conditioning the model to our data.

Question 11

What is the 3rd step of Baysesian modeling?

Answer 11

We criticize the model by checking whether the model makes sense according to different criteria, including the data , expertise on the subject, and sometimes by comparing several models.

Question 12

Describe what an event is in Bayesian statistics.

Answer 12

an event is just any of the possible values(or subset of values) a variable can take.

Question 13

Probabilities are numbers in the _________ interval?

Answer 13

[0,1]

Question 14

Describe the product rule of probability:

Answer 14

p(a,b) = p(A | B)p(B) . the probability of A and B is equal to the probability of A given B, times the probability of B. This is only true if A and B are independent of each other.

Question 15

Probability models are built by ……

Answer 15

properly combining probability distributions.

Question 16

A probability distribution is a mathematical object that ….?

Answer 16

describes how likely different events are

Question 17

A common and useful conceptualization in statistics is to think data is generated from some …?

Answer 17

true probability distribution with unknown parameters. Why ?

Question 18

There are two types of random variables. What are they?

Answer 18

Continuous Variables and discrete variables

Question 19

When dealing with continuous distributions is that the values plotted on the y axis are not probabilities but ….?

Answer 19

probability densities

Question 20

What are the major components of Baye’s Theorem?

Answer 20

1. Prior
2. Likelihood
3. Posterior
4. Marginal Likelihood

Question 21

Describe the Prior:

Answer 21

the prior distribution should reflect what see/know about the value of theta or Hypothesis before seeing the data.

if we know nothing, we could use flat priors that do no convey too much information. Generally we can do better than flat priors.

Why?

Question 22

Describe the Likelihood:

Answer 22

The Likelihood is how we introduce data in our analysis. It is an expression of the plausibility of the data given the parameters/hypothesis.

Question 23

Describe the posterior distribution:

Answer 23

The posterior distribution is the result of bayesian analysis and reflects all that we know about a problem( given our data and model).

The posterior is a probability distribution of the parameter/hypothesis in our model and not a single value.

This distribution is a balance of the prior and likelihood.

Why?