Questions tagged [inference]

Drawing conclusions about population parameters from sample data. See https://en.wikipedia.org/wiki/Inference and https://en.wikipedia.org/wiki/Statistical_inference

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5
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2answers
502 views

MRF MAP inference for non-submodular pairwise terms

I have a multilabel MRF MAP inference problem (a labeling problem). The graph has relatively few nodes, about a thousand or so. The pairwise term is (very) not submodular (it does not satisfy the ...
5
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1answer
149 views

Fiducial Inference in Machine Learning

I was looking at the Fiducial Inference page on wikipedia, which is an alternative to the traditional Frequentist and Bayesian standpoints. Although it was out of favour in mainstream statistics for ...
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1answer
435 views

When will a less true model predict better than a truer model?

In "To Explain or to Predict?", Pr. Galit Shmueli said that sometimes a less true model can predict better than a truer model. Why is it so? When will it happen? How does it happen? Is explanation a ...
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1answer
936 views

Difference between likelihood principle and repeated sampling principle

In statistical inference, there are many fundamental statistical principles, such as likelihood principle and repeated sampling principle. I am wondering whether there are any other principles? And ...
4
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1answer
151 views

Estimating an unknown restricted Markov Chain from partial measurements

There is an Markov chain $M$ defined on states $1, ..., N$ with the special property that it only has transitions $p_i$ from $i$ to $i + 1$ , $q_{i + 1}$ from $i + 1$ to $i$, and $r_i = 1 - p_i - q_i$ ...
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2answers
788 views

Bayesian inference of parameters: residuals are independent but not normally distributed

I would like to compute belief intervals (confidence intervals; CI) for the parameters of an environmental dynamic model within the Bayes' theorem. The measurement model of the data is $$ d(t)=y(\...
11
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1answer
3k views

Estimating probability of success, given a reference population

Suppose you have the following situation: You observed over time 1000 bowling players, who each played a relatively small number of games (say 1 to 20). You noted the strike percentage for each of ...
1
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1answer
272 views

What graphical model to capture conditional relationships between tokens?

I have a list of tokens/words which co-occur with each other. Some of these tokens co-occur more than the others. Moreover, there's a conditional relationship between many. For example, "bat" occurs ...
3
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2answers
234 views

Designing an inference engine for unknown items with known probabilities

I have done some AI projects involving inference, neural networks, etc., but I'm not sure what the right algorithm would be for this problem. Say there is a set of pills, where each type is visually ...
80
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10answers
58k views

Understanding “variance” intuitively

What is the cleanest, easiest way to explain someone the concept of variance? What does it intuitively mean? If one is to explain this to their child how would one go about it? It's a concept that I ...
5
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1answer
210 views

Means of groups A and B differ significantly. I want to classify values into A or B

My data look like this. The variable on the $x$ axis is height in inches. The variable on the $y$ axis is whether someone hovers when urinating at a public toilet. Each of the 103 points is a female ...
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1answer
984 views

Inference with one-sample Likert-type data

In case, one wants to do some inference with one-sample Likert-type data, what tests could one use? Signed Rank Test?
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0answers
280 views

Is there a way to measure the information content (or difference) in two matrices?

Prologue I have a matrix $N$ with dimensions $I\times J$, $I >> J$, and $n_{ij}$ is assumed to follow a Poisson distribution with mean $\lambda_{ij}$. Using a method (say NtoM), I reduce $N$ to ...
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6answers
2k views

Inference to the population when the survey response rate is only 30%

I have conducted a survey in which the questionnaires were sent out to 450 individuals, but only 30% of them answered the questionnaires. Is it still valid to interpret the usual inference analysis (...
3
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2answers
416 views

How do you deal with a “multiple choice” observation in Bayesian inference, when the choices are on a scale?

Suppose I have a questionnaire and I ask respondents how often they eat at McDonalds: Never Less than once a month At least once a month but less than once a week 1-3 times a week More than 3 times a ...
3
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1answer
60 views

How often is data corrupted given how often a 3-way vote passes incorrect data?

Assume we have a noisy system where data is available via sample() and in order to filter out the noise someone has implemented the following voting algorithm: <...
6
votes
2answers
2k views

Standardized residuals vs. regular residuals

I've got an easy question concerning residual analysis. So when I compute a QQ-Plot with standardized residuals $\widehat{d}$ on the y-axis and I observe normal distributed standardized residuals, why ...
4
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1answer
227 views

Bayesian analysis of data

I have a big dataset in the form: $X_1, X_2, X_3, X_4, Y$. All the $X_i, i \in {1,...,4}$ come from different unknown distributions and $Y$ follows a bernoulli distribution, so it can take only values ...
3
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1answer
700 views

Property of entropy

When characterizing an information measure one desires to have the following 'Grouping' property (cf., Cover&Thomas, Ch.2 exercise 46) $$H(p_1, p_2,\dots, p_n)=H(p_1+p_2, p_3,\dots, p_n)+(p_1+...
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2answers
198 views

Resampling within a survey to account for missing data

Suppose I have survey responses that look like this: ...
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0answers
142 views

Inference and noninference parts of statistical theory [closed]

I was wondering from the view of dividing the topics of statistical theory into inference part and non-inference part, what inference topics and non-inference topics statistical theory is covering? ...
6
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2answers
214 views

Inference with Gaussian Random Variable

Let $X = N(0,\frac{1}{\alpha})$, $Y = 2X + 8 + N_{y}$, and $N_{y}$ be a noise $N_{y} = N(0,1)$. Then, $P(y|x) = \frac{1}{\sqrt{2\pi}}exp\{ -\frac{1}{2}(y - 2x - 8)^{2} \}$ and $P(x) = \sqrt{\frac{\...
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1answer
148 views

Can I insert an observation (evidence) to a Winbugs model?

Greetings, Is it possible to use evidence in a Winbug model? For example, a random variable in a model has been observed, and I'd like to update the other variables in the model, pretty much the same ...
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3answers
865 views

Accommodating entrenched views of p-values

Sometimes in reports I include a disclaimer about the p-values and other inferential statistics I've provided. I say that since the sample wasn't random, then such statistics would not strictly apply....
13
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1answer
899 views

Do likelihood ratios and Bayesian model comparison provide superior & sufficient alternatives to null-hypothesis testing?

In response to a growing body of statisticians and researchers that criticize the utility of null-hypothesis testing (NHT) for science as a cumulative endeavour, the American Psychological Association ...
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4answers
642 views

War stories where wrong decisions were made based on statistical information?

I think it is fair to say statistics is an applied science so when averages and standard deviations are calculated it is because someone is looking to make some decisions based on those numbers. ...
4
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2answers
416 views

Why does continuous Bayesian analysis seem to give this contradictory result?

Let's say you have a process that generates data according to r = sin(t) + epsilon, where epsilon ~ N(0,V) is Gaussian noise. The unconditional variance of r is 0.5 + V. Let's say we're forecasting ...
21
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3answers
4k views

Comparison between MaxEnt, ML, Bayes and other kind of statistical inference methods

I'm in no way a statistician (I've had a course in mathematical statistics but nothing more than that), and recently, while studying information theory and statistical mechanics, I met this thing ...
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2answers
3k views

Online resources for learning statistics, exercises (with solutions)?

I'm currently working as a teaching assistant at my university, in an introductory statistics course (for medical students). Offline, there are many books available with information to aid the ...
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2answers
2k views

Comparison of two values in a statistically sound manner

For a university paper, I have to compare whether two program versions are statistically significantly different. The comparison in terms of runtime performance is straightforward -- I determine ...
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4answers
8k views

Intractable posterior distributions

In Bayesian statistics, it is often mentioned that the posterior distribution is intractable and thus approximate inference must be applied. What are the factors that cause this intractability?
7
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1answer
920 views

How much can the “pyramid of evidence” be applied to economics and political sciences?

When trying to assess a validity of a claim relying on statistics, I was taught (in the school of epidemiology) that the scale to use is “the pyramid of evidence“ However, when conducting a ...