Bayesian stats: how to update probability?

[ireland01]

I am trying to use Bayesian methods (Bayes rule) to predict further datapoints (at point n,n+1,n+2 etc..)...

I begin by generating a normal pdf using previous 75 datapoints (prior: n-75 to n-1) with mean value, μ: 1.25 and standard deviation, δ: 3.67.

Note: previous datapoints range from -5 to +5 in value.

I calculate the maximum probabilty of 0.11 for datapoint = 1.30.

Using this will underestimate (predict) the value at n.

I now want to incorporate (into the probability) the fact that I know my previous two datapoints (n-2 to n-1) showed increase towards +ve...

 

[mfb]

You can give your datapoints nearby a higher weight - there are many ways to do this, depending on the type of correlation between the points you expect.

 

[Stephen Tashi]

I am trying to use Bayesian methods (Bayes rule) to predict further datapoints (at point n,n+1,n+2 etc..)...

.

You'll have to explain what probability model you are using and what prior distributions you are using before anyone can give you an answer. A Bayesian method has to be more than the willingness to update estimates. You must also be willing to assume a specific probability model and specific priors.

If this is a real world problem, describe it and someone might suggest a probability model.

 

[Number Nine]

The probability that your datapoint = 1.3 is zero.
This seems like a very strange thing to do. Are your data dependent in some way? If you're just sampling from a normal distributions, then your previous samples are irrelevant. Calculate your probability directly from the normal pdf.

 

[blue_raver22]

Bayesian statistics is a powerful approach to updating probability based on new information. In this case, you are using Bayes rule to predict future datapoints based on previous data. The first step in this process is to generate a normal probability distribution using the previous 75 datapoints as a prior. This distribution has a mean of 1.25 and a standard deviation of 3.67. This gives you a starting point for predicting future datapoints.

However, you have noticed that using this prior alone may underestimate the value at n. To incorporate the fact that the previous two datapoints showed an increase towards a positive value, you can update your probability using Bayes rule. This will allow you to incorporate new information and adjust your prediction accordingly.

Bayesian statistics also allows for the use of prior knowledge and beliefs in the form of prior distributions. This can be helpful in situations where there is limited data available, as it allows you to incorporate existing knowledge into your analysis.

Overall, using Bayesian methods to update probability can provide more accurate predictions by incorporating new information and prior knowledge. It is a valuable tool for scientists in making informed decisions and predictions based on data.