Basic prediction concept

Dear community,

First steps in Bayes statistics using pymc, after constructing a few simple models (and also a mixed model), I got an understanding gap which I will kindly ask for your help to overcome.
The models aim to estimate exponential decay (b).

signal \sim Normal(y,\sigma)
y = a + c \times e^{-b*filter} + \sigma
a \sim Normal(50,20)
b \sim Exponential(0.1)
c \sim Normal(5,10)
\sigma \sim Exponential(1)\

I want to predict a new set of observations’ exponential decay parameter (b). I assume that these observations are from the same distribution. I am interested in samples that are decay slow.
Is it correct to solve the equation for b:

b = - \frac{ln \frac{a-y}{c}}{t}

Where a and c are posterior predicted, y is the observed signal, and t is the corresponded time.

Alternatively, can I feed the new observation to the pm.sample_posterior_predictive from trace?

Thank you very much…

Hi. It’s not clear where t comes from.

But yes, if you get the posterior estimates of the parameters then it seems reasonable to manually calculate using your equation for b with whatever new y data you have.

BUT do you actually have y, or do you have new noisy observations (what you call signal)?

Sorry, t is notated as “filter” in the central equation.
Here is the correction:
b = -\frac {ln \frac{a-signal}{c}}{filter}

I will try to explain the data better.
It is a classification problem based on the decay rate of our measurements.

I am measuring signal decay as a function of the filter.
The filter is a kernel of 80 sequential steps (increase in kernel size).
Training set:
I got 80 observations that split into two groups with a clear difference in their decay rates.

Test set:
Forty observations, where I want to classify if they belong to decay group own or two (based on the b parameter).

The y variable is noise (signal)

Just a quick reply due to time…

The approach I’d use is to work through the logic with a simpler problem, maybe linear regression with a slope and intercept parameter. This may be more easy to reason about, and if the approach doesn’t make sense in that context then it’s unlikely to make sense in a more complicated model.